Search Results (18)

Steel is an important product in many engineering sectors; however, steelmaking remains one of the largest ${\mathrm{CO}}_2$ emitters. Therefore, new governmental policies drive the steelmaking industry toward a cleaner and more sustainable operation such as the gas-based direct reduction–electric arc furnace process. To become carbon neutral, utilizing more scrap is one of the feasible solutions to achieve this goal. Addressing knowledge gaps regarding scrap heterogeneity (size, shape, and composition) is essential to evaluate the effects of increased scrap ratios in basic oxygen furnace (BOF) operations. This review systematically examines heat and mass transfer correlations relevant to scrap melting in BOF steelmaking, with a focus on low Prandtl number fluids (thick thermal boundary layer) and dense particulate systems. Notably, a majority of these correlations are designed for fluids with high Prandtl numbers. Even for the ones tailored for low Prandtl, they lack the introduction of the porosity effect which alters the melting behavior in such high temperature systems. The review is divided into two parts. First, it surveys heat transfer correlations for single elements (rods, spheres, and prisms) under natural and forced convection, emphasizing their role in predicting melting rates and estimating maximum shell size. Second, it introduces three numerical modeling approaches, highlighting that the computational fluid dynamics–discrete element method (CFD–DEM) offers flexibility in modeling diverse scrap geometries and contact interactions while being computationally less demanding than particle-resolved direct numerical simulation (PR-DNS). Nevertheless, the review identifies a critical gap: no current CFD–DEM framework simultaneously captures shell formation (particle growth) and non-isotropic scrap melting (particle shrinkage), underscoring the need for improved multiphase models to enhance BOF operation. Full article

With the development of the agro-processing industry, the efficient cryogenic treatment and resource utilization of porcine bile—a high-value byproduct—has received increasing attention. This study investigates the dynamic behaviour and freezing characteristics of porcine bile droplets upon impact on cold substrates under varying conditions of surface temperature (−10 °C to −20 °C) and impact velocity (0.18–0.59 m/s). The effects of droplet size, dimensionless numbers (Weber, Reynolds, Bond, Ohnesorge, and Prandtl), and thermal gradients were systematically analyzed. A thermoelectric cooling substrate combined with high-speed imaging was used to quantitatively characterize the spreading ratio, retraction ratio, and freezing time of droplets. The results show that the maximum spreading ratio increases with higher impact velocity but decreases with lower substrate temperature. Lower substrate temperatures significantly shorten the freezing time, with a maximum reduction of up to 45%, particularly for smaller droplets. Droplets with high Weber numbers (We > 3) form flattened ice layers with preserved retraction patterns, while those with low Weber numbers (We < 1) generate smooth, hemispherical ice caps. For the first time, the thermophysical properties of porcine bile were incorporated into the framework of droplet impact dynamics on cryogenic surfaces. The findings reveal multiscale freezing mechanisms of biological fluids at low temperatures and provide a theoretical basis for optimizing processes such as freeze-drying and cryogenic sterilization in agro-product processing. Full article

According to Prandtl’s boundary layer theory, the entrance length refers to the axial distance required for a flow to transition from its initial entry condition to a fully developed flow where the velocity profile stabilizes downstream. However, this theory remains applicable only under the assumption of Re ≫ 1, while its validity diminishes under low-Reynolds-number conditions. This study utilizes OpenFOAM based on the finite volume method to numerically examine Newtonian and viscoelastic fluids in a laminar circular pipe flow. The objective is to determine the range of Reynolds numbers for which the differential equations from within the Prandtl boundary layer theory are strictly valid. Additionally, the study explores the effects of Reynolds numbers (Re) ranging from 50 to 100, s solvent viscosity ratio (β) fixed at 0.3 and 0.7, and Weissenberg numbers (Wi) ranging from 0.2 to 5 on the entrance length and friction factor for the Oldroyd-B model. The results indicate the presence of a lower Reynolds number that impedes the attainment of the outcomes predicted by the Prandtl boundary layer theory for the entrance length. The inertia effect, the increase in solvent viscosity contribution, and the elastic effect exhibit a linear relationship with the entrance length and friction factor. Full article

This study is a comprehensive review on the natural convection heat transfer in horizontal and inclined closed rectangular enclosures with internal objects (including circular, square, elliptic, rectangular, and triangular cylinders, thin plates, as well as other geometries) at various heating conditions. The review examines the influence of various pertinent governing parameters, including the Rayleigh number, Prandtl number, geometries, inclination of enclosure, concentration of nanoparticles, non-Newtonian fluids, magnetic force, porous media, etc. It also reviews various numerical simulation methods used in the previous studies. The present review shows that the presence of inner objects at different heating conditions and the inclination of enclosures significantly changes the natural convection flow and heat transfer behavior. It is found that the existing studies within the scope of the present review are essentially numerical with the assumption of laminar flow and at relatively low Rayleigh numbers, which significantly restrict the usefulness of the results for practical applications. Furthermore, the majority of the past studies focused on single and two inner objects in simple shapes (circular, square, and elliptic) and assumed identical objects and uniformly distributed placements when multiple inner objects are presented. Based on the review outcomes, some recommendations for future research on this specific topic are made. Full article

In response to the growing demand for advanced nuclear reactor technologies, this study addresses significant gaps in thermal-hydraulic modelling for dual fluid reactors (DFRs) by integrating Kays correlation to implement a variable turbulent Prandtl number in the Reynolds-averaged Navier–Stokes (RANS) simulations. Traditional approaches employing a constant value of the turbulent Prandtl number have proven inadequate, leading to inaccurate heat transfer predictions for low Prandtl number liquids. The study carefully selects the appropriate formula for the turbulent Prandtl number in the DFR context, enhancing the accuracy of thermal-hydraulic modelling. The simulations consider Reynolds numbers between 15,000 and 250,000, calculated based on the hydraulic diameters at different diameter pipes of the fuel and coolant loops. The molecular Prandtl number is equal to 0.025. Key findings reveal that uneven flow distributions within the fuel pipes result in variable temperature distribution throughout the reactor core, confirming earlier observations while highlighting significant differences in parameter values. These insights underscore the importance of model selection in CFD analysis for DFRs, revealing potential hotspots and high turbulence areas that necessitate further investigation into vibration and structural safety. The results provide a framework for improving reactor design and operational strategies, ensuring enhanced safety and efficiency in next-generation nuclear systems. Future work will apply this modelling approach to more complex geometries and flow scenarios to optimise thermal-hydraulic performance. Full article

This paper presents a comprehensive review of mixed convective heat transfer phenomena involving fluids with varying Prandtl numbers, specifically focusing on their behavior in different geometries and orientations. This study systematically explores heat transfer characteristics for fluids with low, medium, and high Prandtl numbers across a range of tube geometries, including circular, rectangular, triangular, and elliptical cross-sections, and examines their effects in both horizontal and vertical tube orientations. By consolidating existing research findings and analyzing various experimental and numerical studies, this review elucidates the complex interactions between fluid properties, tube geometry, and flow orientation that influence mixed convection heat transfer. Key insights are provided into the mechanisms driving heat transfer enhancements or degradations in different scenarios. In view of the findings from this paper, more than 84% of studies were conducted in a horizontal orientation and circular cross-section with a tendency to use medium-to-high Prandtl numbers as the working fluid for the past 10 years. This paper also identifies critical gaps in current knowledge and suggests future research directions to advance the understanding and application of mixed convective heat transfer in diverse engineering systems. Furthermore, apart from having different geometries applied in industrial applications, there is still room for improvement through the addition of passive methods to the heat transfer system, including helical coils, corrugations, swirl generators, and ribs. Overall, from the literature review, it is found that there are few relevant numerical simulations and experimental studies concentrating on middle Prandtl number fluids. Hence, it is recommended to perform more research on medium Prandtl number fluids that can be used as energy storage systems (ESS) in concentrating solar power plants, nuclear reactors, and geothermal systems. Full article

Bénard–Marangoni convection in an open cavity has attracted much attention in the past century. In most of the previous works, liquids with Prandtl numbers larger than unity were used to study in this issue. However, the Bénard–Marangoni convection with liquids at Prandtl numbers lower than unity is still unclear. In this study, Bénard–Marangoni convection in an open cavity with liquids at Prandtl numbers lower than unity in zero-gravity conditions is investigated to reveal the bifurcations of the flow and quantify the heat and mass transfer. Three-dimensional direct numerical simulation is conducted by the finite-volume method with a SIMPLE scheme for the pressure–velocity coupling. The bottom boundary is nonslip and isothermal heated. The top boundary is assumed to be flat, cooled by air and opposed by the Marangoni stress. Numerical simulation is conducted for a wide range of Marangoni numbers (Ma) from 5.0 × 10¹ to 4.0 × 10⁴ and different Prandtl numbers (Pr) of 0.011, 0.029, and 0.063. Generally, for small Ma, the liquid metal in the cavity is dominated by conduction, and there is no convection. The critical Marangoni number for liquids with Prandtl numbers lower than unity equals those with Prandtl numbers larger than unity, but the cells are different. As Ma increases further, the cells pattern becomes irregular and the structure of the top surface of the cells becomes finer. The thermal boundary layer becomes thinner, and the column of velocity magnitudes in the middle slice of the fluid is denser, indicating a stronger convection with higher Marangoni numbers. A new scaling is found for the area-weighted mean velocity magnitude at the top boundary of u_m~Ma Pr^−2/3, which means the mass transfer may be enhanced by high Marangoni numbers and low Prandtl numbers. The Nusselt number is approximately constant for Ma ≤ 400 but increases slowly for Ma > 400, indicating that the heat transfer may be enhanced by increasing the Marangoni number. Full article

Cooling processes are responsible for a significant portion (20%) of global energy consumption and raise environmental concerns such as ozone depletion, the greenhouse effect, and high energy use. This study investigates the potential of R152a, a refrigerant with low global warming potential (GWP), as a more sustainable alternative. The performance, safety, and operational efficiency of R152a were evaluated under various conditions. Although R152a offers high performance and low GWP, its flammability necessitates caution, especially in certain mixtures. A 12-pass tube-type heat exchanger model was simulated using computational fluid dynamics (CFD) to analyze the fluid behavior within the exchanger. The pressure, density, dynamic pressure, Prandtl number, total pressure, and temperature distributions for both R152a and H₂O (water) were visualized using contour plots. The simulations comprehensively examined the fluid behavior inside and outside the heat exchanger. The results revealed the influence of the temperature on the internal dynamic pressure and density of R152a. Compared with R134a, R152a demonstrated superior performance but a lower coefficient of performance (COP) than R32. Studies also suggest that R152a exhibits lower irreversibility in Organic Rankine Cycle (ORC) systems than R245fa. These findings suggest that R152a holds promise for future refrigeration systems, as supported by existing research on its performance and compatibility. One study focused on optimizing the heat exchanger performance by maximizing the heat capacity and minimizing the pressure drop. This study employed a parallel-flow heat exchanger with R152a as the coolant for the hot process water. The temperature changes, pressure drops, and resulting energy efficiency and thermal performance of both fluids were analyzed. The results highlight the distinct energy efficiencies and thermal performance of the employed fluids. Full article

Natural circulation loops are thermohydraulic circuits used to transport heat from a source to a sink in the absence of a pump, using the forces induced by the thermal expansion of a working fluid to circulate it. Natural circulation loops have a wide range of engineering applications such as in nuclear power plants, solar systems, and geothermic and electronic cooling. The Lattice Boltzmann Method was applied to the simulation of this thermohydraulic system. This numerical method has several interesting features for engineering applications, such as parallelization capabilities or direct temporal convergence. A 2D model of a single-phase natural circulation mini-loop with a small inner diameter was implemented and tested under different operation conditions following a double distribution function approach (coupling a lattice for the fluid and a secondary lattice for the thermal field). An analytical relationship between the Reynolds number and the modified Grashof number was used to validate the numerical model. Two regimes were found for the circulation, a laminar regime for low Reynolds numbers and a non-laminar regime characterized by a traveling vortex near the heater and cooler’s walls. Both regimes did not present flux inversion and are considered stable. The recirculation of the fluid can explain some of the heat transfer characteristics in each regime. Changing the Prandtl number to a higher value affects the transient response, increasing the temperature and velocity oscillations before reaching the steady state. Full article

This paper presents the aerodynamic modeling of a flying wing featuring Ludwig Prandtl’s bell spanload. The aerodynamic models are developed using a medium fidelity vortex-lattice method and using a Reynolds-Averaged Navier–Stokes computational fluid dynamics solution across a wide range of in-flow angle conditions. A methodology is developed to directly compare the spanwise force distributions from each method. Excellent agreement is seen in the prediction of spanwise inertial aerodynamic forces from each method, as well as in stability and control derivatives dominated by lift and moment contributions. The phenomenon of proverse yaw, caused by the twist distribution necessary to produce the bell spanload, is seen in the high and low-order analysis, with similar off-axis control power predicted. Full article

This study presents the design and computational fluid dynamics (CFD) analysis of a mini demonstrator for a dual fluid reactor (DFR). The DFR is a novel concept currently under investigation. The DFR is characterized by the implementation of two distinct liquid loops dedicated to fuel and coolant. It integrates the principles of molten salt reactors and liquid metal cooled reactors; thus, it operates in a high temperature and fast neutron spectrum, presenting a distinct approach in the field of advanced nuclear reactor design. The mini demonstrator serves as a scaled-down version of the actual reactor, primarily aimed at gaining insights into the CFD analysis intricacies of the reactor while minimizing computational costs. The CFD modeling of the MD intends to add valuable data for the purpose of modeling validation against experiments to be conducted on the MD. These experiments can be used for DFR licensing and design optimization. The coolant and fuel utilized in the mini demonstrator are of low Prandtl number (Pr = 0.01) liquid lead, operating at two distinct inlet temperatures, namely 873 K and 1473 K. The study showed a rapid increase in turbulence due to intense mixing and abrupt changes in flow areas and directions, despite the relatively low inlet velocities. Hot spots characterized by elevated temperatures were identified, analyzed, and justified based on their spatial distribution and flow conditions. Flow swirling within pipes was identified and a remedy approach was suggested. Inconsistent mass flow rates were observed among the fuel pipes, with higher rates observed in the lateral pipes. Although lower fuel temperatures were observed in the lateral pipes, they consistently exhibited higher heat exchange characteristics. The study concludes by giving physical insights into the heat transfer and flow behavior, and proposing design considerations for the dual fluid reactor to enhance structural safety and durability, based on the preliminary analysis conducted. Full article

Nanofluids are engineered colloidal suspensions of nanoparticles in the base fluids. At very low particle concentration, nanofluids have a much higher and strongly temperature-dependent thermal conductivity, which enables them to enhance the performance of machining applications such as the cooling and lubrication of the cutting zone during any machining process, the vehicle’s braking system, enhanced oil recovery (EOR), engine oil, and the drilling process of crude oil. In the current work, the density is assumed as an exponential function of temperature due to larger temperature differences. The main focus of this mechanism is the variable density effects on heat and mass characteristics of nanoparticles across the stretching porous sheet with thermophoresis and Brownian motion to reduce excessive heating in high-temperature systems. This is the first temperature-dependent density problem of nanofluid across the stretching surface. The coupled partial differential equations (PDEs) of the present nanofluid mechanism are changed into nonlinear coupled ordinary differential equations (ODEs) with defined stream functions and similarity variables for smooth algorithm and integration. The changed ODEs are again converted in a similar form for numerical outcomes by applying the Keller Box approach. The numerical outcomes are deduced in graphs and tabular form with the help of the MATLAB (R2013a created by MathWorks, Natick, MA, USA) program. In this phenomenon, the velocity, temperature, and concentration profile, along with their slopes, have been plotted for various parameters pertaining to the current issue. The range of parameters has been selected according to the Prandtl number $0.07\le Pr\le 70.0$ and buoyancy parameter $0<\lambda <\infty$, respectively. The novelty of the current work is its use of nanoparticle fraction along the porous stretching sheet with temperature-dependent density effects for the improvement of lubrication and cooling for any machining process and to reduce friction between tool and work piece in the cutting zone by using nanofluid. Moreover, nanoparticles can also be adsorbed on the oil/water surface, which alters the oil/water interfacial tension, resulting in the formation of emulsions. Full article

The interaction of a turbulent, spatially developing crossflow with a transverse jet possesses several engineering and technological applications such as film cooling of turbine blades, exhaust plumes, thrust vector control, fuel injection, etc. Direct Numerical Simulation (DNS) of a jet in a crossflow under different streamwise pressure gradients (zero and favorable pressure gradient) is carried out. The purpose is to study the physics behind the transport phenomena and coherent structure dynamics in turbulent crossflow jets at different streamwise pressure gradients and low/high-velocity ratios (0.5 and 1). The temperature was regarded as a passive scalar with a molecular Prandtl number of 0.71. The analysis is performed by prescribing accurate turbulent information (instantaneous velocity and temperature) at the inlet of a computational domain. The upward motion of low-momentum fluid created by the “legs” of the counter-rotating vortex pair (CVP) encounters the downward inviscid flow coming from outside of the turbulent boundary layer, inducing a stagnation point and a shear layer. This layer is characterized by high levels of turbulent mixing, turbulence production, turbulent kinetic energy (TKE) and thermal fluctuations. The formation and development of the above-mentioned shear layer are more evident at higher velocity ratios. Full article

The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach. Full article

This research numerically studies the transient cooling of partially liquid magma by natural convection in an enclosed magma chamber. The mathematical model is based on the conservation laws for momentum, energy and mass for a non-Newtonian and incompressible fluid that may be modeled by the power law and the Oberbeck–Boussinesq equations (for basaltic magma) and solved with the finite volume method (FVM). The results of the programmed algorithm are compared with those in the literature for a non-Newtonian fluid with high apparent viscosity (10–200 Pa s) and Prandtl (Pr = 4 × 10⁴) and Rayleigh (Ra = 1 × 10⁶) numbers yielding a low relative error of 0.11. The times for cooling the center of the chamber from 1498 to 1448 K are 40 ky (kilo years), 37 and 28 ky for rectangular, hybrid and quasi-elliptical shapes, respectively. Results show that for the cases studied, natural convection moved the magma but had no influence on the isotherms; therefore the main mechanism of cooling is conduction. When a basaltic magma intrudes a chamber with rhyolitic magma in our model, natural convection is not sufficient to effectively mix the two magmas to produce an intermediate SiO₂ composition. Full article