Conjugate Natural Convection Heat Transfer Research Articles

Combined conjugate free convection and thermal radiation in a porous inclined enclosure occupied with Cu-Al2O3 hybrid nanofluid

This study deals numerically with a steady laminar combined conjugate natural convection and thermal radiation heat transfer within an inclined porous enclosure occupied with Cu-Al2O3 /water hybrid nanofluid; the thermal conductivity and nanofluid viscosity are correlated experimentally. The centered heat sink and source are attached respectively to the upper and lower enclosure walls at a set distance of 0.5 from the sidewall and were parameterized with length values of 0.2, 0.4, 0.6, 0.8, and 1. This analysis is performed in wide ranges of enclosure inclination angles (0≤ α ≤ 180°), thermal radiation parameters (0≤ Rd ≤ 200), hybrid nanofluid volume fractions (0.1, 0.33, 0.75, 1, 2, 3, 4, and 5%), Rayleigh numbers (103≤ Ra ≤ 106), Darcy numbers (10−5≤ Da ≤ 10−2), medium porosities (0.1≤ ε ≤ 0.9), and thermal conductivity ratios (1≤ γ ≤ 10). The Nusselt number increases as the heat sink/source length decreases. This trend is even more pronounced when the length of the sink/source is reduced. Furthermore, the average Nusselt numbers for the fluid and solid matrix gradually increase as the inclination angle of the enclosure varies from 0° to 45°. However, beyond 45°, both Nusselt numbers exhibit a noticeable decrease with increasing inclination angle of the enclosure. The average Nusselt number of the fluid significantly increases with varying thermal radiation parameters. When the thermal radiation parameter ranges from 0 to 2 and 0 to 200, the average Nusselt number of the fluid increases by 192% and 7343%, respectively. The Nusselt numbers significantly improve when the porosity decreases and the thermal conductivity ratio increases. For a porosity of 0.1 and a porous thermal conductivity ratio ranging from 1 to 10, the average Nusselt number of the fluid increases by approximately 129% and 141% when the Darcy number increases from 10−5 to 10−2.

Conjugate local thermal non-equilibrium heat transfer in a porous medium-filled cavity with a rotating cylinder: Analysis and insights

In this work, local thermal non-equilibrium effects are examined as they relate to conjugate natural convection heat transfer in a cavity filled with a porous medium. The investigation also considers the rotation of the central cylinder and the undulation of the cavity’s solid sides. Additionally, the analysis includes the consideration of heat transfer bifurcation occurring at the interface between the solid walls and the porous medium. The equations that govern the behavior of the fluid within the porous region and the heat transfer equations for the porous matrix and solid walls are mathematically expressed as partial differential equations. To solve these equations, the finite element method is employed. The study reports and analyzes the influence of parameters such as Darcy number, Rayleigh number, Prandtl number, and thermal conductivity ratio on flow and thermal fields. Additionally, the study examines the effect of rotational cylindrical motion on fluid flow and heat transfer via its speed rotation. The results indicate that undulated walls and rotational speed significantly impact fluid streamlines and isotherm contours within the porous space, as well as the distribution of isotherms within the solid walls. The findings of this study could have practical implications in the design and optimization of porous media-based systems involving heat transfer.

Analyzing heat transfer variations at specific locations in a cave filled with porous media, emphasizing non-equilibrium conditions

ABSTRACT This study focuses on the analysis of conjugate natural convection heat transfer in a cavity filled with a permeable medium. It specifically considers the influence of confined thermal non-equilibrium and the presence of circular solid walls with partially active arcs. The study also explores the bifurcation of heat transfer at the interface of the permeable medium and solid walls. A finite element approach is employed to solve the governing equations for heat transfer in porous spaces, including porous matrices and solid walls, represented as partial differential equations. These equations are transformed into nondimensional forms based on boundary conditions and solved using the finite element method (FEM). The study examines local and overall heat transfer, varying nondimensional parameters, and the influence of active wall positions on flow patterns. Interestingly, the results demonstrate that the position of the active walls has a significant impact on the isotherms and streamlines contours in the permeable region, as well as the isotherms in the concrete walls. Specifically, an angle of 120 ∘ between the warm component and the radiator, both positioned vertically and facing each other, results in the maximum overall temperature transmission. Conversely, the lowest total heat transfer rate occurs when the angle between the hot element and cold radiator is 180°, indicating complete alignment. Moreover, the case (e) exhibits the lowest temperature transmission ratio for both the liquid and the concrete stages of the permeable medium. In the case of modifying of R k from 10 to 0.1, decrease in the temperature transmission by creating isolation regions that perform as thermal walls beside the dynamic fences. This research sheds light on the complex heat transfer behavior in a cavity with permeable media and highlights the crucial role of active wall positioning in shaping flow patterns and temperature distribution.

Heatfunction Analytics of Conjugate Natural Convection Heat Transfer in Partitioned Enclosure Filled with Hybrid Nanofluid Under Magnetic Fields

The need for suitable control of fluid flow and heat transfer for an enhanced performance has led to the use of magnetic field, appropriate design and sizing of the device and the right choice of the flow governing parameters for many industrial processes. This study investigates the effects of uniform magnetic field on the heat flow induced by buoyancy in a square enclosure partitioned into two cavities with a conducting solid body. The cavities are filled with the hybrid nanofluid composed from water and equal proportion of Cu and Al2O3 nanoparticles. The problem is analysed numerically by solving the momentum, energy and heatfunction equation with the finite difference method. The governing parameters including the Rayleigh, Ra, and Hartmann, Ha, numbers, solid concentration of the hybrid nanoparticles, , and the ratio of the thermal conductivity of the hybrid nanofluid to that of the solid conducting partition wall, k* are altered in the range of and respectively. The results show that the average heat function in the left cavity reduces with Ra and Ha while the overall fluid and heat flow are enhanced with the increase in the Ra and k* and retarded by increasing the Ha. The results of this work can be used as baseline data for the design and appropriate sizing of the heat transfer devices.

Analysis of conjugate Marangoni natural convection in a heating system with an open boundary flow

Marangoni natural convection involved in a heating system with an open boundary layer flow has been numerically analyzed in this article. An isoflux heater is placed below a steel pan (material: AISI 4340 steel) which is partially/fully filled with water to make this model more realistic. The surrounding of this pan has a two-dimensional air domain including a water-air interface. Hence, the air domain has three open boundaries within the computational domain. Conjugate natural convection heat transfer takes place from the solid pan to water and then air, whereas Marangoni convection is facilitated at the water-air interface. Two-dimensional, unsteady Navier-Stokes and energy equations are considered as the governing equations, and those are solved with the help of finite element method. Rayleigh number is varied in the range of laminar regime from 6 × 104 to 3 × 107 as the governing parameter under different water level conditions. Thermal and flow fields are visualized qualitatively, whereas quantitative distributions of average Nusselt numbers are taken for further analysis. Finally, the exergy of the system is inspected in terms of total entropy generation at individual flow domains. Here, overall heat transfer performance shows a strong dependency on the change of Rayleigh number.

Conjugate turbulent natural convection with thermal radiation in a vertical and inclined wall with heat sources

This work presents an experimental and numerical study of turbulent conjugate natural convection heat transfer in a plate for vertical and inclined positions containing protruding heat sources mounted on a conductive substrate, with thermal radiation effects. Experiments were performed with seven aluminum protruding heat sources uniformly mounted over an upper substrate fiberglass plate. Insulation and a guard heater were used at the back of the substrate plate. The temperature was measured for each power input and downward inclination angle. Numerical simulations were performed to explore the effects of conductivity, upward and downward inclinations, and heater emissivity. The conjugate problem was numerically addressed for a two-dimensional model, steady-state and incompressible flow under turbulent flow conditions. The main effort was to investigate the effects of power dissipation, conductivity plate-fluid ratio, plate inclination angle, and emissivity of the heater on temperature and Nusselt number distribution. The range of the modified Rayleigh number covers the values between 9 × 105 and 1.3 × 1010. The results found that heat loss by radiation was greater than 35%, the heat transfer became less efficient as the downward angle increased, and a jump in the average Nusselt number was found for upward cases due to plume detachment. A correlation for the Nusselt number was also developed.

Transient conjugate natural convection heat transfer in a differentially-heated square cavity with a partition of finite thickness and thermal conductivity

The transient conjugate natural convection heat transfer in a differentially-heated cavity with a partition of finite thickness and thermal conductivity are investigated numerically over the range of the Rayleigh number from 103 to 108, the thermal conductivity ratio of partition to that of fluid from 0.1 to 1000, and the dimensionless partition thickness from 0.05 to 0.2. An analysis of the obtained temperature contours and profiles, the time for the onset of stratification and the Nusselt number shows that the thermal conductivity ratio effect is significant only over the range of 0.1–10, when the role played by the partition changes, whereas the effect becomes negligible as the thermal conductivity ratio is very large (100 or beyond). It is also found that the scaling relations developed for the non-partitioned cavity are found to be applicable for the partitioned cavity. The results further show that the effect of the partition thickness on heat transfer is significant mainly when the thermal conductivity ratio is small.

Presenting a novel higher-order bounded convection scheme for simulation of multiphase flows and convection heat transfer

The primary aim of the current study is to enhance the stability and accuracy of the Volume-Of-Fluid (VOF) method for modeling free-surface flows with large topological changes and high density ratio. For accurate capturing of fluid interfaces, a novel higher-order bounded convection scheme is first constructed based on the total variation diminishing (TVD) concept and is then employed for the discretization of convection terms in Navier-Stokes, energy and transport equations. In the second step, the classical PISO algorithm is modified according to the two-step projection method (Chorin's model) and the combined model (PISOC) is then applied for the treatment of the pressure-velocity coupling. Moreover, the second-order accurate piecewise-linear interface reconstruction technique (PLIC-ELVIRA) is used for determining the normal direction and curvature of the interface. The robustness and accuracy of the proposed models in handling multiphase flows with interface rupture and coalescence are verified against several experimental and numerical benchmark solutions such as: dam break, Rayleigh-Taylor instability, bubble rising, rotation of a slotted disk (Zalesak's problem), deformation of a 2D disk and pure convection of a step profile. The results show that, the proposed third-order TVD flux-limiter scheme can considerably reduce the false-diffusion errors and ensure the boundedness of the volume fraction while retaining the sharpness and shape of the interface. Furthermore, it is found that the proposed PISOC algorithm has strong stability and convergence characteristics in strongly coupled multiphase problems and is less susceptible to divergence when larger pressure under-relaxation factor is used. The performance and effectiveness of the proposed modifications are further demonstrated by analyzing transient entropy generation due to conjugate natural convection heat transfer in two different canonical test cases (i.e. Differentially Heated Cavity and Rayleigh-Bénard Convection) and good agreements are found with previously published works.

Orientation effects on conjugate natural convection heat transfer from an LED bulb: A numerical study

Natural convection is a widely used cooling technique in LED bulbs. About 75–85% of input power to an LED package is being wasted as heat. Along with the LED packages, a notable amount of heat is generated by the LED driver. Thus, if this generated heat is not removed in a proper way, it can lead to decrease in life-span of the LED. Hence, the present study focusses on the numerical investigation of three-dimensional conjugate natural convection heat transfer from an LED bulb to elucidate the effect of orientation of the bulb on both momentum and heat transfer characteristics. Numerical computations are performed in a finite-volume based solver for the laminar flow regime of Rayleigh number spanning in the range 103 to 107 for various orientations of the LED bulb. Results are pictorially visualized in terms of temperature contours and streamlines to understand the thermal and flow fields, whereas both local and surface average Nusselt numbers are represented to expound the heat transfer from the bulb. The average Nusselt number is directly proportional to the Rayleigh number for all orientations of the bulb, and it is found to increase with an increase in the angle of orientation of the LED bulb from vertically upward to downward. The average Nusselt number at the vertically downward orientation of the bulb is higher than the vertically upward orientation by 86%, 77%, and 39% for Rayleigh number of 107, 105, and 103, respectively.

Conjugate natural convection in a corrugated solid partitioned differentially heated square cavity

Conjugate natural convection heat transfer inside a differentially heated square cavity having a heat conducting and sinusoidal corrugated solid partition has been investigated numerically in the present study. The fluid flow and the heat transfer within the cavity are governed by two-dimensional Navier–Stokes and energy equations, and those are solved using the finite element method. Numerical simulation is carried out for a wide range of Rayleigh number (103 ≤ Ra ≤ 109) with a fixed Prandtl number (Pr = 0.71) since the working fluid in the cavity is considered as air. The variations of both corrugation amplitude and corrugation frequency of the sinusoidal partition wall on the average Nusselt number of the heated wall are observed in order to assess the influence of the roughness of the solid partition on the heat transfer characteristics of the cavity. Moreover, different types of partition material are selected to scrutinize the effect of thermal conductivity of the solid partition on the heat transfer performance. Finally, a correlation is proposed to predict the average Nusselt number of the heated wall of the cavity from the governing parameters (such as Rayleigh number, corrugation frequency and thermal conductivity ratio) within the selected range of the present investigation.

Irreversibility analysis of thermally driven flow of a water-based suspension with dispersed nano-sized capsules of phase change material

A precise understanding of the thermal behaviour and entropy generation of a suspension comprising nano-encapsulated phase change materials (NEPCM) is important for the thermal energy storage and heat transfer enhancement in various engineering applications. Studies to date, have improved the knowledge of the heat transfer of NCPCM. However, a suspension comprising NEPCM in the porous medium could enhance the overall heat transfer performance. Therefore, this study aims to investigate the thermal, hydrodynamic and entropy generation behaviour of the NEPCM-suspensions in a porous medium. Conjugate natural convection heat transfer and entropy generation in a square cavity composed of a porous matrix (glass balls), occupied by a suspension comprising nano-encapsulated phase change materials, and two solid blocks is numerically investigated. Galerkin Finite Element Method is employed to solve the nonlinear coupled equations for the porous flow and heat transfer. The phase transition and the released/absorbed latent heat of the nano-capsules are attributed in a temperature-dependent heat capacity field. The thermal conductivity ratio (1 ≤ Rk ≤ 100), the Darcy number (10−5 ≤ Da ≤ 10−1), the Stefan number (0.2 ≤ Ste ≤ 1), the porosity of porous medium (0.2 ≤ ε ≤ 0.9), the dimensionless fusion temperature (0.05 ≤ Tfu ≤ 0.95), the solid walls thickness (ds = 0.1 and 0.3), and the volume fraction of the nano-capsules (0.0 ≤ φ ≤ 5%) are considered for the numerical calculations. The numerical results illustrate that the rates of heat transfer and the average Bejan number are maximum and the generated entropy is minimum when the fusion temperature of the nano-capsules is Tfu = 0.5. Besides, adding the nano-sized particles of encapsulated phase change materials to the host fluid increases the heat transfer rate up to 45% (for the studied set of parameters) and also augments the average Bejan number. The total entropy generation elevates with the increment of the volume fraction of the nanoparticles, for low values of the Darcy number; however, a downward trend can be found for higher values of the Da. The combination of NEPCM-suspensions (with latent heat thermal energy storage) and a porous medium (with the extended surface area) provides an extensive capability for thermal enhancement and energy storage applications. In this regard, the findings of the current work demonstrate that the selection of the fusion temperature and Darcy number are two essential key parameters, which could change the trend of the results.

Numerical study of conjugate natural convection heat transfer of a blood filled horizontal concentric annulus

Abstract A numerical investigation is accomplished on the natural convection flow and heat transfer in a horizontal concentric annulus in the presence of cylindrical solid wall and Carreau non-Newtonian blood model. The inner circular surface of the cavity is heated to a constant temperature and the outer circular surface is cooled. The boundaries of the annulus are assumed to be impermeable, the fluid within the cavity is assumed to be non-Newtonian blood when the Boussinesq approximation is applicable. The Galerkin weighted residual method is applied numerically to solve the dimensionless governing equations subject to the boundary conditions. The numerical results explained in the form of streamlines, isotherms, local and average heat transfer with variation of the Rayleigh number, Prandtl number, power-law index and the thermal conductivity of the cylindrical solid wall within the range of (103 ≤ Ra ≤ 106), (5 ≤ Pr ≤ 50), (0.2 ≤ n ≤ 0.8) and (0.25 ≤ kw ≤ 1.45), respectively. Validations with experimental/numerical data are accomplished which provide a clear conviction to the numerical data of the existing code. It has been found that a low power-law index improves the fluid flow and increases the rate of heat transfer.

Appraising conjugate heat transfer, heatlines visualization and entropy generation of Ag-MgO/H2O hybrid nanofluid in a partitioned medium

Purpose This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy generation in a partitioned medium filled with Ag-MgO (15-85%)/water. Design/methodology/approach The lattice Boltzmann method (LBM) is used to predict the dynamic and thermal behaviors. Experimental correlations for dynamic viscosity and thermal conductivity versus solid volume fraction are used. The study is conducted for the ranges of Rayleigh number 103 ≤ Ra ≤ 106, the partitioner thickness 0.01 ≤ δ ≤ 0.9, its position 0.15 ≤ Xs ≤ 0.85 and the hybrid nano-suspensions volume fraction 0% ≤ ϕ ≤ 2%. Findings The effects of varying of controlling parameters on the convective flow patterns, temperature contours, heat transfers, the heatlines and the entropy generation are presented. It has been found that the maximum rate of heat transfer enhancement occurs for low Ra numbers (103) and is close to 13.52%. The solid thickness d and its horizontal position Xs have a substantial influence on the heat transfer rate, flow structure, heatline, total entropy generation and Bejan number. Besides, the maximum heat transfer is detected for high Ra and δ ≈ 1 and the percentage of augmentation is equal to 65.55% for ϕ = 2%. According to the horizontal position, the heat transfer remains invariant for Ra = 103 and takes a maximum value near the active walls for Ra ≥ 104. The total entropy generation increases with Ra and decreases with ϕ for Ra = 106. The increase of ϕ from 0 to 2% leads to a reduction in close to 40.76%. For this value of Ra, the entropy is the maximum for δ = 0.4 and Xs = 0.35 and Xs = 0.65%. Moreover, as the Ra increases the Bejan number undergoes a decrease. The Bejan number is the maximum for Ra = 103 independently to δ and Xs. The superior thermal performance manifests at low Ra and high value of δ independently to the positions of the conducting body. Originality/value The originality of this paper is to analyze the hybrid nano-additive effects on the two-dimensional conjugate natural convection in a partitioned medium using the LBM. The experimental correlations used for the effective thermal conductivity and dynamic viscosity give credibility to our study. Different approaches such as heatlines and entropy generation are used.

Free convection flow and heat transfer of nanofluids in a cavity with conjugate solid triangular blocks: Employing Buongiorno’s mathematical model

This study aims to investigate the conjugate natural convection heat transfer of nanofluids in a square enclosure with two solid triangular walls. The left and right walls of the cavity are held at a constant temperature of Th and Tc, respectively, whereas the bottom and top are insulated. To assess the nanoparticles distribution inside the cavity that induced from the thermophoresis and Brownian motion, the Buongiorno’s model was used. The governing nonlinear equations were solved in a non-uniform unstructured grid by employing the Galerkin finite element method. The governing parameters are Rayleigh number (103≤ Ra ≤ 104), thermal conductivity ratio of solid walls to the fluid (1 ≤Rk≤ 500), thermal conductivity parameter (3 ≤ Nc ≤ 15), thermal viscosity parameter (3 ≤ Nv ≤ 15), Brownian motion parameter (5×10−7≤Nb≤5×10−6), Thermophoresis parameter (10−7≤Nb≤ 10−6), thickness of the triangular walls (0.1 ≤ m ≤ 0.75) and the position of the blocks (normal or reverse position). The numerical results are reported as contours of isotherms, streamlines, heatlines and isoconcentrations and the local and average Nusselt numbers. The results show that the presence of the triangular blocks boosts the overall rate of heat transfer. The average Nusselt number increases as the Rk decreases. The overall rate of heat transfer decreases when the triangular walls are placed in the reverse position.

Analysis of Combined Natural Convection and Radiation Heat Transfer in a Partitioned Rectangular Enclosure with Semitransparent Walls

In this paper, we present a two-dimensional numerical analysis of the conjugate natural convection and radiation heat transfer in a double-space enclosure with two semitransparent walls. Two kinds of boundary conditions are considered, the first being the isothermal process of the opaque wall, and the other the incidence of a constant radiation flux in the left semitransparent wall. The renormalization group k–ε model is adopted to simulate the turbulent flow in the enclosure. To compute the radiation heat transfer in a semitransparent medium, the discrete ordinates model is used. We compare the behaviors of enclosures with single and double semitransparent walls and determine the difference in the results obtained for semitransparent and opaque partitions. The results indicate that a semitransparent partition facilitates a reduction in the heat loss or obtains a higher temperature distribution. The transmittance of a semitransparent wall has a great effect on the thermal and flow characteristics in an enclosure. The change of wall temperature is found to be significant when the thermal conductivity values range from 0.05 to 0.5 W/(m·K), and to be small when ranging from 0.5 to 10 W/(m·K). These conclusions are helpful for green design and energy saving in solar buildings.

Conjugate local thermal non-equilibrium heat transfer in a cavity filled with a porous medium: Analysis of the element location

The problem of conjugate natural convection heat transfer in a cavity filled with a porous medium is addressed by considering the local thermal non-equilibrium effects. The thickness of the solid walls of the cavity is taken into account, and the vertical walls are assumed to be partially active. The effect of the heat transfer bifurcation in the interface of the solid walls and the porous medium is also taken into account. The governing equations for the heat and momentum of the fluid in the porous space, heat transfer in the porous matrix, and heat transfer in the solid walls are represented in the form of partial differential equations. The governing equations along with the corresponding boundary conditions are transformed into a generalized form of the non-dimensional equations and solved by the finite element method. Considering various values of the non-dimensional parameters, the effect of the location of the active walls on the flow patterns and the local and overall heat transfer are addressed. The results demonstrate that the location of the active walls can significantly affect the streamlines and the fluid isotherm contours in the porous space and the isotherms in the solid walls. Moreover, it is found that in most of the cases the highest total rate of heat transfer corresponds to the case in which the elements are in the center of the active wells. In contrast, the lowest total rate of the heat transfer corresponds to a case, in which the active hot element is at the top of the wall, and the cold element is at the bottom.

Conjugate natural convection heat transfer in an open-ended square cavity partially filled with porous media

Conjugate natural convection heat transfer in an open-ended square cavity, which is partially filled with porous media, is a useful research prototype to deepen our insight into many important practical applications, such as solar energy collectors. But surprising, until now there is no open literature on it. In addition, for traditional numerical approaches, it is a great challenge to model conjugate problems on fluid-porous interfaces. In the present work, firstly we develop a new lattice Boltzmann (LB) approach to overcome such difficulty. The present LB model is validated by three benchmark tests. With the aid of this LB approach, we investigate the effects of thickness of porous layer, fluid-to-porous thermal conductivity ratio and permeability of porous layer on conjugate natural convection heat transfer in an open-ended porous-partially-filled square cavity, for the first time. It is found that these factors all influence the patterns of flow field and temperature field significantly. Especially, there exist some critical values. A small offset from them will cause a substantial change of heat and mass transfer. Sometimes the change trends are completely reversed. The present results may provide useful theoretical guides for the relevant practical applications.

Numerical investigation of conjugate natural convection heat transfer in a square porous cavity heated partially from left sidewall

Numerical investigation of conjugate natural convection heat transfer in a square porous cavity heated partially from left sidewall

A comparative study of 2-D and 3-D conjugate natural convection from a vertical rectangular fin array with multilayered base subjected to distributed high heat flux

This paper presents a comparative numerical study of 2-D and 3-D steady, laminar conjugate natural convection heat transfer from a vertical rectangular aluminium fin array subjected to a distributed high heat flux related to the cooling of a 105 W LED street lighting luminaire. The effect of radiation is also considered in the aforementioned models. The 2-D model uses the Stream function-Vorticity-Temperature approach. The finite-difference methodology is used to discretize the governing equations. The discretization method in the 3-D model is finite-volume. The solution algorithm is SIMPLE (Semi-Implicit Method for Pressure-linked Equations). A detailed parametric study based on a realistic lamp data is conducted to observe the effect of heat flux, fin spacing, fin height, fin width, fin thickness and fin material (aluminium, brass, copper, mild steel) on the fluid (air) velocity and temperature distributions, heat transfer and LED junction temperature. A novel finding of this work is the revelation of asymmetric flow and thermal fields in the successive channels of the fin array, as predicted by the 3-D model. In contrast with the existing studies in which fin base is treated as isothermal, an optimal fin spacing is found to exist corresponding to the maximum heat transfer coefficient in the present study. The difference between 2-D and 3-D model-predicted average heat transfer coefficients increases with increase in fin height to fin spacing ratio. The contribution of radiation heat transfer is about 8–14% of the total heat transfer in the range of dimensions of the fin array considered in this work. A penalty function based optimization study is carried out to maximize the average heat transfer coefficient while maintaining the LEDs below the safe limit of 353 K. Finally, correlations for predicting the average heat transfer coefficient in the vertical rectangular fin array heat sink, and the maximum LED temperature as a function of luminaire wattage and geometric parameters of the fin array have been presented.

Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model

ABSTRACTThe natural convection heat transfer in a cavity filled with three layers of solid, porous medium, and free fluid is addressed. The porous medium and free fluid layers are filled with a nanofluid. The porous layer is modeled using the local thermal nonequilibrium (LTNE) model, considering the temperature difference between the solid porous matrix and the nanofluid phases. The nanofluid is modeled using the Buongiorno’s model incorporating the thermophoresis and Brownian motion effects. The governing equations are transformed into a set of nondimensional partial differential equations, and then solved using finite element method in a nonuniform grid. The effects of various nondimensional parameters are discussed. The results showed that the Brownian motion and thermophoresis effects result in significant concentration gradients of nanoparticles in the porous and free fluid layers. The increase in Rayleigh (Ra), Darcy (Da), the thermal conductivity ratios for the solid wall and solid porous matrix, i.e., Kr and Rk, enhanced the average Nusselt number. The increase in the convection interaction heat transfer parameter between the solid porous matrix and the nanofluid in the pores (H) increases the average Nusselt number in the solid porous matrix but decreases the average Nusselt number in the nanofluid phase of the porous layer.