Thermal Conductivity Ratio Research Articles

Inverse Estimation of Thermal Contact Resistance Between Two Layers of Cylindrical Wall

This study presents a method for estimating the space-dependent thermal contact resistance between the two-layer walls of a furnace using the boundary element method (BEM) and conjugate gradient method (CGM) for the heat conduction problem. The global solution equation in matrix form is derived using the interface conditions, and the BEM is used to solve the direct problem. The CGM minimizes the objective function and calculates the sensitivity coefficients with the complex variable derivation method (CVDM). Comparative results show that the present approach is more accurate, stable, and efficient than the conventional CGM, which is attributed to the calculation of the sensitivity coefficients by CVDM. The effects of the value of thermal contact resistance, thermal conductivity ratio, Biot number, initial guess, measurement error, and the number and position of measurement points on the inversion results are also analyzed. Finally, the effectiveness of this approach is demonstrated through numerical examples, and the inversion results show its stability, efficiency, and accuracy in identifying different and complex distributions of thermal contact resistance. Furthermore, this approach is feasible for nonintrusive measurement, which is very meaningful in practical applications.

Investigating double-diffusive natural convection in a sloped dual-layered homogenous porous-fluid square cavity

This article investigates natural convection with double-diffusive properties numerically in a vertical bi-layered square enclosure. The cavity has two parts: one part is an isotropic and homogeneous porous along the wall, and an adjacent part is an aqueous fluid. Adiabatic, impermeable horizontal walls and constant and uniform temperatures and concentrations on other walls are maintained. To solve the governing equations, the finite element method (FEM) employed and predicted results shows the impact of typical elements of convection on double diffusion, namely the porosity thickness, cavity rotation angle, and thermal conductivity ratio. Different Darcy and Rayleigh numbers effects on heat transfer conditions were investigated, and the Nusselt number in the border of two layers was obtained. The expected results, presented as temperature field (isothermal lines) and velocity behavior in X and Y directions, show the different effects of the aforementioned parameters on double diffusion convective heat transfer. Also results show that with the increase in the thickness of the porous layer, the Nusselt number decreases, but at a thickness higher than 0.8, we will see an increase in the Nusselt number. Increasing the thermal conductivity ratio in values less than one leads to a decrease in the average Nusselt number, and by increasing that parameter from 1 to 10, the Nusselt values increase. A higher rotational angle of the cavity reduces the thermosolutal convective heat transfer, and increasing the Rayleigh and Darcy numbers, increases Nusselt. These results confirm that the findings obtained from the Finite Element Method (FEM), which is the main idea of this research, are in good agreement with previous studies that have been done with other numerical methods.

Pulsatile MHD Flow of Two Immiscible Nanofluid through a Porous Channel with Slip Effects

The present study is carried out to investigate the effects of shape factor nanoparticles on the oscillatory MHD flow of a nanofluid in two immiscible liquids in a horizontal porous channel with velocity and thermal slip on the walls. Thermal radiation, Joule heating, viscous and Darcy dissipations have been accounted for in the model. We have considered and as nanoparticles, in the lower region (Region-I) and upper region (Region-II) respectively, with water as a base fluid. The effective ratio of thermal conductivity of the nanofluid is evaluated using the Maxwell-Garnetts model. Graphical behavior of velocity, temperature, and rate of heat transfer distributions have been depicted for the cases of slip and no-slip effects. This study has been made to understand the impact of different nanoparticle shape factors on temperature and heat transfer rate. For various parameters, values of shear stress distribution at the walls and the mass flux are shown in tabular form. Our study asserts that with the increase of the strength of the magnetic field, the velocity of the liquid falls and enhances the temperature of the liquid. The influence of different combinations of nanoparticles, on the flow variables, have also been discussed. In order to validate the analytical results, the numerical evaluation of the closed-form results, for the velocity distribution, has been compared with those of the numerical method, by using the NDSolve command in MATHEMATICA, and a good agreement is observed.

Effects of varying heat transfer rates for borehole heat exchangers in layered subsurface with groundwater flow

The existence of groundwater flow adds a convective heat component to shallow geothermal heat pump systems, significantly improving heat transfer efficiency. Numerous analytical and numerical methods have been proposed to assess the impact of groundwater flow on ground heat exchangers. However, numerical simulations often require significant resources and time, while conventional analytical solutions overlook the time and depth-varying heat transfer rates, leading to inaccurate temperature predictions. This study proposes a computationally efficient semi-analytical solution by extending the line source solution and coupling it with a thermal resistance model. This approach addresses variations in heat transfer rate over time and depth, overcoming the limitations of conventional analytical solutions. Compared with a three-dimensional numerical model constructed in COMSOL Multiphysics, the average absolute percentage error (MAPE) of borehole wall temperatures for a U-shaped borehole heat exchanger (BHE) is approximately 1 %, across a wide range of water flow velocities and thermal conductivity ratios between two contacting geological layers. A significant advantage of the proposed solution is its computational efficiency. The proposed solution can complete long-term simulations with over 9,000 time steps in about 10 min, as opposed to numerical models that typically require several hours. The excellent computational efficiency and substantial accuracy make the proposed solution a simple and effective tool for the design and optimization of BHEs in engineering applications.

Pool boiling heat transfer of ammonia outside enhanced tubes with various fin structures

Pool boiling heat transfer of ammonia on a smooth tube and three enhanced tubes was investigated at the saturation pressure ranging from 6.15 to 11.7 bar, which corresponds to the saturation temperature from 10 to 30 °C. The test tube with a length of 796 mm was immersed in the liquid pool of ammonia inside a cylindrical chamber having an internal diameter of 254.4 mm, and convection or pool boiling heat transfer outside the test tube was generated by flowing hot water through the tube. Three enhanced tubes of a low-finned tube (Low-fin), a low-finned tube with oblique cuttings (Turbo-C), and a finned tube having re-entrant cavities (Turbo-E) were prepared to examine the pool boiling enhancement on various finned tubes. Boiling hysteresis on the smooth tube was observed between when the heat flux increases and when the heat flux decreases, which resulted in the deviation of the heat transfer coefficients from the previous correlations when the heat flux decreases. A suitable correlation was suggested to compensate for the deviation of the heat transfer coefficients in case of decreasing the heat flux by modifying the Stephan-Abdelsalam correlation. Three enhanced tubes exhibited considerable enhancement in the heat transfer coefficients compared with the smooth tube, and boiling performance on the Turbo-E tube having re-entrant cavities was highly affected by the variation of the bubble diameter according to the saturation pressure. Enhancement factors of the enhanced tubes were obtained from the ratio of thermal conductance on the enhanced tube to that on the smooth tube.

Boosting diesel generators power with thermoelectric generators and integrated oil tank – Thermal modeling and parametric study

In this paper, a unique method for using thermoelectric generators (TEGs) to generate electricity is introduced, a technique that makes use of a cold oil tank and hot exhaust gases from generators. A set of TEGs and an integrated cold oil tank are connected to the diesel generator as part of the suggested design. A pertinent thermal modeling was designed and a thorough parametric study was carried out to show the validity of this innovative concept. The parametric study has demonstrated that when the generator power and the thickness to thermal conductivity ratio of each TEG in the system are increased, the temperature differential in each TEG module and the power produced by the assembly of TEGs both exhibit linear increases. The length of the TEG plate and the height of the exhaust gas duct cause an exponential increase in the temperature differential across each TEG module. The TEG assembly's power output increases linearly with TEG surface length and decreases exponentially with exhaust gas duct height. Using an exhaust gas duct height of 0.05 m, and a TEGs plate length of 1 m, the parametric study showed that power generation of up to 2778 W is feasible under the predetermined circumstances of a diesel generator with an output of 125 kW. When compared to a conventional setup, the new hybrid generator in this scenario may be able to increase power generation by up to 2.22 %.

EFFECT OF INNER BOUNDARIES GEOMETRY ON NATURALCONVECTION HEAT TRANSFER IN HORIZONTAL ANNULI

An analytical modeling of natural convection in physically-based analysis is developed for investigate free convective heat transfer in horizontal eccentric annulus between a circular outer cylinder and heated different shape inner envelope with used four models of the shapes of the inner cross section of (circular, triangular, square and hexagon inner boundary). The main objective of this paper was taking a composite model based on asymptotic solutions for three limiting cases: pure conduction, laminar boundary layer convection and transition flow convection. Laminar conditions up to Rayleigh number RaPi of 5×104 were investigated. By using data from MATLAB simulations for a wide range of two cylinder temperature difference in order to study the effects of annulus diameter ratio, Rayleigh number, and the cross section geometries of inner cylinder on the Nusslte number and the ratio of thermal conductivity. The numerical result illustrated for the circular the increasing the Rayleigh number leading to slightly increasing the non-dimensional Nusslte number with various value of annulus diameter ratio and when used the high annulus perimeter ratio (Po/Pi( about (4.5,2.6,1.6 and 1.175). There is rapid increasing in the non-dimensional ratio of thermal conductivity with increasing the Rayleigh number at the high values of (Po/Pi(, and the result showed that the non-dimensional ratio of thermal conductivity and the Nusslte number values of the (triangular, square and hexagon) less than in the case of circular inner boundary, but the hexagon model showed the Nusslte number more that than in the (triangular and square). the mathematical results compared with model developed by pervious numerical the model and data are in good agreement, with an average RMS difference of 10.6% for the circular annulus of dimensional Nusselt number (NuPi) and less than 4.9 % and 9.8% for the square inner geometry non-dimensional ratio thermal conductivity.

Transport Coefficients for the Simple Reacting Spheres Kinetic Model II: Thermal Conductivity, Diffusion, Thermal-Diffusion Ratio

We investigate the transport coefficients for a dilute reactive mixture of four constituents undergoing a chemical reaction of type A+B⇌C+D\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A+B \\rightleftharpoons C+ D$$\\end{document}, which is described by the Simple Reacting Spheres (SRS) kinetic model. The dynamics of the SRS model is very interesting and relatively simple. Both reactive and inert collisions obey to the hard spheres potential and the collisional operator incorporates a “correction” term that singles out those pre-collisional pairs of particles having enough energy to react chemically. Starting from this setting, we consider the mixture in a chemical regime for which both elastic and reactive collisions occur with comparable characteristic times and use the Chapman–Enskog method to determine the first-order approximation of the non-equilibrium solution to the SRS system. In a preceding paper (part I), the focus was on the coefficients associated to reaction rate and shear viscosity and in the present work we are interested on the coefficients associated to thermal conductivity, diffusion, and thermal-diffusion ratio. These coefficients are analysed numerically for both exothermic and endothermic reactions. The analysis allows to investigate the influence of the chemical reaction and the impact of the “correction” term proper of the SRS model on the transport coefficients.

Optimization of thermophysical properties of nanofluids using a hybrid procedure based on machine learning, multi-objective optimization, and multi-criteria decision-making

The rheological and thermal behavior of nanofluids in real-world scenarios is significantly affected by their thermophysical properties (TPPs). Therefore, optimizing TPPs can remarkably improve the performance of nanofluids. In this regard, in the present study, a hybrid strategy is proposed that combines machine learning (ML), multi-objective optimization (MOO), and multi-criteria decision-making (MCDM) to select optimal parameters for water-based multi-walled carbon nanotubes (MWCNTs)-oxide hybrid nanofluids. In the first step, four critical TPPs, including density ratio (DR), viscosity ratio (VR), specific heat capacity ratio (SHCR), and thermal conductivity ratio (TCR), are modeled using two efficient ML techniques, the group method of data handling neural network (GMDH-NN) and combinatorial (COMBI) algorithm. In the next step, the superior models are subjected to a four-objective optimization by the well-known non-dominated sorting genetic algorithm II (NSGA-II), which aims to minimize DR/VR and maximize SHCR/TCR. This study considers volume fraction (VF), oxide nanoparticle (NP) type, and system temperature as optimization variables. In the final step, two prominent MCDM techniques, TOPSIS and VIKOR, were used to identify the desirable optimal points from the Pareto fronts generated by the MOO algorithm. ML results reveal the COMBI algorithm's superior reliability in accurately modeling various TPPs. The pattern of Pareto fronts for all oxide-NPs indicated that over one-third of the optimal points have a VF > 1.5 %. On the other hand, the distribution of optimal points across different temperature ranges varied significantly depending on the type of oxide-NPs. For Al2O3-based nanofluid, around 90 % of the optimal points were within 40–50 °C. Conversely, for nanofluids containing CeO2 NPs, only approximately 24 % of the optimal points were found within the same temperature range. Considering diverse scenarios for weighting TPPs in the MCDM process implied that combining CeO2/ZnO oxide-NPs with MWCNTs in water-based nanofluids is highly effective across various real-world applications.

Box–Behnken experimental design for optimization of chitosan foam materials reinforced with cellulose and zeolite

AbstractFoam materials produced from biopolymers stand out as a more environmentally friendly insulation material solution. This study presents a comprehensive investigation into the development and optimization of chitosan‐based foam materials using a Box–Behnken design. The foams were engineered using varying proportions of chitosan (0.5–3%), cellulose (0.5–3%), and zeolite (0.5–3%), targeting their application as thermal insulators. The physical and thermal properties of the foams that were produced were affected by the type and ratios of components, with density and thermal conductivity ranging from 0.0853 to 0.1915 g cm−3 and 0.0324 to 0.0921 W mK−1, respectively. Higher chitosan content improved insulation properties and mechanical strength whereas zeolite increments increased density and thermal conductivity. Using statistical analysis through the Box–Behnken design, we optimized the foam formulations, achieving minimum thermal conductivity and maximum compression strength at an averaged density, suggesting a strong potential for environmental sustainability applications. The recommended optimal chitosan:cellulose:zeolite composition ratio of 3:3:0.88 provides a valuable insight for tailored foam material formulation. This study shows the relationships between the composition of a composite material and its resultant properties, optimizing its preparation for industrial applicability in an environmentally conscious way within the context of insulation and construction. This investigation contributes to the field of material science by highlighting the versatility and potential of biopolymers but also aligns with the increasing need for green building materials.

Experimental Investigation of the Anisotropic Thermal Conductivity of C/SiC Composite Thin Slab

Fiber-reinforced composites possess anisotropic mechanical and heat transfer properties due to their anisotropic fibers and structure distribution. In C/SiC composites, the out-of-plane thermal conductivity has mainly been studied, whereas the in-plane thermal conductivity has received less attention due to their limited thickness. In this study, the slab module of a transient plane source method is adopted to measure the in-plane thermal conductivity of a 2D plain woven C/SiC composite slab, and the test uncertainty is analyzed numerically. The numerical investigation proves that the slab module is reliable for measuring the isotropic and anisotropic slabs with in-plane thermal conductivity greater than 10 W⋅m−1⋅K−1. The anisotropic thermal conductivity of the 2D plain woven C/SiC composite slab is obtained within the temperature range of 20–900 °C by combining with a laser flash analysis method to measure the out-of-plane thermal conductivity. The results demonstrate that the out-of-plane thermal conductivity of C/SiC composite decreases with temperature, while its in-plane thermal conductivity first increases with temperature and then decreases, and the ratio of in-plane thermal conductivity to out-of-plane thermal conductivity is within 2.2–3.1.

A novel numerical method to evaluate the heat transfer characteristics of complicated CICC structures

In this article, we propose a numerical model for calculating the external heat transfer coefficient between the bundle region and its wall for cables in conduit conductor (CICC). With the assumption of local thermal equilibrium, one macro equation describing the steady heat transfer on the cross section of the CICC can be obtained. A key parameter, the effective transverse thermal conductivity keff, which takes the contribution of both strands and flowing fluid into consideration, is introduced. To calculate the effective transverse thermal conductivity keff, we first obtain the true distribution of different phases (fluid, copper and superconducting material) on a cross section of CICC with the help of the image recognition technique. Based on this, the value of the effective transverse thermal conductivity keff can be calculated numerically. Due to the large difference among the component thermal conductivities (at 4.5 K, typical values of the thermal conductivity of liquid helium, superconducting material and copper are kHe=0.024Wm−1K−1, kNb3Sn=0.04Wm−1K−1 and kCu=708Wm−1K−1; and the maximal ratio of thermal conductivity can be as high as about 30,000), the high-performance finite analytical method (FAM) is recommended to calculate keff. After obtaining the effective transverse thermal conductivity keff of the bundle region, the heat transfer coefficient can be calculated directly by solving a simple Poisson equation under proper boundary conditions. Two case studies are performed, including the JT-60 Super Advanced (JT-60SA) CICC and the dual channel International Thermonuclear Experimental Reactor, Toroidal Field Performance Sample (ITER-TFPS). The calculated values of heat transfer coefficient are consistent with the experimental results, which verifies our proposed model.

Impact of magnetized nanoparticle aggregation over a Riga plate with thermal radiation in water‐Al2O3 based nanofluid flow

AbstractThe nanoparticle (NP) volume fraction is a critical variable in fluid models, including the Brinkman, Einstein, and Maxwell designs. The temperature does not affect the nanofluid's normalized shear viscosity. The aggregation model elucidates such traits. Furthermore, the experimental results show a larger increase in the thermal conductivity of nano liquids than the values obtained using standard fluid models. The impact of nanoparticle aggregation (NPAgs) is ignored, which contributes to the disparity. Therefore, it is essential to study the thermal conductivity ratio while considering the kinematics of NPAgs. Therefore, the radiation impact is investigated here by examining NPAgs on the Riga surface in the context of a porous media. The circulation and temperature governing equations are transformed using suitable similarity variables into ordinary differential equations (ODEs). The Runge‐Kutta‐Fehlberg 4‐5 order (RKF‐45) and shooting method is used to simplify the resulting equations numerically. The graphic representation illustrates the influence of many non‐dimensional factors on significant physical quantities. The velocity of the nanofluid has a positive correlation with the modified Hartmann number, whereas it demonstrates a negative correlation with the porosity parameter. A better thermal distribution occurs with higher levels of radiation constraint. The inclusion of a higher solid volume percentage results in a decrease in the velocity profile while concurrently improving the thermal distribution. It is worth noting that NPs that exhibit aggregation have a more prominent thermal distribution than those that do not aggregate, results in greater rate of thermal distribution in the former scenario. The present investigation outcomes will useful in advanced cooling systems, improving energy efficiency, material, environmental and biomedical engineering.

Conjugate free convection in a non-uniform heating walled enclosure filled by ternary hybrid nanofluid under magnetic field

A study was conducted using numerical simulations to analyse the behaviour of heat transfer in a square enclosure filled with a ternary hybrid nanofluid in the occurrence of a magnetic field. The flow in the enclosure is characterised by steady and laminar conjugate-free convection. The enclosure has a vertical border with a finite thickness, while the other three borders are assumed to be very thin. The investigation aims to analyse the impact of several key factors on the average Nusselt number using the finite element method. These parameters include the volume fraction of ternary hybrid type nanoparticles (ranging from 0 to 0.03), Rayleigh number (varying from 103 to 106), solid wall thickness (changing from 0.1 to 0.3), Hartmann number (varying from 0 to 100), and the ratio of thermal conductivities (ranging from 0.1 to 10). A notable enhancement in heat transfer is found by employing a ternary hybrid nanofluid. This enhancement becomes more significant for small Rayleigh numbers, where heat conduction governs the primary means of heat transfer. Also, at low levels of Ra, the development of energy transfer strength becomes insignificant in the existence of a magnetic field. This magnetic field effect is primarily controlled by high values of Ra, which consequently leads to an enhancement in the strength of energy transmission.

Thermal Conductivity Switching in Pd-Catalyzed Gd and GdH2 Films Upon Gasochromic Hydrogenation and Dehydrogenation

Thermal conductivity switching in Pd-catalyzed Gd hydride films was investigated using in situ analyses of electrical, optical, structural, and thermophysical properties upon gasochromic hydrogenation/dehydrogenation at room temperature. These reactions allow the films to reversibly switch between the metallic (GdH2) phase in the hydrogenated state and the semiconductor (GdH3) phase in the dehydrogenated state. We fabricated three-layered films comprising Pd (5 nm)/Gd or GdH2 (300 nm)/Mo (100 nm) using DC magnetron sputtering using Pd, Gd, and Mo targets, respectively, on unheated synthetic quartz substrates. Ar or mixture of Ar + H2 (H2: 5 % to 50 %) gases were used for the deposition of the Gd or GdH2 films, respectively. The thermal conductivities of the Gd or GdH2 films were analyzed using in situ rear-heating/rear-detection type time-domain picosecond pulsed light heating thermoreflectance measurements by employing a gas mixture of N2/Ar and H2 (H2: 3 %) at 1 atm, which is below the explosive limit for hydrogen. The thermal conductivities of Gd and GdH2 films were measured for one and two hydro-/dehydrogenation cycles, respectively. The thermal switching ratios of the ON state thermal conductivity to the OFF state thermal conductivity were 6.4 and 2.9–5.4 for the Gd film and the GdH2 (H2: 5 %–50 %) films, respectively. The thermal conductivity of the Gd hydrides films changed along with those estimated from the Wiedemann–Franz Law and electrical conductivities.

Numerical simulation prediction of critical heat flux for 5 × 5 rod bundle with multiple grid spacers and different cladding materials

The critical heat flux (CHF) is one of the safety standards for core thermal design and is crucial for the normal operation of the reactor. The CHF problem of rod bundles with grid spacers is a hot topic in related research. The successful design of grid spacers can improve channel CHF by affecting the flow of downstream coolant, and this detection analysis can be achieved through numerical simulation methods. In addition, most simulation studies have not considered the solid region of the cladding, so there is little research on the effect of cladding materials on CHF. The role of grid spacers in rod bundle CHF is the focus of this paper, and the influence of cladding materials is another discussion direction. In this paper, following meticulous mesh generation and computational model validation, a study on the CHF of the 5 × 5 rod bundle with multiple grid spacers and different cladding materials is carried out by using CFD software. The verification results indicated that the physical model established in this study can reasonably predict the generation location and critical power value in the 5 × 5 rod bundle with grid spacers. Furthermore, the study identified that the grid spacer exerts a significant influence on coolant flow within the channel, while the weakening of the mixing effect of the grid spacer on the coolant flow is the main factor to lead the boiling crisis upstream of the grid spacer. By comparing the effects of thermal properties of different materials on CHF, it was found that when the thermal conductivity ratio of the two materials is 1.08, CHF is almost identical under the condition of a reference heat flux of 0.1 MW/m2 as a step size. In addition to thermal properties, further attention may be paid to the influence of surface characteristics of materials on CHF in future work.

Magnetohydrodynamic flow of two immiscible hybrid nanofluids between two rotating disks

The two-layer model of the magnetohydrodynamic flow of hybrid nanofluid (HNF) between two disks of the same radii is analyzed in this study. The base fluids of both the hybrid nanofluids are immiscible so that these two fluids form an interfacial layer making the study more unique and innovative. The heat source/sink with viscous dissipation effect on energy equation is discussed. The governing equation is in the form of PDEs that are later reduced to ODEs with the help of the Von Karman transformation. The resulting ODEs are solved using the RK method and the results are interpreted graphically. In addition to temperature and concentration gradient, the radial, tangential and axial velocities for different parameters are studied. The results indicate that the physical ratios such as viscosity and thermal conductivity ratios can improve the fluid motion and temperature even in the presence of magnetic field. Also, the ratio of stretching rate produced by the rotation of disk can effectively control the fluid motion. The two fluid flow between two rotating disk forms an interfacial layer between the fluids results in the increment of heat transfer rate which finds application in the field such as heat ex-changer equipment, Cryogenic systems, electronic appliances, and solar collectors.

An Analytical Study of the Impact of an Inclined Magnetic Field on Couette Flow with Jeffrey Fluid under Local Thermal Non-Equilibrium (LTNE) and Viscous Dissipation

In this work, we examine the effects of viscous dissipation and local thermal non-equilibrium (LTNE) on Couette flow in a duct filled with a porous media under the influence of an angled magnetic field. The bottom plate of the duct is in motion and subjected to a constant heat flux, while the top plate remains stationary and adiabatic. The Jeffrey fluid flow model is consistent with the unidirectional flow in the porous zone. The studies provide more precise measurements of the effects of the Jeffrey parameter (λ), inclined angle (ϕ), Hartmann number (MW), thermal conductivity ratio (ν), Brinkman number (BrW), and Biot number (BiW) on improving heat transmission. The governing equations are solved analytically. The present investigation gives dimensionless temperatures for fluid-solid phases and fully developed Nusselt number (FDNN) profiles. Variation of Jeffrey parameter, inclined angle, Brinkman number, and Hartman number in the temperature field in both phases and FDNN. Furthermore, the temperature in the solid phase is higher than the temperature in the fluid phase for the Jeffrey parameter and Hartman number in the Couette flow, which supports LTNE validation.

Enhancing Heat Transfer: Unraveling the Dynamics of Mixed Convection in a Vertical Porous Cavity

Mixed convection inside a vertical square porous cavity is investigated numerically, with special attention given to left-side heating. In the study, the importance of the problem, methods used, main results, conclusions, and novelty of the work are discussed. The Brinkmann-Forchheimer-Darcy coupled momentum equations and the Local Thermal Equilibrium energy (LTE) equation are solved using the finite volume technique. Several elemental parameters are investigated, including Reynolds number (50 × Re × 300), Darcy number (0.01 × Da × 100), Richardson number (0 × Ri × 30), and porosity (0.5 × ε ≥ 0.95). The thermal conductivity ratio of solid to liquid was (1<Kr<105), and the inlet port width between (0.05<d/H<0.3). Results show that Nusselt number increases with Reynolds number, Richardson number, and pore thermal conductivity. With increasing porosity, an inverse relationship was observed. Nusselt number was maximized by finding the optimal inlet aperture size (d/H = 0.25). It provides valuable insights into how different parameters affect mixed convection in vertical square porous cavities. Heat transfer processes in porous media are improved by these results. This work goes beyond previous efforts in the literature in exploring a wide parameter space and determining the optimal inlet aperture size.

Analytical and numerical investigation of heat transfer of porous fin in a local thermal non-equilibrium state

This research employs a local thermal non-equilibrium (LTNE) model to analyze the heat transfer phenomenon through a porous fin, considering natural convection and radiation effects. The infiltration velocity within the porous medium is evaluated using the Darcy model, and buoyancy effects are accounted for using the Boussinesq approximation. The Akbari-Ganji method (AGM) is applied to address the governing energy equations. The accuracy of the proposed solution is verified by comparing it with numerical results obtained from the finite difference method (FDM), the finite element method (FEM), and earlier investigations. The results are presented regarding the total average Nusselt number and temperature profiles. These results shed light on the influence of several important parameters, such as the thermal conductivity ratio, dimensionless thickness, convectional heat transfer, and external and internal radiation. The analysis reveals that decreasing Rayleigh and Biot numbers reduces the temperature profiles of the solid phase. Additionally, when the Rayleigh number is low but the assigned Biot number is high, the temperature difference between the solid and fluid phases diminishes. Furthermore, increased thermal conductivity ratio and dimensionless thickness for assigned Biot and Rayleigh numbers lead to higher solid phase temperatures. The Nusselt number exhibits a decreasing trend with a decreasing thermal conductivity ratio but increases with higher Rayleigh and Biot numbers and increased external radiation.