Conjugate Natural Convection Research Articles

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.

Numerical Investigation of the Effect of Baffle Inclination Angle on Nanofluid Natural Convection Heat Transfer in A Square Enclosure

The characteristics of the conjugate natural convection of (Al2O3-water) nanofluid inside differentially heated enclosure is numerically analyzed using COMSOL Multiphysics (5.3a). The enclosure consists of two vertical walls, the left wall has a thickness and maintain at a uniform hot temperature, while the opposite wall at cold temperature and the horizontal walls are isolated. A high thermal conductivity thin baffle has been added on the insulated bottom wall at a different inclination angles. The effect of the volume fractions of nanoparticles (f), Rayleigh number (Ra), solid wall thermal conductivity ratio (Kr), baffle incline angles (Ø) and the thickness of solid wall (D) on the isothermal lines, fluid flow patterns and the average Nusselt number (Nu) has been investigated. At low Rayleigh number (Ra=103 to 104) the Isothermal lines are parallel with the vertical wall which is characteristic of conduction heat transfer. on the other hand, when Rayleigh number increase to (Ra=106), the isotherms lines distribution in the inner fluid become parallel curves with the adiabatic horizontal walls of the enclosure and smooth in this case convection heat transfer becomes dominant. As the Rayleigh number further increases, the average Nusselt number enhance because of buoyancy force become stronger. In addition, the fluid flow within the space is affected by the presence of a fin attached to the lower wall that causes blockage and obstruction of flow near the hot wall, hence the recirculation cores become weak and effect on the buoyant force. The maximum value of the stream function can be noticed in case of nanofluid at (Ø=60), whereas they decrease when (Ø > 60), where the baffle obstruction causing decreases in flow movement. So that the left region temperature increases which cause reduction of the convective heat transfer by the inner fluid temperatures. This is an indication of enhancing of insulation. When the inclination angle increases (Ø >90), the baffle obstruction on flow and fluid resistance becomes smaller and the buoyancy strength increase, as a result, the heat transfer is increasing in this case. As a result of increasing the thermal conductivity from 1 to 10, an increase in the amount of heat transferred through the solid wall to the internal fluid have been noticed. This change can be seen in the isothermal lines, also, there was growth and an increase in the temperature gradient. The increasing of wall thickness from (D=0.1 to 0.4) leads to reduce the intensive heating through the solid wall as well as small heat transferred to the inner fluid. Therefore, it can be noticed that when the wall thickness increases the stream function decrease.

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.

A lattice Boltzmann analysis of the conjugate natural convection in a square enclosure with a circular cylinder

In this paper, an improved lattice Boltzmann model that incorporates the effect of heat capacity is adopted to simulate the conjugate natural convection in a square enclosure with a circular cylinder, and the square cavity considered is bounded by four finite thickness and conductive walls. Influences of Rayleigh number, wall thermophysical properties, and wall thickness on streamlines, isotherms and Nusselt number are analyzed. It is found that the heat transfer rate obtained for different wall thicknesses is usually smaller than that for the zero wall thickness, while this difference is not apparent for a larger thermal conductivity ration. Additionally, the study also shown that the increase of the outer wall thickness tends to decrease the heat transfer rate. The effects of the geometric parameter, including aspect ratio and vertical cylinder location, on heat transfer are also studied.

Characteristics and enhancement of heat transfer from heat-generating blocks mounted on back wall of a 3D cabinet to an ambient natural convective air stream

In this study, the physical system under consideration is a three-dimensional (3D) cabinet with arrays of heat-generating blocks mounted on inner surface of back wall of the cabinet. The heat-generating blocks dissipate heat to the surrounding of cabinet through conjugate conduction and natural convection. Efforts are performed to investigate the cooling performance enhancement of the blocks by constructing circular air vents in walls and installing round fins onto back wall of the cabinet. Results show that the air vents and fins can significantly reduce the hot spot temperature of heat-generating blocks, and improve temperature uniformity of the blocks. The maximum reduction in hot spot temperature can be up to 26.2% for cases under investigation in this study.

Effects of nonhomogeneous nanofluid model on convective heat transfer in partially heated square cavity with conducting solid block

In this study, the conjugate natural convection in a square cavity filled with $$\hbox {Al}_2\hbox {O}_3$$ –water nanofluid with an inner conducting solid block is studied numerically using nonhomogeneous Buongiorno’s two-phase model. The left wall of the cavity is partially heated and the remaining parts of the wall are adiabatic, while the right wall is fully cooled. The top and bottom horizontal walls are adiabatic. The numerical simulations are based on the finite difference method. The results are simulated for various values of the nanoparticle volume fraction $$(0\le \phi \le 0.04)$$ , Rayleigh number $$(10^2\le Ra\le 10^6)$$ , thermal conductivity of the conjugate square $$(k_{\mathrm{w}}=0.28, 0.76, 1.95, 7.0)$$ and 16.0 (epoxy: 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16), the size of the inner solid $$(0\le D\le 0.7)$$ , and the length of the heater ( $$0.1\le H\le 1.0$$ ). The numerical results for the average and local Nusselt numbers, isotherms, distribution of nanoparticles, and streamlines are presented graphically. The findings indicate that increasing the average solid volume fraction and the size of the solid block as well as the thermal conductivity will enhance the rate of the heat transfer at low values of Rayleigh number $$Ra=10^3$$ . On the other hand, increasing these parameters at high values of Rayleigh number ( $$Ra>10^5$$ ) decreases the average Nusselt number.

Effects of two-phase nanofluid model on natural convection in a square cavity in the presence of an adiabatic inner block and magnetic field

PurposeThe purpose of this paper is to study problem of conjugate MHD natural convection of Al2O3-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model numerically.Design/methodology/approachAn isothermal heater is placed on the left wall of the square cavity, while the right wall is maintained at a constant cold temperature. The horizontal top and bottom walls are kept adiabatic. The boundaries of the annulus are assumed to be impermeable, the fluid within the cavity is a water-based nanofluid having Al2O3 nanoparticles. The Boussinesq approximation is applicable. The governing equations subject to the boundary conditions are solved using the finite difference method.FindingsNumerical results are presented graphically in the form of streamlines, isotherms and nanoparticles distributions as well as the local and average Nusselt numbers. The results show that the effect of the nanoparticles addition on the average Nusselt number is essential for low Rayleigh, high Hartmann and high values of length ratio when attenuated the convective flow.Originality/valueAccording to exist studies and to the authors’ best knowledge, so far, there have been no studies of conjugate natural convection of Al2O3-water nanofluid in a square cavity with a conductive inner block using Buongiorno’s two-phase model with the effect of the magnetic field. Thus, the authors believe that this work is new and valuable. The aim of this study is to investigate the MHD natural convection of Al2O3-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model.

Conjugate natural convection in a fluid‐saturated porous enclosure with two solid vertical partitions

AbstractConjugate natural convection in a fluid‐saturated square porous enclosure with two solid vertical partitions of finite and equal thickness equispaced from center of enclosure is investigated in this paper. The primary objective is to attenuate the Nusselt number (Nu) and hence the heat transfer rate across a differentially heated enclosure. Darcy's model is considered. Numerical computation is performed using successive accelerated replacement and explicit scheme. Partition ratio, partition length, thermal conductivity ratio, and modified Rayleigh number are the parameters under study. Fluid flow is analyzed by observing transient changes of streamlines and isotherms for partition length 0.3‐1, thermal conductivity ratio 0.5‐2, partition ratio 0.1‐0.3 and modified Rayleigh number 100 and 1000 where partition ratio is the ratio of distance between center of enclosure and either of the partition center to the total length of the enclosure; while Nusselt number is calculated to estimate the heat transfer rate for each configuration. It is found that, employing a solid partition within the enclosure most definitely reduces the Nusselt number. The drop in Nusselt number is more for partition length 0‐0.6 after which it does show a drop in Nu but only very subtle. Further, Nu is the least for partition ratio 0.2. Also, Nusselt number is proportional to thermal conductivity ratio which is the ratio of thermal conductivity of solid to porous medium.

Conjugate natural convection of nanofluids inside an enclosure filled by three layers of solid, porous medium and free nanofluid using Buongiorno’s and local thermal non-equilibrium models

The natural convective heat transfer of nanofluids was addressed inside a square enclosure filled by three different layers: solid, porous medium and free fluid. The behavior of the porous layer has been simulated using local thermal non-equilibrium model. The Buongiorno’s model was utilized to evaluate the distribution of nanoparticles inside the enclosure that arose from the thermophoresis and Brownian motion. The governing equations were solved by the Galerkin finite element method in a non-uniform grid. The governing parameters are Rayleigh number Ra = 103–106, porosity e = 0.3–0.9, Darcy number Da = 10−5–10−2, interface parameter Kr = 0.1–10, H = 0.1–1000; ratio of wall thermal conductivity to that of the nanofluid, Rk = 0.1–10, dimensionless length of the heater B = 0.2–0.8; dimensionless centre position height of the heater Z = 0.3–0.7 and Lewis number Le = 10–100. A considerable concentration gradient of nanoparticles was found inside the enclosure. In some studied cases, the non-dimensional volume fraction of nanoparticles is about 10% higher than the average volume fraction of nanoparticles at the region near the cold wall. The variability of Darcy and the Rayleigh numbers indicated significant effects on heat transfer rate and the concentration patterns of the nanoparticles and inward the cavity. The increase in Le and Nr amplifies and decreases the heat transfer rates through fluid and solid phases, respectively. In addition, it can be seen that the increment in heat transfer rates with Le increases as Nr increases.

Efficient monolithic projection method for time-dependent conjugate heat transfer problems

We propose herein an efficient monolithic projection method (MPM) to solve time-dependent conjugate heat transfer problems involving not only natural convection in the fluid domain and heat conduction in the solid domain, but also the thermal interaction between solid and fluid domains across the solid–fluid interface. We obtain a global discretized linearized system by advancing the buoyancy, nonlinear convection, and linear diffusion terms in time using the Crank–Nicolson scheme and introducing the second-order central finite difference in space along with linearizing the nonlinear convection terms in both momentum and energy equations. The energy equations are simultaneously and implicitly discretized in both solid and fluid domains with the implemented Taylor series expansion for thermal interaction normal to the interface without an involved sub-time step iteration. Approximated lower–upper decompositions and an approximate factorization are also imposed to speed up the computation. Thus, we obtain a non-iterative monolithic projection method over the entire domain. Numerical simulations of two-dimensional (2D) conjugate natural convection and 2D conjugate Rayleigh–Bénard convection and periodic forced flows are performed to investigate the numerical performance of the proposed method. Consequently, the MPM correctly predicts the solution of the conjugate natural convection problem involving strong thermal interactions and provides a more stable and efficient computation than the semi-implicit projection method proposed by Kim and Moin (1985) [21] with a loosely or strongly coupled algorithm for the solid–fluid interface, while preserving the second-order temporal and spatial accuracy. Finally, the proposed method reasonably simulates a typical real-world problem, namely conjugate heat transfer through double-pane windows, by considering 2D heat conduction in each pane of glass for three different climatic conditions. Using the proposed MPM, we also investigate the effects of the air layer thickness ranging from 5 mm to 40 mm on the averaged Nusselt number and the distribution of temperature as well as fluid motion.

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

Unsteady Conjugate Natural Convective Heat Transfer and Entropy Generation in a Porous Semicircular Cavity

The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall.

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.

Modelling of the conjugate natural convection in a closed system with the radiant heating source radiant energy distribution by Lambert’s cosine law

Various types of emitters are often used as energy sources in real engineering systems and technological processes. Investigations of heat transfer basic laws in such systems are of interest. We conducted mathematical modelling of conjugate heat transfer in a closed rectangular cavity under conditions of radiant energy source operating. The 2-D problem of conjugate natural convection in vorticity stream function-temperature dimensionless variables has been numerically solved by means of the finite difference method. Radiant energy distribution along the gas-wall interfaces was set by Lamberts? cosine law. We obtained fields of temperature and stream functions in a wide range of governing parameters (Rayleigh number 104 ? Ra ? 106, the length of radiant heating source 0.15 ? D ? 0.6). Then we analyzed how heat retaining properties of finite thickness heat conducting walls made of different materials affect the heat transfer intensity. Differential characteristics distribution showed significant non-uniformity and non-stationarity of the conjugate heat transfer process under study.

Численное исследование сопряженного свободно-конвективного теплообмена в замкнутой полости с треугольным элементом объемного тепловыделения

Numerical investigation of unsteady laminar conjugate natural convection in a square enclosure with a triangular heat generating source located in a center of bottom wall has been carried out. Vertical walls of the cavity were isothermal and they can be considered as heat removal system. The process of heat, mass and momentum transfer inside the enclosure has been described by the system of partial differential equations using the modified variables “stream function – vorticity”. The boundary-value problem has been solved by the finite difference method using the structured grid. The special focus has been given to analysis of evolution of streamlines and isotherms, which describe the behavior of hydrodynamics and heat transfer. Also the study of impact of the surface emissivity of heater walls and cavity walls has been performed. The features of unsteady thermal plume, distributions of both local and integral characteristics at different Ra numbers have been shown.

The effect of conductive baffles on natural convection in a power-law fluid-filled square cavity

This research involves the numerical study of the conjugate natural convection of a power-law fluid in a two-dimensional square cavity with a pair of conducting baffles. The lower wall of the cavity contains a heat source with constant heat flux, while a pair of conductive baffles is embedded on its upper wall. The left and right side walls and some parts of the lower wall of the cavity are thermally insulated and its upper wall is kept at a low temperature. The governing equations along with the corresponding boundary conditions are solved using the numerical finite difference method based on the control volume formulation and SIMPLE algorithm. The effects of pertinent parameters on flow and temperature fields and heat transfer rate are investigated. From the results of the numerical solution, increasing the Rayleigh number and baffles thermal conductivity enhance the thermal performance of the cavity. So that for $$ Ra = 10^{6} , $$ with an increase in the thermal conductivity ratio from $$ 1 $$ to $$ 100, $$ the average Nusselt number increases by about 14% for both cases $$ n = 0.6 $$ and $$ n = 1.2 $$ . As well as a decrease in power-law index, except in low Rayleigh numbers, increases the heat transfer rate. Based on the results, the increase of the average Nusselt number is about 283% for a power-law index reduction in the range of $$ 0.6 \le n \le 1.2 $$ at $$ Ra = 10^{6} $$ . Also, an increase of the length of the baffles deteriorates the thermal performance of the cavity at high Rayleigh numbers, while enhances it at low Rayleigh numbers.

Conjugate natural convection of Al2O3–water nanofluid in a square cavity with a concentric solid insert using Buongiorno’s two-phase model

The problem of conjugate natural convection of Al2O3–water nanofluid in a square cavity with concentric solid insert and isothermal corner boundaries using non-homogenous Buongiorno’s two-phase model is studied numerically by the finite difference method. An isothermal heater is placed on the left bottom corner of the square cavity while the right top corner is maintained at a constant cold temperature. The remainder parts of the walls are kept adiabatic. Water-based nanofluids with Al2O3 nanoparticles are chosen for the investigation. The governing parameters of this study are the nanoparticle volume fraction (0 ≤ ϕ ≤ 0.04), the Rayleigh number (102 ≤ Ra ≤ 106), thermal conductivity of the solid block (kw=0.28, 0.76, 1.95, 7 and 16) (epoxy: 0.28, brickwork: 0.76, granite: 1.95, solid rock: 7, stainless steel: 16) and dimensionless solid block thickness (0.1 ≤ D ≤ 0.7). Comparisons with previously experimental and numerical published works verify good agreement with the proposed method. Numerical results are presented graphically in the form of streamlines, isotherms and nanoparticles volume fraction as well as the average Nusselt number and fluid flow rate. The results show that the thermal conductivity ratio and solid block size are very good control parameters for an optimization of heat transfer inside the partially heated and cooled cavity.

Analysis of conjugate natural convection within a porous square enclosure occupied with micropolar nanofluid using local thermal non-equilibrium model

This work aims to study the conjugate natural convection of micropolar nanofluid within a porous enclosure considering local thermal non-equilibrium model. The Galerkin finite element method is employed to solve the coupled and non-linear equations. The governing parameters are Darcy–Rayleigh number Ra=10–1000, porosity ε=0.1–0.9, interface parameter H=1–1000, Kr=0.1–10, volume fraction of the nanofluid φnf=0–0.08, vortex viscosity parameter Δ=0–3, the width of the solid wall d=0.1–0.4 and ratio of wall thermal conductivity to that of the base fluid Rk=0.1–10. It has been revealed that the power of micro-rotations increases with Darcy–Rayleigh number, vortex viscosity parameter, ratio of wall thermal conduction to that of base fluid, interface parameter (Kr and H) in conditions that declines with thickness of the solid wall and porosity. The Nusselt numbers for both phases in the porous medium significantly decline as thickness of the solid wall rises, with the exception of d=0.35. Also, it can be concluded as the porosity parameter increases for the passing flow, the nanofluid flow is governed by the classic Navier-Stokes equations.