# Energy Benefits of Heat Pipe Technology for Achieving 100% Renewable Heating and Cooling for Fifth-Generation, Low-Temperature District Heating Systems

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## Abstract

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_{2}emissions responsibility in terms of both direct, avoidable, and embodied terms. In this respect, a new heat pipe radiator prototype is presented, performance analyses are given, and the results are compared with a standard radiator. Comparative results show that such a new heat pipe radiator may be less than half of the weight of the conventional radiator, which needs to be oversized three times more to operate at 35 °C below the rated capacity. The application of heat pipes in renewable energy systems with the highest energy efficiency and exergy rationality establishes the second prong of the paper. A next-generation solar photo-voltaic-thermal (PVT) panel design is aimed to maximize the solar exergy utilization and minimize the exergy destruction taking place between the heating equipment. This solar panel design has an optimum power to heat ratio at low temperatures, perfectly fitting the heat pipe radiator demand. This design eliminates the onboard circulation pump, includes a phase-changing material (PCM) layer and thermoelectric generator (TEG) units for additional power generation, all sandwiched in a single panel. As a third prong, the paper introduces an optimum district sizing algorithm for minimum CO

_{2}emissions responsibility for low-temperature heating systems by minimizing the exergy destructions. A solar prosumer house example is given addressing the three prongs with a heat pipe radiator system, next-generation solar PVT panels on the roof, and heat piped on-site thermal energy storage (TES). Results showed that total CO

_{2}emissions responsibility is reduced by 96.8%. The results are discussed, aiming at recommendations, especially directed to policymakers, to satisfy the Paris Agreement.

_{2}emissions responsibility; heat pipe; heat pipe radiator; solar PVT; low-temperature district heating; 100% renewable heating and cooling; thermal storage; equipment oversizing; cascaded heat pumps; nearly-zero carbon building

## 1. Introduction and Literature Survey

#### 1.1. Overview

_{2}-equivalents by 2050. This concentration is well over the limit of 450 ppm (parts per million) to have at least a 50% chance of meeting the Paris Agreement goals [2].

_{2}never increased more than 30 ppm during the last thousand years, but it did so during the past twenty years and continuing [4]. Despite serious measures taken to reduce the CO

_{2}emissions and other particulates, Figure 1 reveals that there must be a fundamental flaw in the current theory and applications due to a lack of understanding about the missing mechanism of the unexplained CO

_{2}emissions, which is either unknown or ignored. In the year 2020, the ‘calculated’ global CO

_{2}emissions exceeded 36 billion tons. This calculation was carried out based on different fractions of coal, oil, gas, and renewable energy sources worldwide, all of which have different unit content of CO

_{2}. This result is an outcome of such a simplistic calculation concerning only the supply side. However, no one asks where these fuels and energy sources are used and how exergy-rational the utilization rate of their useful work potential is. Exergy is the useful work potential (quality) of a given amount or flow of energy quantity. Energy may be stored and recovered. Exergy may not be stored or recovered but destroyed, according to the 2nd Law of thermodynamics. Therefore, when the term energy is used, it is accompanied by two vectors, namely the quantity and quality. According to the ideal Carnot Cycle, exergy is always less than the quantity of energy (Exergy = (1 − T

_{ref}/T

_{sup}) times the energy quantity, and T

_{ref}> 0 K). For example, if natural gas, which has a useful work potential of 87% of its energy content and burns almost at 2000 °C, is simply used in a condensing boiler for comfort heating at 20 °C, then the rationality of spending such a valuable fuel only for heating on the demand side is only about 10%, although condensing boilers are generally claimed to be more than 95% efficient. Natural gas, for example, could be used in power generation, industry, and finally, the waste heat could be serviced to the buildings. Otherwise, almost 80% of the useful work potential is destroyed irreversibly in a condensing boiler in buildings. This destruction leads to additional CO

_{2}emission responsibility. This responsibility is the missing part of the strategies for decarbonization and is a simple matter of recognition of the 2nd Law for energy quality, exergy.

_{2}emissions is critical in emissions control for taking a sustainable position against climate emergencies [5]. Some concerned scientists and engineers have first announced the importance of exergy in the EU by releasing an opinion paper in 2016, with a ‘Think Exergy, not Energy’ [6]. They explained the concept of exergy and its application to energy efficiency, reaching out to policymakers to call for the formation of an International Exergy Panel to specifically address exergy destructions and their implications on the environment. Although this panel did not materialize, it generated enough interest for partial recognition of the importance of the 2nd Law of Thermodynamics. The EU is preparing new roadmaps to mobilize low-exergy (temperature) resources like waste heat, low-temperature solar heat, and low-enthalpy geothermal energy resources. These are widely available but untapped so far. Among various opportunities, buildings, representing almost 40% of the global energy consumption and a similar rate of CO

_{2}emissions, present the largest asset of decarbonization efforts by utilizing such low-exergy sources on the horizon.

#### 1.2. Buildings and the Environment

_{eq}). Nowadays, the EU is considering moving towards ultra-low temperature district energy systems with temperatures as low as 35 °C (T

_{sup}) [8,9]. In the Framework of International Energy Agency (IEA) Annex 37, a comprehensive compilation of research was carried out by IEA on low-temperature heating and its potential implications and the so-called side effects [10]. They argued that adding passive building systems for better retaining of solar gains and other internal sources, a continuous but lower thermostat settings shave off the peak loads and somehow enhance the utilization of low-temperature heat supplies. They considered floor heating, wall heating, oversized radiators and convectors, and air heating. Their studies were not too conclusive about energy performance, which were limited to the 1st Law of Thermodynamics only, and they did not investigate the effect of district piping and pumping on energy benefits or disadvantages. The potential impacts of low-temperature heating from the perspective of buildings about indoor air quality (IAQ), comfort, and energy have been further investigated by Eijdems, Boerstra, and Veld, without considering the conflict between energy supply temperature and the equipment demand temperature [9]. For public understanding and acceptance, they termed the low-exergy (Low-Temperature) energy as ‘low valued’ energy. They overviewed the impact of low-temperature supply to heating equipment for several types of equipment, including radiant floor and wall panels, low-temperature air heating. They qualitatively claimed that IAQ and sensation of comfort improve mainly by using radiant panels, which already permit low temperatures for operation. However, they did not study how low-temperature heating may be made possible by designing new equipment and or existing oversizing equipment, except noting that heat pump COP values may increase due to reduced temperature deficit between the supply and demand [9]. Figure 2 models this conflict of at least 35 °C of temperature deficit. When a low-temperature source is provided at T

_{sup}, Figure 2 also shows that over insulation of the old buildings may reduce the gap.

_{ref}, T

_{a}, and T`

_{sup}(Exergy Triangle). The side between points T

_{a}–T

_{ref}represents the unit demand exergy. The side (T`

_{sup}–T

_{ref}) represents the unit supply exergy. The side T

_{a}–(T`

_{sup}− 1/2 ΔT) represents the exergy of a unit thermal load (Q = 1 kW), E

_{XH}. The triangular area Δs represents the optimization objective, which needs to be maximized within the given temperature constraints and given design temperatures. For a detailed explanation of Figure 2, please refer to Appendix A.

_{a}and the rated supply temperature requirement of the conventional heating equipment, T

_{eq}, there is a temperature deficit between the low-temperature district supply, T

_{sup}, and T

_{eq}. The thermal load, Q, may be reduced by additional thermal insulation (Over insulation). This measure also reduces T

_{eq}to T`

_{eq}, reducing the temperature gap between the thermal supply and equipment requirements. However, over insulation has both economic and thermophysical limits, and therefore over insulation is a weak tool to resolve the problem. It is possible to determine an optimum relation between the over-insulation and equipment oversizing by referring to the Rational Exergy Management Efficiency (REMM), ψ

_{R}[11]. The term ψ

_{R}is the key for sustainably meeting the Paris Agreement goals because it is an indicator of nearly-avoidable CO

_{2}emissions, namely ΔCO

_{2}, emanating from exergy destructions (ε

_{sup}− ε

_{dem}). Any mismatch is reflected upon ψ

_{R}. The term ψ

_{R}has been defined by the ideal Carnot Cycle applied to the unit exergy demand, ε

_{dem}, and the unit exergy supply from source to equipment, ε

_{sup}.

_{R}, the denominator may be minimized if T

_{a}is fixed. By differentiating the denominator concerning T

_{sup}and then equating it to zero:

_{ref}is the reference environment temperature. A fixed value of 283 K in heating and 273 K in cooling were selected as common bases for all analyses. Then, the exergy-based (Equation (2)) sensitivity for maximum rationality at a given supply temperature is proportional to the uncertainties in the supply temperature, and it is twice as much. Therefore, for a narrow margin of sensitivity required about the maximum ψ

_{R}at low supply temperatures as desired by the EU roadmaps, uncertainties in the supply temperature must be minimal. This is a critical issue for control systems of 5DE districts with renewables in terms of exergy because T

_{sup}is low, and ΔT`

_{eq}must also be kept minimum, making the condition hard to satisfy. Figure 3 shows the trend of variables according to different T

_{sup}values. Maximum possible exergy rationality, ψ

_{R}, which is 0.40 is obtained at T

_{sup}= 30 °C. At this supply temperature, the insulation must be too heavy that the Q` will be about 50% of the design heating load, which is not practical. If T

_{sup}is 35 °C (308 K) and the reference temperature is 283 K, then T`

_{eq}is 335 K (62 °C) for maximum ψ

_{R}at these temperatures. If T

_{a}= 24 °C (297 K), ψ

_{R}will be:

_{sup}

_{0}is the original supply design temperature of the heating equipment, like 70 °C.

_{0}, is known, then the need for over insulation may be estimated from Equation (4). T

_{o}is the outdoor design temperature. Decreasing U` is also an optimality condition for heat pump COP (See Section 2.4.3).

_{sup}is 35 °C, buildings need to be insulated such that their heating loads are reduced by about 78%. Then the value is locally maximized to 0.29 (29% on the graph). At T

_{sup}= 39 °C, no additional insulation is necessary. This simple exergy-based model shows how the exergy analysis may be effective. For example, now a designer may choose whether to insulate the building more or choose a higher supply temperature mix or blend of waste heat or go deeper in geothermal well if low-enthalpy geothermal energy is to be used.

_{R}to be 0.117, which is significantly less than 0.70, which is the limit for green districts [11]:

_{s}is approximated by the following equation:

_{f}may be defined for steam by simply equating ε

_{s}from Equation (6) to (1 − T

_{ref}/T

_{f}):

_{R}of about 0.23, and indicates that the supply temperature may be less than about 39 °C to allow for better exergy rationality and give some room for over insulation.

_{S}of 488 K at a pressure of 20 bar ε

_{sup}is 0.406 kW/kW, and T

_{f}is 476.4 K, which is very close to T

_{S}in this case. On the other hand, if moderate-quality coal with unit exergy of 0.75 kW/kW was used in a steam boiler of that era, the steam unit exergy output of 0.406 kW/kW means an exergy destruction of (0.75–0.406) kW/kW from fuel to steam generation.

_{2}emissions responsibility:

_{2}will be the sum of the above two values, which is 0.301 kg CO

_{2}/kW-h. A second solution applying the ψ

_{R}value in Equation (5) (0.117) from coal (ε

_{fuel}= 0.75 kW/kW) to comfort, estimates exergy destructions in steps (2) and (3):

_{2}/kW-h and 0.301 kg CO

_{2}/kW-h, is an estimate about exergy destructions for Step 3, for exergy mismatches between pumping electricity and thermal exergy. ΔCO

_{2}emissions described above exclude direct CO

_{2}emissions yet from a coal boiler, which generates steam.

#### 1.3. Evolution of District Energy Systems

_{2}emissions in addition to direct emissions from the plant stacks. The supply temperatures were high, and steam heating was popular. The only advantage was the minimization of pumping demand in the district while steam was conveyed. In-situ age (2DE) expanded the district size and introduced the combined heat and power concept at supply temperatures close to 100 °C. This generation transformed from steam to hot water. Solar energy, geothermal energy, and biomass were introduced in 3DE. Metered and monitored supply heat at a temperature below 100 °C were carried through pre-insulated pipes.

_{2}emission responsibilities were also significantly reduced. In the 4DE system, supply temperatures decreased below 60 °C, while efficiencies kept increasing. Today, the 5DE systems keep decreasing the supply temperatures as low as 35 °C. This reduction facilitates the achievement of 100% renewable heating. This very low-temperature target, however, goes beyond the economic and technical capability of conventional heating systems to satisfy the heating loads resulting in the need for excessive oversizing and temperature peaking. Heat pump temperature peaking defeats the purpose of decarbonization because they are responsible for exergy destructions and nearly-avoidable CO

_{2}emissions in addition to the ozone-depleting potential (ODP) of the refrigerants via the relationship with their still high global warming potential (GWP). ODP and GWB are interrelated. Therefore, a state-of-the-art refrigerant with zero ODP does not guarantee that it is an ozone-free substance because its GWP values are high.

_{2}/kW-h) burning steam with an efficiency of 0.75:

_{2}/kW-h is the sum of Equations (7) and (8). Therefore, district heating systems transitioned away from the steam age, namely from 2G (2DE) systems to temperatures below 100 °C to reduce the exergy destructions. This example shows that the yet untold, unseen, and unexplained nearly avoidable emissions ΔCO

_{2}is about 55% of the direct CO

_{2}emissions. This means that we see the complete problem but know only half of the solutions, which can only be revealed by exergy rationality.

_{R}, by decreasing the supply temperatures. However, steam and hot water district heating systems still exist despite the obvious exergetic disadvantages. For example, 500,000 Copenhageners are still district heated with 500 MW steam and 1000 MW hot water [17]. Termis

^{®}is a commercial hydraulic modeling tool, which simulates the flows, pressure, and thermal conditions in a district network [18,19]. On the contrary, one of the earlier computer-based modeling tools was a computer code-named HEATMAP, designed for low-temperature geothermal energy district energy systems [20]. They argued that where geothermal waters are not warm enough to use directly, water-source heat pumps can be used to peak the temperature to required levels, such as in Lund, Sweden; Chateauroux, France; and Ephrata, Washington, USA [21,22,23,24].

#### 1.4. District and Heat Pumps

_{sup}: 0.87 kW/kW) replaces the heat pump, COP is replaced by its thermal efficiency, like η

_{I}= 0.85, then ε

_{des}will be much higher (0.93 kW/kW). In the heat pump case, the high-exergy electrical power (0.95 kW/kW) is generated first at the origin of the fuel-to-power phase. This electrical power is finally converted to thermal power just for low-exergy comfort heating. This process chain using electrical power through the heat pump could be accomplished by low-exergy sources like waste heat or solar thermal energy. Therefore, the heat pump destroys the opportunity of utilizing the high-exergy electrical power in better ways with high-exergy demanding applications like industry or electrical mobility. The destroyed unit exergy is responsible for the so-called nearly-avoidable CO

_{2}emissions ΔCO

_{2}. It is avoidable because it could be largely eliminated by removing the need for temperature peaking with low-temperature heating equipment. It is nearly avoidable because there will always be some exergy destruction inevitably present in any process. The exergy loss of electrical power input to the heat pump and then to the thermal exergy supply at 65 °C needs to be offset, most likely by consuming fossil fuels somewhere by someone and by some means. Referencing this offset amount of unit exergy to an on-site power generator with natural gas, Equation (10) gives the emission responsibility due to exergy destruction for power.

_{2}/kW-h, 0.87 kW/kW), or grid power on natural gas and the primary energy factor (PEF) of 2.75: 0.2/0.87 × 2.75 = 0.63. This positive emissions responsibility adds to the direct emissions depending upon where and how the electrical power is generated and transmitted: Therefore, the use of heat pumps for temperature peaking does not sequester carbon. This example shows that temperature peaking with heat pumps or other means defeat the decarbonization roadmap for total electrification by wide-scale application of heat pumps. Even if heat pumps are not used, consider indoor electric resistance heating using electricity generated by on-site, roof-mounted PV panels. Let the unit exergy demand for indoor heating at a Dry-Bulb (DB) comfort air temperature of 293 K (20 °C) in reference to 283 K (10 °C) environment temperature. Then the unit exergy demand, ε

_{dem}, will be (1 − 283 K/293 K) = 0.034 kW/kW.

_{R}= ε

_{dem}/(0.95/η

_{PV}) = 0.007, which renders solar PV installation useless. Here η

_{PV}is 0.20. If solar heating is the only aim, then a domestic hot-water collector would have better rationality.

_{R}will be raised only by a factor of COP. To be even with the unit exergies of the input (solar electricity) and the output (heat) in the above calculation, the necessary COP value (1/0.006) is impossible when compared with the theoretical Carnot-Cycle limit for heat pumps, even if a case of infinitely cascaded heat pumps in parallel is considered [25]. The theoretical ideal limit is the ratio of T

_{peak}/(T

_{peak}− T

_{sup}). For example, if a heat pump peaks the low-temperature thermal supply (Source Temperature) at 308 K to 350 K (Peaked Temperature), the theoretical limit for COP is 8.3. Instead, series cascading of smaller heat pumps may keep increasing the peaking temperature. For example, two smaller heat pumps in series stepping up the temperature towards the final peaking temperature in two equal steps (42 K/2 = 21 K, each) relax the ideal COP limits. The first heat pump has a theoretical COP limit of (308 + 21)/21 = 15.66. The second heat pump has a theoretical COP limit of 350/21 = 16.66.

_{2}embodiments and operating emissions. Another solution, which seems to be already available, is to use radiant panels, which may be made readily compatible with 5DE systems. However, these systems carry the same problems of the additional expense of more tubing (less tube spacing on centers) and ancillaries according to their material, energy, and CO

_{2}embodiments and pumping demand, plus their difficulty to retrofit existing buildings. All these challenges call for new heat pipe technologies in space heating and cooling at low-exergy systems.

_{p}) [12].

_{sup}= 35 °C, such that at this supply temperature, about 18% more heat at ΔT of 5 K may be generated (Q/Q

_{o}= 1.18). The practical range is 15 K and below. About 10 K is the common point for all supply temperatures for Q/Q

_{o}= 1 base (See Figure 7). Below 10 K, this ratio particularly increases above one for 5DE systems. Therefore 10 K is the lower bound. In the same token, the upper bound is 15 K if the Q/Q

_{o}is permitted only down to 80%.

_{p}is the number of parallel circuits instead of a single main district piping system. This approach may be helpful provided that N

_{p}is optimized in terms of cost, energy, all associated embodiments, physical constraints, and terrain.

#### 1.5. Low-Temperature District Energy Systems

_{FC}) and the fan power (P) required, they also proposed that small electric fans on the top surface of the radiator increase the thermal capacity by forced convection. The authors did not report the fan power demand in their experimental setup. The exergy balance may probably be negative in cases where the fan power demand is high. To avoid such a case (Exergy destruction), it would be prudent to check the following non-negativity condition, which compares the thermal exergy and the pumping power exergy:

_{a}is the indoor DB air temperature, and T

_{s}is the average panel surface temperature. For example, if ΔQ

_{FC}is 400 W, T

_{a}is 293 K (20 °C), and T

_{s}is 304 K (31 °C), the fan power must not exceed 15.2 W. Otherwise, the exergy benefit of enhancing thermal power by forced convection will be negative. Furthermore, there will be CO

_{2}responsibility of the electrical energy consumed, depending upon how and where the electric power is generated and transmitted minus the CO

_{2}emissions savings from the thermal gain by an amount of ΔQ

_{FC}.

#### 1.6. Objectives

## 2. Material and the Method of the Exergy-Based Model and Research

_{H}> 10, Step 3, either at the district plant or individually at the buildings), solar prosumers (Step 4) with conventional or new heat pipe types of heating equipment.

- Decarbonizing the built environment is possible by tapping into the widely available low-temperature renewable and waste heat sources.
- District energy systems may be helpful to achieve this goal.
- However, low-Temperature district energy systems can be successfully applied provided that:
- (a)
- District circuit loop length is optimal concerning pumping exergy spending and thermal exergy distribution. This issue has already been answered (Refer to Reference [37])
- (b)
- The temperature difference between the supply and return piping must be small at low supply temperatures
- (c)
- New low-temperature heating equipment must be developed to minimize or eliminate the necessity for equipment oversizing and temperature peaking.
- (d)
- Temperature peaking with heat pumps defeats the decarbonization objective unless the COP approaches 10. Such a high value may be achieved by cascading heat pumps and de-centralizing.
- (e)
- Heat pipes, wherever they may replace pumps or fans, reduce the CO
_{2}emissions responsibilities economically.

- District size with the number and capacity of the interconnected solar prosuming buildings must be small due to low solar heat temperatures being shared in the circuit. In this respect, sometimes detached solar buildings may be more rational
- Especially in low-temperature applications, exergy rationality must be prioritized.

#### 2.1. Research Design

_{2}emissions due to exergy destructions will be established and facilitated.

_{2}emissions.

#### 2.2. Impossible Cases with Existing Comfort Heating Equipment

#### 2.2.1. Case 1

_{sup}is peaked at the central plant by heat pumps (HP, Step 3). Temperature-peaked thermal power is distributed in the district (Step 2) by circulation pump stations, demanding a total electrical power of P. Assuming that more recent models of hydronic heating equipment are used in the buildings, such that the supply temperature is 65 °C. The return temperature is 55 °C (ΔT = 10 °C), just after one tour of thermal power distribution in the district, the waste heat or centralized solar thermal power field will become useless because the return temperature to the heat exchanger (55 °C) will be higher than the input temperature of 35 °C. This result defeats the purpose of using low-temperature thermal sources for decarbonization, while exergy destructions of the following amounts will occur, with non-zero unit exergy destructions and DCO

_{2}amounts as shown in the following calculations These results ultimately end the operation of Case 1.

_{2}emissions of the heat pump(s) power supply sources delivering electricity to the heat pumps and circulation pumps. Such positive exergy destructions render this application to be impossible right at the beginning of the process by not permitting the use of low-temperature thermal sources, as EU countries target for, thus also defeats the strategy of using widely available low-temperature thermal resources. In general, to make this solution workable, the return temperature must satisfy Equation (14), which shows that either equipment oversizing and or partial temperature peaking is necessary for the building.

_{2}emissions responsibilities as well as ozone-depleting emissions with positive ODP (Ozone-Depleting Potential) of the refrigerant). Although at a higher ΔT pumping power, demand will be smaller. Case 2 shows equipment oversizing, which eliminated temperature peaking. Electric power for the heat pump and the district loop pump(s) come with direct and nearly-avoidable CO

_{2}emissions.

#### 2.2.2. Case 2

#### 2.2.3. Case 3

#### 2.3. Possible Case: New Heating Equipment without or Little Support from Cascaded Heat Pumps

#### Case 4

#### 2.4. Models of Each Step (1 to 4)

#### 2.4.1. Optimum Pump Control in PVT Panel

_{out}is solved for give solar insolation and operating conditions.

_{out}, while T

_{E}or T

_{m}calculates instantaneous PV efficiency with the corresponding temperature T

_{out}. The pump selection is critical and must be dynamically controlled for net-positive exergy gain, as given in Equation (19).

_{X}will be a simple function of the dynamically adjusted flow rate:

_{2}(c` = 0.2 kg CO

_{2}/kW-h for natural gas).

_{2}emissions according to PEF, P, Q, and boiler efficiency. PEF, which is the fuel-to-plug electricity generation and transmission (The current standard value in practice is 2.5 in the EU). First of all, there are four different methods to evaluate PEF, which ranges between 2.09 and 1.84 for 2020 (Target values). Furthermore, current methods with different uncertainties do not account for exergy destructions in the power mix and the power chain. Even further, specific values for the countries are different. Therefore, the uncertainty of dCO

_{2}depends largely on PEF if other terms are fixed, namely:

_{2}is also sensitive to the pump power, which is a function of the loads, $\dot{Q}$. The boiler efficiency is also a function of the loads and the environmental conditions. E` is the ratio of the power output increase after PV cooling during positive generation of heat, Q:

#### 2.4.2. PV Life

_{p}(years), decreases in a logarithmic fashion, depending upon the cumulative number, N

_{f}and the average magnitude of the temperature swings as a function of T

_{m}, as shown in Figure 17.

_{max}, by comparing the exergy of the thermal power, namely ${\dot{Q}}_{D}$, which is shared among the prosumers and the central district plant by the district consuming exergy for district pumping, P

_{E}[37]. The following formulations show that L

_{max}must be determined first from the 2nd Law [37].

_{max}and then solving related equations simultaneously, the following expression for the maximum allowable total pumping power, namely P

_{Emax}, is obtained.

_{E}for minimum total CO

_{2}emissions, including avoidable emissions during the operation of the district energy system:

_{max}expressions and imposed ΔT limitations provide helpful information in selecting the supply and return temperatures at optimum flow rates. Equation (29) also shows that ΣCO

_{2}is a linear function of the circuit length. It may be presumed that by using multiple circuits in (nn) number of shorter identical district lengths, L

_{i}emissions may be reduced while pressure head is also reduced. This condition is possible only if Equation (30) is satisfied, which brings another optimization dimension by an optimum number of parallel circuits. The term h is the pump head for a single loop pipe length of L.

_{DS}, the maximum allowable district distance from the plant also decreases. Therefore, 5DE systems must be shorter in heating because they rely on ultra-low temperatures. For example, L

_{max}decreases by 1/1.54 when T

_{DS}decreases from 345 K to 308 K. In cooling, L

_{max}must also be shorter at higher supply temperatures. This condition is a trade-off between utilizing low exergy thermal sources and more infrastructural embodiments. There is a definite relationship between the average number of floors, n and the pay-back period, Y(n):

_{p}represents the effect of the pipe wall thickness on its pressure resistance according to diameter. Terms C, l, and k depend on the specifics of a district energy system. Then, Equation (31) deduces the economics of the district energy system size, i.e., decentralization versus centralization.

- If $(\frac{{m}_{p}}{2}+1)-k$ > 0, then the pay-back period increases with n,
- If $(\frac{{m}_{p}}{2}+1)-k$ = 0, then the pay-back period is independent of n,
- If $(\frac{{m}_{p}}{2}+1)-k$ < 0, then the pay-back period decreases with n.

_{o}prosumer T

_{UL}: When the supply temperature is less than the design value of given indoor heating equipment, then the equipment capacity decreases. To recover the design heating capacity, the equipment needs to be oversized. Figure 20 compares the oversizing issue about a standard radiator and a heat pipe radiator, without any external temperature peaking like a heat pump. Equation (32) gives the oversizing formula, which also considers exergy loss in a standard radiator, while it only approaches the design capacity asymptotically. According to Figure 20, T

_{4}is the effective temperature at the final oversizing step (i = 4). Exergy Penalty Factor represents the thermal exergy drift from T

_{UL}to T

_{4}. The exponent (n) is an equipment characteristic [12]. For radiant floor panels, (n) is 1.1. For standard radiators, it is 1.33. For fan-coils, it is 1.4 up to 1.5. The second additive exponent (m) is a new coefficient, which has been derived to represent the diminishing oversizing effect (Figure 20). Dry-Bulb (DB) indoor air temperature and Area-Averaged Unheated Surface Temperature (AUST) are assumed to be equal and constant in all steps.

- n—Capacity Factor
- m—Temperature Drift Factor

**Example 1.**

_{m}= 65 °C, T

_{a}= 20 °C, T

_{E}= T

_{UL}= 32.5 °C, T

_{4}= 25 °C.

_{m}= 65 °C, T

_{a}= 20 °C, T

_{E}= T

_{4}= T

_{UL}= 32.5 °C.

_{2}emissions responsibility, and pumping requirement. It may be concluded that heat pipe technology is technically, environmentally, and economically feasible and applicable as a retrofit tool, including old buildings. For HPR, the exponent (m) is less than zero because heat pipe performance usually overshoots while it is customizable to adapt for low mean supply temperatures, ability to employ thinner heat pipe thickness by reducing the heat pipe pressure, and smaller heat pipe diameter for better fin performance. A negative m value represents this overshooting. There is only one oversizing step instead of oversizing cascades in a standard radiator. A standard radiator (SR) in Figure 20 undershoots the target capacity, Q in every oversizing cascade, and requires further oversizing steps in a diminishing return until the limit of laminar flow is reached because the fluid flow in each parallel heat transfer pipe decreases with oversizing.

#### 2.4.3. Solutions for Figure 20

_{s}between the fluid and the pipe’s inner wall decreases with oversizing. This negatively affects the overall performance of the radiator. Once the radiator is oversized by adding more tubes sidewise in the same proportion of oversizing, F`, each tube receives a smaller heat load in an inverse proportion of F`. The average fluid velocity, V, in each tube also decreases with F`. These affect the heat transfer convection coefficient, h

_{s}between the fluid and the inner pipe surface. h

_{s}is a function of the fluid Reynolds Number raised to the power 0.8. Thus, it is a function of V

^{0.8}, provided that all other variables and fluid properties are fixed. The original design value of V before oversizing is equal to V

_{o}. Figure 22 shows the simple thermal resistance diagram.

_{eq}is the combined heat transfer flux due to surface radiation observing AUST (assumed to be equal to T

_{a}), and the surface natural convection observing Dry-Bulb (DB) indoor air temperature T

_{a}. T

_{E}changes with oversizing of standard radiators, as shown in Figure 20. T

_{p}is assumed to be uniform across the front panel of the radiator (ideal fin efficiency). The term r

_{eq}was defined for a panel area of M

_{oc}× 1 m of tube height. The thermal resistance of the tube wall is neglected [40]. r

_{f}may be derived from the literature [45].

_{Ei+}

_{1}:

_{i+}

_{2}, after returning (z) times to Equation (32), which accumulates the oversizing value to ƩF`

_{z}until the solution converges to an error function, ε or meets the laminar flow limit, whichever comes first. A simple computer program solves (m) by comparing the overall oversizing factor to the original one at step 1. The computer program further refines (m) iteratively by replacing (n) with (n + m) in each repetitive run of the nested loop in the computer program until the solution finally converges for (m).

_{UL}, the content composition, and gas pressure along with different wick constructions, and even the heat pipe diameter and its wall thickness may be better optimized with less critical strength limitations to increase the overall heat transfer rate from the radiator, such that this customizable feature may lead to a negative m value. For example, at 65 °C (Design Supply Temperature), a patented 3-phase heat pipe (EHP) fill reaches a pressure of 12 bar [41]. The same heat pipe filling during operation at 35 °C stays at 6 bars at a concentration of 0.4758 g/m

^{3}. EHP does not require external power to actuate the nanoparticles. In other words, the lower the supply temperature, the lower is the pressure. This relationship lets the designer better deal with the hoop and axial stresses, such that the pipe wall thickness may be reduced, which further reduces the radiator weight, embodiments, cost, and at the same time, increases the surface temperatures for a higher convection coefficient. Pipe diameter may increase to maximum fin efficiency, better contacts, thus higher radiation, and convection coefficients. Despite these advantages, the heat pipe’s effective thermal conductance may decrease, affecting the response time for fluctuating thermal loads in the indoor space. Therefore, a supply temperature-responsive design is possible with m ≤ 0. This feature is not available for radiators without heat pipes. Figure 23 compares the hydrodynamics of SR and HPR. An HPR type of heating equipment has a material weight advantage by a factor of more than two for the same heating capacity. On the other hand, water content density per oversizing, F`/W

_{W}is negative for an HPR radiator, concerning a reference of 1 kg of water fill per kW heating capacity:

^{+}) district energy systems, the supply temperature may be around 313 K (40 °C) or even less. If the transition of the standard heating equipment is possible only by oversizing them like adding more radiator sections or adding more radiator units, mostly in series in the latter case, which applies for many moderately old buildings, then pressure heads do increase. This increase is coupled with higher pumping power at the start-ups in an on-off type of controls facing larger volumes of heat transfer fluid accelerated in the entire system due to oversizing. These disadvantages may be offset by installing larger-diameter pipes, but this is quite unpractical in the existing building stock, which also adds embodied cost, energy, and CO

_{2}emissions. New heating equipment with heat pipe technology may play an important role in overcoming such problems. For example, new radiator designs with 3-phase heat pipe technology, which is symbolized in Figure 23 [41], contain a minimal amount of heat transfer liquid, only in the hydronic supply pipe at the bottom, which is slightly larger in diameter, D when compared to standard radiators (SR). Heat is transferred and distributed to the radiator by heat pipes instead of water tubes. The exponent (n) is 1.1, which makes the temperature control more manageable and more responsive, while it also helps reduce the need for oversizing the units with a negative (m) value in many cases in practice.

_{fopt}(Point C in Figure 24):

_{f}

_{1}for the heat pump and T

_{f}

_{2}for the equipment, the temperature may be further peaked by an amount dT

_{t}using an auxiliary heater, requiring an additional LCC factor, C

_{t}.

_{f}

_{2opt}and satisfies Equation (53).

_{HP}) number of tandem heat pumps with equal temperature lifts. For a high-performance heat pump, typical q and r values may be 5 and 0.04 K

^{−1}, respectively. Then Figure 26 gives an example with two tandem heat pumps (N

_{HP}= 2) [39]. At the break-even point of net exergy gain, each heat pump needs to have at least a COP value of 3.45.

_{2}emissions in terms of a given mix of the unit CO

_{2}content of fuels for power generation corresponding to a specific country, c`. A typical c` value is 0.26 and 0.53 is a given value for η

_{pp}. At the break-even point, both exergy and energy gains are zero, yet less power is on-demand while more low-exergy resources are demanded.

_{BE}in Figure 26, a cheaper and simpler heat pump with a single-stage compressor with q = 4 and r = 0.1 K

^{−1}may satisfy the COP = 3.45 condition with ΔT = 5 K. Therefore, such an exergy rationality analysis also reveals cheaper investments with the constraint on COP

_{i}.

_{ins}is the COP-optimized insulation thickness after over insulation. An increase of the COP means utilizing more renewable energy sources at low temperatures at the expense of more insulation investment versus revenues from investing in smaller-capacity heat pumps and less operating costs.

_{i}, most probably as a result of abrupt changes in the outdoor conditions, especially if the building is not insulated, must be responded to by modulating the mean temperature of the heat transfer fluid passing through the known equipment by an amount, dT

_{mi}at the indoor DB temperature T

_{ai}at an instant (i). Taking the derivative of Equation (61), concerning Q

_{i}:

_{m}becomes independent of the absolute value of the existing heat load, Q

_{i}, when there occurs an incremental change in the load, ΔQ

_{i}. Therefore, the response will be linear and independent of Q

_{i}.

_{i}approaches 100% of the design load (increasing order), for reaching the steady-state comfort regime, increasingly more precise temperature control of ΔT

_{mi}is required (control difficulty) to respond to heat load perturbations. This is the period, which also requires a steady increase of the indoor air temperature, T

_{ai}to reach its design value. However, it is counteracted by the proportionately increasing heat losses to the outdoors, momentarily forcing T

_{ai}to stall or even drop, which is another control input. This issue becomes more critical when equipment with higher n values is present. The above discussion may also be interpreted so that the transient time for reaching the steady-state conditions with equipment having a higher exponent (n) will be longer.

_{mD}of two different equipment with two different c

_{i}and n

_{i}values, the following relationship was derived:

_{1}to the ideal condition of one, the necessary c

_{j}for a given exponent n

_{j}, which is different from one, may be expressed in terms of ΔT

_{mD}:

_{i}≤ 100%) takes place for equipment (j) with (n

_{j}) greater than one. This difference is represented by integrating the incremental difference represented by the dT

_{mi}× dq

_{i}infinitesimal element.

_{j}is zero, and c

_{j}equals c

_{1}.

## 3. Analysis of Heat Pipe Radiator

#### 3.1. Comparison with Standard Radiator

_{2}is 1.8 kg CO

_{2}/kg material. An additional ΔCO

_{2}term, 0.8, is not accounted for in the standard embodiments table (Based on the 1st Law only). On a single radiator basis: 132.411 × 1.8 = 238.4 kg CO

_{2}embodied per radiator. In an apartment with 100 identical radiators, this is 23.8 tons of CO

_{2}.

_{2}savings, including DCO

_{2}due to exergy destructions concerning pumping power required by HPR (heating capacities adjusted) compared to SR, as a function of T

_{m}. At lower temperatures, an SR type of radiator needs more lateral oversizing, which sharply reduces pumping power demand due to more parallel pipes in the row such that each pipe receives a smaller flow. However, DT needs to be decreased to accommodate low T

_{m}(See Figure 23), while pumping power need for HPR increases slowly.

_{av}, it takes different time intervals, t

_{SR}, and t

_{HPR}to replace the radiator contents with the heated fluid supplied by the boiler through on-off pumps, driven by indoor comfort thermostats. Figure 30 shows the t

_{SR}and t

_{HPR}values at different T

_{av}values.

_{2}emissions sequestration potential compared to SR systems. Heat pipe radiators are equally effective in sensible comfort cooling with radiant heat transfer mode in dominance. This enables the decoupling of latent loads, ventilation loads, and sensible loads such that with 100% fresh air-conditioning becomes much more energy-efficient, exergy rational, and more pandemic resistant with less operating costs [41]. Figure 32 shows a typical ceiling heat pipe radiator for cooling. Fans may also be used for forced convection. Heat pump performance in terms of COP in heating or cooling decreases by an increase (Decrease in cooling) in temperature peaking amount, if required. Therefore, the ΔT between the heat pump and the radiator must be kept minimum. Only this case allows the temperature peaking to become exergy-rational with minimal ΔT values, which is possible with COP values up to 9 (above the threshold value of about 8 in heating) if ΔT is below 10 K and 15 K in cooling if ΔT is below 10 K. In Figure 32, the electric fan power exergy must not exceed the cooling exergy supplied.

#### 3.2. Exergy-Levelized Cost, ELC

_{p}), price of the radiators for the same capacity, (PC), oversizing factor, F`, (ε

_{dem}), and the embodiment of the radiator material in terms of energy and CO

_{2}off-set costs (EM). The term k is the ratio of embodied cost, EM to the radiator price, P. Here the term I

_{test}times A

_{p}represents the installed capacity.

_{UL}is 37 °C. Such a cost comparison reveals the actual benefits of HPR for the following typical inputs:

- For HPR:k = 0.2 kg
^{−1}ΔE_{XH}= 1 (See Figure 20)F` = 1.9W_{p}= 12 kg - For SR:k = 0.3 kg
^{−1}ΔE_{XH}= 0.95 (See Figure 20)F` = 6W_{p}= 22 kg$$\frac{EL{C}_{HPR}}{EL{C}_{SR}}=\frac{{\left(\frac{\left[F`+k{W}_{p}\right]}{\Delta {E}_{XH}}\right)}_{HPR}}{{\left(\frac{\left[F`+k{W}_{p}\right]}{\Delta {E}_{XH}}\right)}_{SR}}=\frac{{\left(\frac{\left[1.9+0.2\text{}\times \text{}12\text{}\mathrm{kg}\right]}{1}\right)}_{\mathrm{HPR}}}{{\left(\frac{\left[6+0.3\text{}\times \text{}32\text{}\mathrm{kg}\right]}{{0.95}_{\mathrm{XH}}}\right)}_{\mathrm{SR}}}=\frac{4.3}{16.42}=0.262$$

_{2}emissions implications towards decarbonization and the Paris Agreement.

_{o}, RRM provides a comparison tool per radiator weight, W

_{p}, and necessary oversizing F` for a given low-supply temperature. For the above example:

_{WP}may also be used as a separate metric, which is (Q

_{o}/W

_{p}) calculated at standard test conditions. The power density is similar to Q

_{WP}, but it quantifies the physical volume occupied by a heating radiator per kW of heating capacity at standard test conditions.

## 4. Case Study: To Centralize or Not to Decentralize Solar Prosumers

#### 4.1. Dezonnet Project

_{2}emissions [48].

#### 4.1.1. Description of the Project

_{2}emission responsibilities that need to be corrected using the 2nd Law. The critical mistake stems out from the fact that electric power consumed by the heat pumps, district pumps, ATES operations, etc. has very high unit exergy (0.95 kW/kW), while the solar heat generated, stored, and then used in buildings has a very low quality of energy (In the order of 0.1 kW/kW). If the flow rates, pipe diameters, and district distances are not carefully optimized, the exergy demand for electricity may exceed the exergy gain from the prosumers and be distributed in the district, which is in the form of low temperature (LT). Such a negative exergy gain means exergy of resources are irreversibly wasted (destroyed), and a significant consequence is CO

_{2}emissions responsibility, instead of sequestration, even though no fossil fuels are used. For example, heat pumps need to have a COP value of greater than seven in heating and ten in cooling to have a positive exergy gain, thus CO

_{2}sequestration, even if they are operated with on-site solar power systems, like PV or PVT.

_{2}emissions at the power plants will occur, depending upon the fossil fuel and renewable energy mix in the national energy budget. This, however, brings the Legionella problem. In this project, AC power requires AC-to- DC inverter(s) downstream of the PVT panels.

_{2}emissions responsibilities of the original Dezonnet project, which has a sum of 4.925 kg CO

_{2}/kW-h.

#### 4.1.2. Individual Solar Houses with Heat Pipe Technology

^{3})/2 m height = pD

_{s}

^{2}

_{s}is about 7 m. This is a disc-shaped concrete tank with thermal insulation in the ground with a 2 m depth. These dimensions can fit the backyard of a typical Dutch house. PCM material with properly selected operational temperatures. It is pumpless, which operates with heat pipes. During the day, PCM melts and absorbs solar heat from the PVT3 panels, while they also store some heat for night time and TEG operation (Negative DC Polarity) during this period. This additional power generation may be at 10%of the daytime capacity, depending on the meteorological conditions and the demand. In winter, the heating load is high, and the supply temperature to the heating equipment must be higher unless the equipment has been oversized at the design stage. If the heating season is too long, TES will be empty. So, the TES tank must also act as a thermal collector of the ground heat by vertical heat pipe loops in the ground to extract ground heat for the in-house heat pumps. Heat pipe controls are needed to open or close this loop so that when not in use, heat does not escape from the TES tank (except excess amount) to the ground. In the summer cooling period, the excess heat from the PVT3 panels and reject heat from the heat pumps may thermally charge not only the TES tank but also the ground loop in a controlled manner. There is an optimum sizing between the TES tank and the PVT3 panels regarding the limited roof area and the exergy needed for the on-demand, tankless electric boiler for temperature peaking the DHW service water.

_{2}emissions responsibility of this set of modifications over the original projects is about 0.155 kg CO

_{2}/kW-h, compared to 4.925 kg CO

_{2}/kW-h. The difference in emissions responsibility shows a 96.8% reduction, and the Dezonnet House becomes a nearly-zero Carbon Building (nZCB).

- The solar district system has been changed to individual solar buildings in a disconnected mode. This approach eliminates to large central thermal storage (ATES) system and eliminates the district pumping stations and pumps. This measure also eliminated the entire district piping, which comes with large embodiments and infrastructural costs. The savings were directed to new heat-pipe radiators and ceiling panels instead of oversizing standard radiators. In the same manner, savings were used to retrofit commercial PVT panels with PVT3 panels.
- Heat Pump COP optimized additional thermal insulation was applied to exterior walls.
- Heat pipe technology was extensively used in PVT panels, heating and cooling equipment, and local TES systems.
- Heat Pump refrigerant was changed from commercial refrigerants to CO
_{2}gas. By using CO_{2}gas, ozone depletion and global warming effects have been eliminated down to negligible proportions. Furthermore, by using CO_{2}gas, the same amount is deducted from the emissions stock. - Heat pump COP was increased by using two tandem heat pumps. This method reduces the solar electricity demand on board the building and at the same time minimizes CO
_{2}refrigerant leakages from them. - Night cooling from the PVT3 panels with a heat pipe connection indoors reduces the cooling loads.

## 5. Overall Discussion

_{2}/kW-h emissions. Although no fossil fuels are used in the building, direct emissions responsibility is 3.48 kg CO

_{2}/kW-h.

_{2}emissions “calculations” and the reality is essential to sustainably reduce global warming according to the Paris agreement goals. This difference is about 80% of the calculated values. The current calculations ignore the rationality factor; measures yet to be taken miss about half of the solution opportunities. Figure 35 shows the projection of variables like the 1st Law efficiency, energy rationality, the average unit CO

_{2}emissions factor, the ratio of renewables in the energy stock. For example, in 2020, the global average efficiency in all sectors like mobility, heating, cooling, agriculture, industry, etc., is estimated to be around 0.4. Sectoral penetration of renewables to the energy supply stock is around 20%, the global average of the degree of rationality, which shows how useful work potentials are balanced, among the supply and demand sides in the entire sector is only 0.2 (Reference).

_{2}/kW-h in the best scenario of today’s strategies. In 2060, the Paris Agreement goal will also be missed by about 0.3 kg CO

_{2}/kW-h. Even worse, a 30% renewable target of around 2025 will stay above the requirements for reducing climate crisis and remain there unless all nations abandon the recent natural gas craze and insistence on coal. Generating hydrogen from coal will not be a solution either, and it will stay at a high emissions point if the hydrocarbon economy continues. Figure 35 further shows that whatever measures are taken, we will not reach a negative carbon state unless we embrace nature and incorporate it with rational carbon capture methodologies. As a result, all strategists and energy policymakers need to recognize the importance of the rationality factor in all applications. Then new methodologies, new equipment, machinery, and performance metrics need to be developed to rate these applications towards truly minimum CO

_{2}emissions responsibilities, which have a definite effect on global warming. In this quest, the goal must be to minimize useful work potential destructions. After all, rationality is a matter of wisdom, and we can all do that because all we need is a change of today’s mindset.

## 6. Conclusions

_{2}/kW-h energy spending, which was about 0.15 in the pre-industry era. Now, it is 3. Today the global average of exergy rationality is about 20%. Referring to the ideal in Figure 35, the share of renewables will increase, increasing exergy rationality. However, their impact is not entirely linear upon CO

_{2}emissions because there will always be a residual fossil fuel use necessary to offset remaining exergy destructions to manufacture renewable energy systems. The curve at the bottom represents the additional positive impact of heat pipe technology. The figure shows that the Paris Agreement Target of lowering the CO

_{2}emissions below the pre-industrial era level is not precisely possible even with 100% renewables and exergy rationality reaches about 90%. Yet this reduction level is expected to be sufficient such that nature will take over by natural carbon sequestration. Hydrocarbon economy will be useful but must be based on 100% surplus renewables, which is not the case, represented by two points on the figure.

_{2}O

_{3}nanofluid in a copper oscillating heat pipe [51]. In their experiments, the authors have observed that the addition of FE

_{2}O

_{3}nanoparticles and the application of an external electromagnetic field improved both the thermal performance and the heat transfer coefficient. Their experiments indicated a 16% improvement in thermal performance when the nanoparticles and magnetic field were applied. The magnetic field typically demanded electrical power with a 2-ampere current for 0.274-tesla magnetic field at their experimental scale needs to be taken into account. In practice, the electrical energy and exergy involved in spending for magnetization must be less than the additional energy and exergy gains by applying the field for thermal performance enhancement. It must be noted that usually, the thermal exergy gain has low unit exergy while electrical power exergy is 0.95 kW/kW.

_{2}/kW-h is the average emissions factor for the fuel mix in the power sector. If P is 50 W (0.05 kW) for a typical single PVT panel of 1 m

^{2}, then removing the pump with heat pipes in the design will save 0.034 kg CO

_{2}per hour during its life cycle. If the total number of hours is 40,000, then this single heat pipe PVT will save a total emission of around 1.4 tons of CO

_{2}. The overall impact may also be seen in Table 2 and Table 3 regarding Figure 33 and Figure 34. According to Figure 36, the overall impact of heat piping on the heating and cooling sector by the year 2050 may be estimated to be 50% more reduction in CO

_{2}emissions when coupled with 5DE systems.

- This paper is expected to holistically extend the vision already opened by Shukuya, to the policymakers for improving their road maps and expanding their current strategies for decarbonization. The following takeaways may be recognized:
- Development and commercialization of low-temperature heating and high-temperature cooling equipment with minimum CO
_{2}, energy, cost, exergy embodiments, and affordable enough for easy retrofit must be prioritized, and R&D activities supported specifically with EU grants and other mechanisms, worldwide. - Heat pipe technology for aiming the maximum efficiency and minimum exergy losses, savings in material, and weight in the buildings must be prioritized along three main vectors, namely the solar PVT systems, short-term energy storage (With PCM), and the equipment themselves.
- Until new heating and cooling equipment widely penetrate the building sector, tools for optimum design of oversizing the existing heating and cooling equipment and assisting with high-COP heat pumps in a tandem format must be developed and provided to the design market and building engineers and architects.
- New-generation solar PVT systems must be implemented to utilize the solar exergy for given solar insolation areas in and around the buildings.
- Public and government awareness about the exergy dimension of the solution for global warming must be raised by publications, seminars, and online educational packages. It must be emphasized that the methodology presented in this paper makes the information transition and practice much easier to grasp and implement.
- District energy concepts with low-temperature heating and high-temperature cooling are rising in the political and engineering agenda. This seemingly effective way of decarbonization, the district thermal exergy circulated versus the pumping exergy demand must be noted by policymakers, and future designs for 100% RHC cities must be a prerequisite.
- Total electrification by heat pumps concept is also on the rise by the influence of the heat pipe industry. Yet according to the 2nd Law of Thermodynamics, as clearly explained in this paper, COP values must be increased by innovations, and optimum cascading of heat pumps must become a general practice.
- The concept of Renewable Energy Cities must be transitioned to the concept of Renewable Exergy Cities if sustainable decarbonization is the real agenda with the recognition that decarbonization is a matter of minimizing exergy destructions, beyond increasing the energy efficiency.
- Today, exergy becomes first within the general energy, environment, water, and welfare nexus. This must be widely acknowledged by all means (see [53]).
- It must be realized that the exergy rationality concept is not only a game-changer but moreover is a game maker that must be taken into an advantage.
- Sometimes low-temperature district energy systems may not be effective in CO
_{2}emissions responsibility. Then individual green buildings or smaller-sized districts must be on the energy agenda.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

Symbols | |

A_{p} | Solar Panel Area, m^{2} |

AUST | Area Average of Un-Conditioned Indoor Surface Temperatures, K |

c | Equipment heating capacity factor (Equations (48) and (61)), kW/K |

c` | Unit CO_{2} emission value of fossil fuel, kg CO_{2}/kW-h |

c``, c``` | Constants in Equation (35) |

C_{p} | Specific Heat, J/kg K |

CO_{2} | Direct CO_{2} emissions, kg CO_{2}/kW-h |

COP | Coefficient of Performance (Heat Pump) |

d | Constant in Equation (60) |

dT_{t} | Temperature Deficit Between Optimum Heat Pump Output (supply) Temperature and Optimum Equipment Input Temperature, (Equation (50)) K |

C_{1} | T_{fhp} − T_{g}, K (Figure 24) |

C_{2} | T_{feq} − T_{a}, K (Figure 24) |

C_{eq} | Life-Cycle Cost Factor for Equipment, €/kW-h [46] |

C_{hp} | Life-Cycle Cost Factor for Heat Pump, €/kW-h [46] |

C_{t} | Life-Cycle Cost Factor for Auxiliary Heater, €/kW-h [46] |

C_{o-t} | Life-Cycle Cost of Auxiliary Heater (to be added to equipment and heat pump life-cycle costs) |

E | Electric Power, kW |

ELC | Exergy-Levelized Cost, €/(kW_{EXpeak}/m^{2}) |

ELC_{CO2} | Exergy-Levelized CO_{2} Emissions Cost, kg CO_{2}/(kW_{EXpeak}/m^{2}) |

E_{XH} | Thermal Exergy, kW |

F` | Oversizing Factor (Equation (32)) |

GWP | Global Warming Potential |

h | Heat Transfer Coefficient, kW/m^{2}K |

ID | Internal Tube (Pipe) Diameter, m |

I_{n} | Solar Insolation Normal to the PV Panel Surface, kW/m^{2} |

l | Oversizing Multiplier in Equation (11) |

L | Length of District Loop, m |

L_{P} | Life of Solar Panel |

M_{OC} | Tube Spacing on Centers, m (Equation (38)) |

n | Number of Floors in a Building |

ODI | Ozone Depleting Index |

ODP | Ozone Depletion Potential |

R_{EX} | Exergy-based share of renewable energy sources by installed capacity in the energy stock |

N_{p} | Number of Parallel Piping in the District Energy System |

N_{f} | Temperature Life Cycle |

P | Pump Power, kW |

q, r | Heat Pump COP multipliers (Equation (56)), q is dimensionless r has a unit of K^{−1} |

Q | Heat Load, Heat Supply, kW |

Q_{o} | Rated Heat Capacity, kW |

Q_{WP} | Q_{o}/W_{p}, kW/kg |

q | Heat Flux, kW/m^{2} |

r | Thermal Resistance, m^{2}K/W |

RRM | Radiator Capacity Increase per Oversizing Ratio, kW/kg |

T | Temperature, K or °C |

t | Time, s |

U` | Heat Load Coefficient of The Building, kW/K |

$\dot{V}$ | Volumetric Flow Rate, m^{3}/s |

W | Weight, kg |

w | Constant in Equation (25) |

WD | Weight Metric (Equation (47)), kg^{−1} |

W_{p} | Weight of the Radiator, kg |

W_{W} | Weight of Water Content of the radiator (SR), kg |

y | Constant in Equation (28) |

Greek Symbols | |

ΔCO_{2} | Nearly-Avoidable CO_{2} Emissions Due to Exergy Destructions, kg CO_{2}/kW-h |

ΣCO_{2} | Total CO_{2} emission (Sum of Direct and Nearly-Avoidable Emissions), kg CO_{2}/kW-h |

ΔH | Heat Deficit, kW |

ψ_{R} | Rational Exergy Management Efficiency |

E | Unit exergy, kW/kW |

B | Thermal constant of PV Efficiency |

η, η_{I} | First-Law Efficiency |

R | Mass Density, kg/m^{3} |

Subscripts | |

_{a} | Indoor Air |

_{Boiler} | Boiler |

_{D} | District |

_{dem} | Demand |

_{des} | Destroyed |

_{eq} | Equipment |

_{f} | Carnot Cycle-Based Equivalent (Virtual) Energy Source Temperature-related or adiabatic flame temperature of fossil fuel, or source temperature of renewable thermal energy sources-related, fuel |

_{fuel} | Fuel |

_{H} | Heat |

_{HE} | Heat Exchanger |

_{in} | Inner, input |

_{ins} | Thermal Insulation |

_{m} | Mean (Average) Temperature, K |

_{max} | Maximum |

_{mo} | Electric Motor |

_{0} | Original (Design, Rated) Value |

_{opt} | Optimum |

_{P} | Panel, pump |

_{out} | Out |

_{peak} | Peak |

_{ref} | Reference |

_{S} | Steam |

_{sup} | Supply |

_{UL} | Ultra-Low (Temperature) |

_{x} | Exergy |

Superscripts | |

` | Modified, Secondary |

^{n} | Equipment Heating Capacity Exponent |

^{m} | Additional Equipment Heating Capacity Exponent |

Abbreviations | |

ATES | Aquifer Thermal Energy Storage |

1DE (or 1G) | First-Generation District Heating |

5DE | Fifth-Generation District Energy System |

5DE^{+} | Beyond 5DE |

AC | Alternating Current |

ATES | Aquifer Thermal Energy Storage |

BAU | Business as Usual |

CC | Carbon Capture |

CCS | Carbon Capture and Storage |

DC | Direct Current |

EHP | Enover Heat Pipe |

EU | European Union |

F/C | Fan Coil |

G | Generation (District Energy System) |

GHG | Green House Gas Emissions |

HPR | Heat Piper Radiator |

HVAC | Heating, Ventilating, and Air Conditioning |

IAQ | Indoor Air Quality |

HP | Heat Pump |

IEA | International Energy Agency |

LT | Low-Temperature |

LowEx | Low-Exergy (Building) |

OECD | Organization for Economic Co-operation and Development |

PCM | Phase-Changing Material |

PMPPT | Direct Power MPPT (Maximum Power Point Tracking) |

PV | Photovoltaic Cell (Panel) |

PVT | Photo-Voltaic-Thermal |

PVT1 | First-Generation (Simple) PVT |

REMM | Rational Exergy Management Model |

100REC | 100% Renewable Energy City |

100REXC | 100% Renewable Exergy City |

RHC | Renewable Heating and Cooling |

SR | Standard (Conventional) Hydronic Radiator for Indoor Heating |

TES | Thermal Energy Storage |

TEG | Thermo-Electric Generator |

## Appendix A. Explanation of Figure 2

_{ref}, T

_{a}, and T`

_{sup}(Exergy Triangle). The side T

_{a}–T

_{ref}represents the unit demand exergy. The side T`

_{sup}–T

_{ref}represents the unit supply exergy. The side T

_{a}–(T`

_{sup}− 1/2 × ΔT) represents the exergy of a unit thermal load (Q = 1 kW), E

_{XH}. The triangular area Δ

_{s}represents the optimization objective, which needs to be maximized within the given temperature constraints and given design temperatures.

_{a}, T`

_{sup}are the optimization variables with the non-negativity conditions:

_{a}≥ 290 K

(Depending upon the heating or cooling system, Relative Humidity, and AUST)

_{R}and thereby minimize ΔCO

_{2}responsibility by minimizing Δ

_{s}.

_{a}− T

_{ref}) = 2Δ

_{s}/(T

^{`}

_{sup}− T

_{ref}). This relationship simplifies Equation (A7) for a design input of k = T

^{`}

_{sup}/T

_{a}

_{R}< 1 (v) Maximum ψ

_{R}yields minimum ΔCO

_{2}through Equation (A3):

_{sup}, and the triangle area decrease, which means that ψ

_{R}also decreases. According to Equation (A9), any decrease in ε

_{sup}reduces ΔCO

_{2}

_{,}but at the same time, any decrease in ψ

_{R}, according to Equation (A9), increases ΔCO

_{2}. A small decrease in T

_{a}may offset this increase if indoor comfort requirements permit. At any rate, this discussion shows that it is also possible to determine an optimum over insulation by using Figure 2.

_{a}to T`

_{a}decreases the area of the bounded triangle when supply temperature, reference temperature, and ΔT are kept fixed. Thus, this figure graphically optimizes the Rational Exergy Management Efficiency, ψ

_{R}, and minimizes the ΔCO

_{2}emissions responsibility. If it is possible to decrease the design value of ΔT any further, the constraint (A3) is relaxed so that the area may increase. Therefore Figure 2 may be a useful graphical design tool to optimize the thermal performance of a given design.

_{a}is changed:

_{ref}and T`

_{sup}are fixed.

_{sup}is decreased for a given T

_{ref}temperature, the sensitivity of ψ

_{R}on any change in T

_{a}decreases because c decreases.

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**Figure 1.**Atmospheric CO

_{2}Concentration Predictions for Three Scenarios, including the business-as-usual (BAU) scenario. From [3].

**Figure 2.**Exergy Triangle with three sides representing ε

_{dem}, ε

_{sup}, and the unit thermal exergy supply, E

_{XH}.

**Figure 3.**Variation of Over Insulation in Terms of (Q`/Q), ψ

_{R}, and T`

_{eq}with the Supply Temperature.

**Figure 4.**Historical Evolution of District Energy Systems from Steam to 100% Renewables. Developed from [16].

**Figure 5.**Length of Steam Pipes of Different Diameters in District Energy Systems Over the Years. From [17]. This figure shows that district loop lengths (in meters) composed of steam pipes have been significantly reduced since the 1950–1954 period. First, this results from the transition from steam to hot water, and second the recognition of the fact that pumping power demand-related emissions versus embodied emissions of large pipe diameters have an optimum point, which generally calls for shorter distances and moderately-sized pipe diameters. That is why larger pipes like DN350 pipes are not used anymore.

**Figure 7.**Change of Series-Oversizing Rates with ΔT. Reference ΔT is taken 20 K at No-Oversizing Condition (Oversizing: 1). Indoor Air Temperature T

_{a}= 20 °C. This figure shows that equipment oversizing increases while ΔT through the equipment is increased. The corresponding ΔT for no-oversizing is 10 K. The point representing Reference 27 shown on the same curve calls for an oversizing multiplier of 2. Large ΔT values are limited due to aeration problems in hydronic circuits and reduction in heating equipment capacity.

**Figure 8.**Temperature Profiles of the Fluid Flow in Series Oversizing of the Equipment at Different ΔT and Supply Temperatures, T

_{sup}.

**Figure 9.**Impossible Case 1. Low-Temperature Source is Peaked at the District Plant by Heat Pump(s). Supply temperature is 65 °C, up to 90 °C. This case enables the retention of the standard equipment without any need to oversize. However, more pipe insulation is required to eliminate additional heat losses. The COP of the central heat pump station is not high due to the temperature peaking requirement from 35 °C to 65 °C and higher.

**Figure 10.**Impossible Case 2. Removal of Central Heat Pumps (Case 1) with Individual Heat Pumps in the Buildings. Standard Equipment Without Oversizing. In this case, each building is equipped with individual heat pumps. The main district supply line has a lower temperature, thus does not require additional insulation. However, because the return temperature will be higher (55 °C) than the temperature of the solar/waste heat (35 °C), this option defeats the purpose of utilizing low-temperature thermal sources. At the same time, the district return piping needs to be additionally insulated.

**Figure 11.**Case 3: Utilization of Low-Temperature Sources with Oversized, Standard Equipment. In this case, the district loop is at a low temperature. No temperature peaking is necessary because the standard equipment is oversized, and ΔT must be lowest (5 K). This case increases pumping power demand and embodied costs of equipment oversizing.

**Figure 12.**Case 4. Ultimate Solution for 5DE District Heating with Heat Pipe Radiators (HPR). Heat pipe radiators are more adjustable to low-temperature supply and require less oversizing. Optimization with small heat pumps will be more feasible if temperature peaking is necessary.

**Figure 13.**Change of Sensitivity with Low District Temperatures. Moving to low source temperatures increases the sensitivity of the thermal response and leads to control issues, although lower supply temperatures enable the broader use of low-temperature resources.

**Figure 14.**Experimental Heat-Pipe Natural Convector. Fins are attached to horizontal heat pipes. Reprinted with permission, Elsevier, 2021 [42].

**Figure 15.**Photo of the Prototype Enover Heat-Pipe Radiator (HPR). This prototype was tested in certified labs.

**Figure 16.**Simplified PVT Thermal and Electric Power Diagram with a Pump, including the heat exchanger, main pump, and the thermal energy storage. PMPPT: Direct Power MPPT (Maximum Power Point Tracking). P ~ 0 if heat pipes are used.

**Figure 17.**Life of PV cells depending upon the number of Temperature Cycles. This symbolic figure shows that PV cell life decreases with the number of thermal cycles at higher PV temperatures with little or no cooling.

**Figure 18.**Pumpless Solar PVT System with Heat Pipes, a Flat Plate Collector Layer on the Top, Additional Power Generation with TEG Units, and thermal energy storage with Embodied PCM Layer. Reprinted with permission, Elsevier, 2021 [44].

**Figure 20.**Standard Radiator Performance: Diminishing Effect of Oversizing on the Heating Capacity with the Supply Temperature Drift from the Design Value, T

_{m}= T

_{o}to T

_{UL}and further. Fluid velocity, V drifts from V

_{o}to V

_{k}. ΔT = Fixed. F` is area oversizing H × L.

**Figure 21.**A Typical Cross-Sectional Top View of a Standard, Finned Radiator. T

_{m}approaches T

_{UL}.

**Figure 23.**Two Types of Radiators with Oversizing to Accommodate Low-Temperature (LT) Heating. Note that the oversizing requirement is more for a standard radiator. Reprinted with permission, Elsevier, 2021 [41].

**Figure 24.**The Conflict Between Heat Pump and the Heating Equipment. From [46]. At low supply temperatures, in this case, the ground source temperature, the heat pump COP decreases and requires capacity oversizing to maintain the required thermal output. The HVAC equipment also requires oversizing. An optimum mix of heat pump oversizing and equipment oversizing is available at T

_{fopt}(Point C). See Equations (49) and (51).

**Figure 25.**Temperature Peaking with a Multitude of N

_{HP}number of Smaller Heat Pumps in Tandem. Each heat pump experiences a small ΔT; thus, their COP is high. Reprinted with permission, Elsevier, 2021 [41].

**Figure 26.**Energy and Exergy Gains with Individual COP

_{i}value of Two Heat Pumps in Tandem. According to this figure, the break-even COP

_{BE}before exergy gain is about 3.4. However, the exergy gain must be high enough to reach zero exergy destruction level, which is COP

_{imin}= 10. Reprinted with permission, Elsevier, 2021 [41].

**Figure 27.**Change of Equipment Heating Capacity, Q

_{i}with Mean Temperature, and (n). The relationship is linear for the n = 1 condition, which corresponds to easier control.

**Figure 29.**Average CO

_{2}Savings for a 10-unit Apartment (100 radiators) During One Heating Season in Ankara.

**Figure 33.**Original Dezonnet Project: Large Central District Thermal Storage, Heat Pumps, and PVT1 Panels. The terms c is the constant for pressure drop per unit district length, L. η

_{PM}is the pump-motor efficiency.

**Figure 35.**Linearized Estimates for Best-Case Scenario with Renewables Until 2060. While it is expected that the share of renewables will increase (In this figure assumed to be a linear increase with time), renewable system improvements and low-temperature heating and high-temperature cooling equipment in 5DE systems will help to increase exergy rationality and the 1st Law efficiency, resulting in the reduction of CO

_{2}emissions.

**Figure 36.**ΣCO

_{2}Emissions per Year, kg CO

_{2}/kW-h with Linear Penetration Interpolation of Renewables, 5DE District Energy Systems, and Heat Pipe Technology. Developed from [41].

EHP Position | |||
---|---|---|---|

Vertical | Horizontal | ||

Thermal Conductance W/(m × K) | Mean Temperature, T_{m}, °C | Thermal Conductance W/(m × K) | |

13,840 | 90 | 13,340 | |

11,950 | 60 | 11,650 | |

9249 | 35 | 9050 |

**Table 2.**Different CO

_{2}Emissions Responsibilities of the Primary Components of the Original Dezonnet Project (Embodiments are excluded).

Component | ODP | GWP | ODI | ΔCO_{2} | CO_{2} | ΣCO_{2} |
---|---|---|---|---|---|---|

kg CO_{2}/kW-h | ||||||

PVT1 pumps | - | - | - | 0.15 | 0.30 | 0.450 |

Heat Pump | 0 | 550 | 0.124 | 0.045 | 0.33 * + 0.05 ** | 0.425 |

District Pumps | - | - | 0.70 *** | 2.5 *** | 3.20 | |

ATES | - | - | - | 0.35 *** | 0.15 *** | 0.450 |

Domestic Pumps | - | - | - | 0.20 | 0.15 | 0.350 |

Total | 1.445 | 3.48 | 4.925 |

_{2}equivalent of ODI (Ozone Depletion Index). ** Annual grid power share of 1/3, assuming natural gas power plant, PEF: 2.5, annual average COP is 3. *** Prorated to each building. Note: Due to the limited amount of data available, some values are estimates.

**Table 3.**Different CO

_{2}Emissions Responsibilities of the Primary Components of the Revised DeZonnet Project shown in Figure 33 (Embodiments are excluded).

Component | ODP | GWP | ODI | ΔCO_{2} | CO_{2} | ΣCO_{2} |
---|---|---|---|---|---|---|

kg CO_{2}/kW-h | ||||||

PVT3 (No pump) | - | - | - | 0.05 | - | 0.05 |

Cascaded Heat Pumps | 0 | 1 * | Negligible ** | 0.045 | Negligible | 0.425 |

Local TES with PCM and TES | - | - | - | 0.01 | - | 0.01 |

Domestic Pumps | - | - | - | 0.05 | - | 0.05 |

Total | 0.155 | Negligible | 0.155 |

_{2}gas is used as refrigerant. ** Because GWP is only one for CO

_{2}.

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## Share and Cite

**MDPI and ACS Style**

Kılkış, B.; Çağlar, M.; Şengül, M.
Energy Benefits of Heat Pipe Technology for Achieving 100% Renewable Heating and Cooling for Fifth-Generation, Low-Temperature District Heating Systems. *Energies* **2021**, *14*, 5398.
https://doi.org/10.3390/en14175398

**AMA Style**

Kılkış B, Çağlar M, Şengül M.
Energy Benefits of Heat Pipe Technology for Achieving 100% Renewable Heating and Cooling for Fifth-Generation, Low-Temperature District Heating Systems. *Energies*. 2021; 14(17):5398.
https://doi.org/10.3390/en14175398

**Chicago/Turabian Style**

Kılkış, Birol, Malik Çağlar, and Mert Şengül.
2021. "Energy Benefits of Heat Pipe Technology for Achieving 100% Renewable Heating and Cooling for Fifth-Generation, Low-Temperature District Heating Systems" *Energies* 14, no. 17: 5398.
https://doi.org/10.3390/en14175398