Search Results (145)

The Pennes bioheat equation is the most widely used model for describing heat transfer in living tissue during thermal exposure. It is derived from the classical Fourier law of heat conduction and assumes energy exchange between blood vessels and surrounding tissues. The literature presents various numerical methods for solving the bioheat equation, with exact solutions developed for different boundary conditions and geometries. However, analytical models based on this framework are rarely reported. This study aims to develop an analytical three-dimensional model using MATHEMATICA software, with subsequent mathematical validation performed through COMSOL simulations, to characterize heat transfer in biological tissues induced by laser irradiation under various therapeutic conditions. The objective is to refine the conventional bioheat equation by introducing three key improvements: (a) incorporating a non-Fourier framework for the Pennes equation, thereby accounting for the relaxation time in thermal response; (b) integrating Dirac functions and the telegraph equation into the bioheat model to simulate localized point heating of diseased tissue; and (c) deriving a closed-form analytical solution for the Pennes equation in both its classical (Fourier-based) and improved (non-Fourier-based) formulations. This paper investigates the nuanced relationship between the relaxation time parameter in the telegraph equation and the thermal relaxation time employed in the bioheat transfer equation. Considering all these aspects, the optimal thermal relaxation time determined for these simulations was 1.16 s, while the investigated thermal exposure time ranged from 0.01 s to 120 s. This study introduces a generalized version of the model, providing a more realistic representation of heat exchange between biological tissue and blood flow by accounting for non-uniform temperature distribution. It is important to note that a reasonable agreement was observed between the two modeling approaches: analytical (MATHEMATICA) and numerical (COMSOL) simulations. As a result, this research paves the way for advancements in laser-based medical treatments and thermal therapies, ultimately contributing to more optimized therapeutic outcomes. Full article

Based on admirable porous media performance and the popularity of additive manufacturing technology, gradient porous media are progressively being applied in increasing fields. In this study, convection heat transfer within a square vented cavity, partially occupied by two copper metal foam layers of $10$ and $20$ PPI saturated with nanofluid, was assessed numerically. The left wall was heated uniformly and non-uniformly by applying multi-frequency spatial heating following a sinusoidal function. Governing equations, including continuity, the Darcy–Brinkmann–Forchheimer model, and local thermal non-equilibrium energy equations, were adopted and solved by employing the finite volume method. The influences of relevant parameters, including nanoparticle concentrations $\left(0\%\le \phi \le 10\%\right)$, Reynolds number ($1\le Re\le 100$), inlet and outlet port aspect ratios $\left(0.1\le D/H\le 0.4\right)$, three outlet vent opening locations ($\left(S_o=0\right)$ left, ($S_o=\left(H/2-D/2\right)$) middle, and ($S_o=\left(H-D\right)$) right), sinusoidal offset temperature (${\theta }_o=0.5$, $1$), frequency ($f=1, 3, 5$), and amplitude ($A=0-1$), were examined. The results demonstrate that flow and heat transfer fields are impacted mainly by these parameters. Streamlines are more intensified at the upper-left corner when the outlet opening vent is shifted towards the right-corner upper wall. Fluid- and solid-phase Nusselt number increases $Re$, $D/H$, ${\theta }_o$, $A$, and $f$ are raised, specifically when $A\ge 0.3$. The Nusselt number remains constant when the frequency is raised from $3$ to $5$, definitely when $D/H\ge 0.25$. In uniform and non-uniform heating cases, the Nusselt number of both phases remains constant as the outlet port is shifted right for $Re\le 10$ and slightly for higher $Re$ as the outlet vent location is translated from left to right. Full article

Fluids that exhibit self-rewetting properties, such as aqueous long-chain alcohol solutions, display a unique quadratic relationship between surface tension and temperature and are marked by a positive gradient. This characteristic leads to distinctive patterns of thermocapillary convection and associated interfacial dynamics, setting self-rewetting fluids apart from normal fluids (NFs). The potential to improve heat transfer using self-rewetting fluids (SRFs) is garnering interest for use in various technologies, including low-gravity conditions and microfluidic systems. Our research aims to shed light on the contrasting behaviors of SRFs in comparison to NFs regarding interfacial transport phenomena. This study focuses on the thermocapillary convection in SRF layers with a deformable interface enclosed inside a closed container modeled as a square cavity, which is subject to nonuniform heating, represented using a Gaussian profile for the heat flux variation on one of its sides, in the absence of gravity. To achieve this, we have enhanced a central-moment-based lattice Boltzmann method (LBM) utilizing three distribution functions for tracking interfaces, computing two-fluid motions with temperature-dependent surface tension and energy transport, respectively. Through numerical simulations, the impacts of several characteristic parameters, including the viscosity and thermal conductivity ratios, as well as the surface tension–temperature sensitivity parameters, on the distribution and magnitude of the thermocapillary-driven motion are examined. In contrast to that in NFs, the counter-rotating pair of vortices generated in the SRF layers, due to the surface tension gradient at the interface, is found to be directed toward the SRF layers’ hotter zones. Significant interfacial deformations are observed, especially when there are contrasts in the viscosities of the SRF layers. The thermocapillary convection is found to be enhanced if the bottom SRF layer has a higher thermal conductivity or viscosity than that of the top layer or when distributed, rather than localized, heating is applied. Furthermore, the higher the magnitude of the effect of the dimensionless quadratic surface tension sensitivity coefficient on the temperature, or of the effect of the imposed heat flux, the greater the peak interfacial velocity current generated due to the Marangoni stresses. In addition, an examination of the Nusselt number profiles reveals significant redistribution of the heat transfer rates in the SRF layers due to concomitant nonlinear thermocapillary effects. Full article

This study investigates the structure of a metal hydride (MH) cartridge as a hydrogen storage tank for small-scale fuel cells (FCs). This cartridge is designed to be stacked and used in layers, allowing flexible capacity adjustment according to demand. MH enables compact and safe hydrogen storage for small-scale fuel cell (FC) applications due to its high energy density and low-pressure operation. However, because hydrogen desorption from MH is an endothermic reaction, an external heat supply is required for stable performance. To enhance both the heat transfer efficiency and cartridge usability, we propose a heat supply method that utilizes waste heat from an air-cooled proton-exchange membrane fuel cell (PEMFC). The proposed cartridge incorporates four cylindrical MH tanks that require uniform heat transfer. Therefore, we proposed the tank arrangements within the cartridge to minimize the non-uniformity of heat transfer distribution on the surface. The flow of exhaust air from the PEMFC into the cartridge was analyzed using computational fluid dynamics (CFD) simulations. In addition, an empirical correlation for the Nusselt number was developed to estimate the heat transfer coefficient. As a result, it was concluded that the heat utilization rate of the exhaust heat flowing into the cartridge was 13.2%. Full article

Accurately simulating the thermal behavior of wheel–brake shoe friction on long downhill ramps is challenging due to the complexity of modeling appropriate heat source models. This study investigates heat generation during the frictional braking process of freight train wheels and brake shoes under long-slope conditions. Four heat source models—constant, modified Gaussian, sinusoidal, and parabolic distributions—were developed based on energy conservation principles and validated through experimental data. A thermomechanical coupled finite element model was established, incorporating a moving heat source to analyze the effects of different models on wheel tread temperature distribution and its evolution over time. The results show that all four models effectively simulate frictional heat generation, with computed temperatures, deviating by only 6.0–8.2% from experimental measurements, confirming their accuracy and reliability. Among the models, the modified Gaussian distribution heat source, with its significantly higher peak local heat flux (2.82 times that of the constant model) and rapid attenuation, offers the most precise simulation of the non-uniform temperature distribution in the contact region. This leads to a 40% increase in the temperature gradient variation rate and effectively reproduces the “hot spot” effect. The new non-uniform heat source model accurately captures local temperature dynamics and predicts frictional heat transfer and thermal damage trends. The modified Gaussian distribution model outperforms others in simulating local temperature peaks, offering support for optimizing braking system models and improving thermal damage prediction. Future research will refine this model by incorporating factors like material wear, environmental conditions, and dynamic contact characteristics. Full article

Proton exchange membrane fuel cells (PEMFCs), recognized as promising sources of waste heat for space heating, domestic hot water supply, and industrial thermal applications, have garnered substantial interest owing to their environmentally benign operation and high energy conversion efficiency. Since the uniformity of oxygen diffusion toward catalytic layers critically governs electrochemical performance, this study establishes a three-dimensional, non-isothermal computational fluid dynamics (CFD) model to systematically optimize the cathode flow channel width distribution, targeting the maximization of power output through enhanced reactant homogeneity. Numerical results reveal that non-uniform flow channel geometries markedly improve oxygen distribution uniformity, reducing the flow inhomogeneity coefficient by 6.6% while elevating maximum power density and limiting current density by 9.1% and 7.8%, respectively, compared to conventional equal-width designs. There were improvements attributed to the establishment of longitudinal oxygen concentration gradients and we alleviated mass transfer limitations. Synergistic integration with gas diffusion layer (GDL) gradient porosity optimization further amplifies performance, yielding a 12.4% enhancement in maximum power density and a 10.4% increase in limiting current density. These findings validate the algorithm’s efficacy in resolving coupled transport constraints and underscore the necessity of multi-component optimization for advancing PEMFC design. Full article

The low thermal conductivity of phase change materials (PCMs) limits their widespread application in practical energy storage systems. The integration of fins has emerged as an effective approach to enhance PCM melting rates. This study numerically investigates the effects of fin length and tilt angle variations on PCM melting processes through two-dimensional modeling. A rectangular container with vertical constant-power heating was simulated, which incorporated natural convection effects. Initially, the analysis of equal-length fins with varying dimensions revealed that longer fins and appropriate tilt angles could significantly accelerate the PCM melting. Subsequent investigation under constant total fin lengths demonstrated that two factors enhanced the heat transfer and reduced the melting duration: large fin length differences and the enclosed regions between the fins and the container bottom. Studies of extreme tilt angles during angular variation indicated that the configuration with a 30 mm length difference with limit angles could positively affect the melting performance. The findings offer valuable insights for the optimal design of phase change energy storage systems. Full article

The porous solar receiver (PSR) is a promising technology in advanced high-temperature applications. However, the non-uniform distribution of concentrated solar flux (CSF) and the dense pore structure lead to localized overheating and significant thermal losses for the PSR. This review focuses on the optimization strategies to enhance the thermal performance of the PSR, including porosity parameters, spectral selectivity, geometric configurations, and optical windows. Furthermore, mitigation strategies for addressing localized high temperatures in the PSR were thoroughly discussed, including methods for homogenizing CSF and improving the velocity of heat transfer fluid (HTF). Additionally, a numerical simulation and experimental measurements were introduced and evaluated. Additionally, the paper emphasizes the need to optimize the macroscopic geometry of OPSRs to improve their flow and heat transfer performance, thereby enhancing their practical value. It also suggests designing PPSRs that integrate adjustments for HTF mass velocity, CSF, optical window load, and reflection losses. Consequently, future studies should focus on developing efficient simulation and validation methods to advance the practical application of PSRs. Full article

Models were developed to study the heat-mass transfer and stress–strain process in carrots during hot air drying. The distribution and variation in temperature, moisture content, strain, and stress of the samples were investigated at different drying temperatures. The results showed that the models developed could be used to simulate the hot air drying process of carrots; the maximum weighted absolute percentage errors were 9.01%. The difference between the heat flux and vapor diffusion flux in the regions led to a non-uniform temperature and moisture content distribution, which resulted in non-uniform strain, causing stress within the carrots. The value of the thermal strain and stress was small compared to that of the moisture strain and stress. The thermal stress and moisture stress increased first and then decreased; the peak values of thermal stress and moisture stress occurred in the middle period of the whole drying process. When the hot air drying temperature was higher, the peak value of stress was higher. These results are helpful for understanding the drying mechanism and optimizing operating conditions in carrot drying. Full article

This study investigates the influence of electrolytic cell parameters on the electrolyte boiling rate during electrolytic plasma processing, a critical stage for plasma formation and subsequent surface modification. Focusing on a coaxial cell configuration with a conical anode and cylindrical cathode, this research employs analytical calculations based on the solution of the Laplace equation in spherical coordinates, validated by numerical simulations using the finite element method (Elcut 6.6), to predict electrolyte boiling times. These results are compared with experimental data, demonstrating good agreement, particularly at higher voltages (−200 V). The analysis reveals that while a simplified model provides a reasonable first approximation, it deviates at lower voltages (−50 V) due to the increasing importance of heat removal, neglected in the model construction. This discrepancy underscores the need for more sophisticated models accounting for non-uniform current distribution and heat transfer effects in complex cell geometries. The findings contribute to a deeper understanding of cathodic electrolytic plasma processing (EPP) dynamics and provide a foundation for optimizing cell design and process parameters for industrial applications such as diffusion saturation of steel components. Full article

This study presents an advanced mathematical model for the high-energy shaker mill process, incorporating thermal interactions among the milling ball, shaker mill vial, and the air contained within. Unlike previous models focusing solely on the ball’s temperature, this research emphasizes the heat produced by impacts and the thermal exchange among all three components. Incorporating these thermal interactions allows the model to provide a more comprehensive depiction of the energy dynamics within the system, leading to more precise predictions of temperature changes. Utilizing a lumped parameter method, the study simplifies complex airflow dynamics and non-uniform temperature distributions in the milling system, enabling efficient numerical analysis. Hamilton’s equations are extended to include supplementary state variables that account for the internal energies of both the vial and the air, in addition to the thermomechanical state variables of the ball. High-energy milling techniques are essential in mechanochemical synthesis and various industrial applications, where the optimization of heat transfer and energy efficiency is crucial. Numerical simulations computed using the Bogacki–Shampine integration algorithm significantly align with experimental data, confirming the model’s accuracy. This comprehensive framework enhances understanding of heat transfer in one-dimensional ball motion, optimizing milling parameters for better performance. The mathematical model facilitates the computation of heat production due to collisions, based on operational parameters like shaking frequency and amplitude, thereby allowing for the anticipation of chemical reaction activation potential in mechanochemistry. Full article

The purpose of this study is to analyze the large deflection problem of bimodular functionally graded truncated thin conical shells under the transverse mechanical load and non-uniform thermal load, in which two different boundary constraints of the truncated shell with two ends simply supported and fully fixed are considered. It is assumed that the temperature distribution along the thickness direction satisfies the Fourier law of heat transfer, and the material properties change exponentially along the thickness direction while different properties in tension and compression are considered. The geometric equation of the conical shell is established based on the equivalent method of curvature correction of von-Kármán deformation theory, and the analytical solution of the problem is obtained by Ritz method. Numerical simulation of bimodular functionally graded conical shells under the thermal and mechanical loads is carried out by Abaqus, and the numerical solution agrees with the theoretical solution. The results show that the introduction of bimodular functionally graded material will affect the maximum displacement and this effect has different rules under the mechanical load and thermal load. In addition, factors such as the cone apex angle and the truncated distance have a great influence on the maximum displacement and its location of the conical shell. Full article

To enhance the performance of combustors in micro thermophotovoltaic systems, this study employs numerical simulations to investigate a planar microscale combustor featuring a counter-flow flame configuration. The analysis begins with an evaluation of the effects of (1) equivalence ratio Φ and (2) inlet flow rate V_i on key thermal and combustion parameters, including the average temperature of the combustor main wall (${\overline{T}}_w$), wall temperature non-uniformity (${\overline{R}}_{Tw}$) and radiation efficiency (${\eta }_r$). The findings indicate that increasing Φ causes these parameters to initially increase and subsequently decrease. Similarly, increasing the inlet flow rate leads to a monotonic decline in ${\eta }_r$, while the ${\overline{T}}_w$ and ${\overline{R}}_{Tw}$ exhibit a rise-then-fall trend. A comparative study between the proposed combustor and a conventional planar combustor reveals that, under identical inlet flow rate and equivalence ratio conditions, the use of the counterflow flame configuration can increase the ${\overline{T}}_w$ while reducing the ${\overline{R}}_{Tw}$. The Nusselt number analysis shows that the counter-flow flame configuration micro-combustor achieves a larger area with positive Nusselt numbers and higher average Nusselt numbers, which highlights improved heat transfer from the fluid to the solid. Furthermore, the comparison of blow-off limits shows that the combustor with counter-flow flame configuration exhibits superior flame stability and a broader flammability range. Overall, this study provides a preliminary investigation into the use of counter-flow flame configurations in microscale combustors. Full article

This study presents analytical solutions grounded in three-dimensional (3D) thermo-elasticity theory to predict the bending behavior of cross-laminated timber (CLT) panels under thermo-mechanical conditions, incorporating the orthotropic and temperature-dependent properties of wood. The model initially utilizes Fourier series expansion based on heat transfer theory to address non-uniform temperature distributions. By restructuring the governing equations into eigenvalue equations, the general solutions for stresses and displacements in the CLT panel are derived, with coefficients determined through the transfer matrix method. A comparative analysis shows that the proposed solution aligns well with finite element results while offering superior computational efficiency. The solution based on the plane section assumption closely matches the proposed solution for thinner panels; however, discrepancies increase as panel thickness rises. Finally, this study explores the thermo-mechanical bending behavior of the CLT panel and proposes a modified superposition principle. The parameter study indicates that the normal stress is mainly affected by modulus and thermal expansion coefficients, while the deflection of the panel is largely dependent on thermal expansion coefficients but less affected by modulus. Full article

The migration of acid gases through the pressure sheath of flexible pipes may induce a corrosive environment that can lead to steel armors’ failure by SCC (stress corrosion cracking). This permeation process depends on temperature, partial pressures, materials, and the pipe’s geometry. However, there are few works related to permeation modeling in flexible pipes, and these works usually contain significant simplification in pipes’ geometry. Hence, this work proposes two finite element (FE) permeation models and discusses the effects of the pipe’s characteristics. The models were developed in Ansys^®, considering two- (2DFE) and three-dimensional (3DFE) approaches, and rely on gas fugacities instead of concentrations to describe the mass transport phenomenon. A radial temperature gradient is also considered, and the heat transfer is uncoupled from the mass transfer. Dry and flooded annulus analyses were conducted with the proposed models. In dry conditions, the results obtained with the 2DFE and the 3DFE approaches showed no significant differences, demonstrating that 3D effects are irrelevant. Hence, the permeation phenomenon is ruled by the permeation properties of the polymeric layers (pressure and outer sheaths) and possible shield effects promoted by the metallic armors. In contrast, the flooded annulus analyses resulted in a non-uniform fugacity distribution in the annulus with significant differences between the 2DFE and the 3DFE approaches, showing the importance of modeling the helical geometries of the metallic armors in this condition. Finally, a conservative 2DFE approach, which neglects the contribution of the pressure sheath, is proposed to analyze the flooded annulus condition, aiming to overcome the high computational cost demanded by the 3DFE approach. Full article