Mixed Convection in a Vertical Channel with Discrete Heat Sources Using a Porous Matrix

In this work, we present the mixed convection air-cooling of two identical heat sources mounted in a vertical channel by using a porous matrix. The flow field is governed by the Navier–Stokes equation in the fluid region, the Darcy–Brinkman–Forchheimer equation in the porous region, and the thermal field by the energy equation. The effects of the Richardson number, Darcy number, thermal conductivity, and thickness of the porous matrix on the flow and heat transfer were studied. Results show that a better cooling is obtained for the channel completely filled with a porous material, except the components, with the Richardson number (Ri = Gr/Re² = 0.25), where Gr = 10⁴ is the Grashof number and Re = 200 is the Reynolds number, and for all Darcy numbers (10^?5 ≤ Da ≤ 10^?3). It was also seen that for Gr/Re² = 20, where the buoyancy effect is stronger, the average Nusselt number with porous matrix is higher than without porous matrix for all Richardson numbers (Ri = 0.25, 1, 10, and 20). As a result, we can economize the energy of the fan. Finally, the insertion of the porous matrix with high thermal conductivity ameliorates the cooling of the heat sources.     

Natural Convection in a Vertical Annuli with Discrete Heat Sources

In this article, we numerically study natural convection heat transfer in a cylindrical annular cavity with discrete heat sources on the inner wall, whereas the outer wall is isothermally cooled at a lower temperature, and the top wall, the bottom wall, and unheated portions of the inner wall are assumed to be thermally insulated. To investigate the effect of discrete heating on the natural convection heat transfer, at most two heating sources located near the top and bottom walls are considered, and the size and location of these discrete heaters are varied in the enclosure. The governing equations are solved numerically by an implicit finite difference method. The effect of heater placements, heater lengths, aspect ratio, radii ratio, and modified Rayleigh number on the flow and heat transfer in the annuli are analyzed. Our numerical results show that when the size of the heater is smaller, the heat transfer rates are higher. We also found that the heat transfer in the annular cavity increases with radii ratio and modified Rayleigh number, and can be enhanced by placing a heater with the smaller length near the bottom surface.     

Simulation Studies on Buoyancy-Aided Conjugate Mixed Convection With Radiation From a Vertical Plate With Multiple Nonidentical Heat Sources

This paper documents certain salient results of the simulation studies performed on conjugate mixed convection with surface radiation from a vertical electronic board equipped with multiple nonidentical flush-mounted discrete heat sources. Air that is assumed to be radiatively transparent with constant thermophysical properties subjected to the Boussinesq approximation is considered to be the cooling agent. The governing fluid flow and heat transfer equations without the boundary-layer approximations are initially transformed into vorticity-stream function form and are later appropriately normalized. The resulting equations, along with pertinent boundary conditions, are subsequently solved using a finite-volume-based finite-difference method coupled with Gauss–Seidel iterative technique. An extended computational domain has been used to capture the fluid flow and heat transfer adequately employing optimum combination of finer and coarser grids. A computer code is specifically written for the job. Effects of modified Richardson number, surface emissivity, and thermal conductivity on local temperature distribution, peak board temperature, and contributions of mixed convection and radiation in heat dissipation have been clearly elucidated. Two correlations that help in calculation of maximum and average nondimensional plate temperatures have also been developed.     

Three-Dimensional Mixed Convection Heat and Mass Transfer in a Rectangular Duct: Case of Longitudinal Rolls

This article presents numerical study of 3-D thermosolutale mixed convection (TSMC) in horizontal rectangular channels. The contribution of this work is to characterize the travelling wave's appearance and to generalize the behavior of Poiseuille-Rayleigh-Benard (PRB) systems for a broad range of dimensionless parameters, which control the double diffusive mixed convection. The numerical results consist of analyzing the flow regimes of the steady longitudinal thermoconvectives rolls for the case of purely thermal mixed convection (TMC) and for both thermal and mass transfer (TSMC). The transition from opposed volume forces to cooperating ones at fixed Rayleigh (Ra), Reynolds (Re), and Lewis (Le) numbers, considerably affects the birth and the development of the longitudinal rolls (noted R_//). The heat and mass transfers distribution, presented by the average Nusselt and Sherwood numbers, are also examined.     

Mixed Convection Heat Transfer in a Grooved Channel with Injection

Improved heat transfer is very important for the energy efficiency, higher performance, and size reduction of a system. In this context, the paper presents an efficient way for improving mixed convection heat transfer in a grooved channel by dividing total flow into main flow and injection under the assisting flow configuration. The influences of the pertinent injection parameters (e.g., position, size, and injection flow) are investigated systematically for Richardson number 0.1–10 and Reynolds number 50–200 using an in-house CFD code. The results reveal that performance with injection is always superior and heat transfer enhancement is found to increase from 50 to 218% depending upon injection, Richardson number, and Reynolds number.     

Mixed Convection and Non-Gray Radiation in a Horizontal Rectangular Duct

Numerical studies for fluid flow and heat transfer in a horizontal rectangular duct are carried out. The flow is considered to be laminar, hydrodynamically and thermally developing. Heat transfer by both forced and natural convection is taken into account. The radiation from the gas is modeled with weighted sum of gray gases (WSGG) model. While considering non-gray radiation with WSGG, the fluid is considered to be a mixture of CO₂ and H₂O. Simulations are carried out with lower wall temperature than the inlet temperature of the gas. The effect of buoyancy and radiation on bulk mean temperature and Nusselt number are studied. The effects of temperature dependent properties are discussed. Comparative studies are carried out among forced convection, mixed convection, gray and non-gray gas radiation. It is found from the simulations that the assumption of gray gas can produce an error of ±10% over a non-gray model with WSGG for the cases studied.     

Enhanced Three-Dimensional Mixed Convection in a Horizontal Channel Using a Baffle

Three-dimensional mixed convection inside a horizontal rectangular channel with a square heated surface on one of the vertical sidewalls and an infinitely thin baffle installed on the opposite insulated sidewall is numerically investigated. Attention is focused on the influence of the baffle position (?2 to 2), the inclination angle between the baffle and the horizontal (15° to 90°), and the baffle height (0.2 to 0.9) on the flow and thermal characteristics. The other parameters remain unchanged: the Reynolds number (100), Grashof number (50,000) and Prandtl number (0.71). The results show recirculation around the top portion of the heated surface due to strong buoyancy. The heat transfer depends strongly on the relative positions of the baffle and the recirculation. Heat transfer enhancement is obtained with a higher baffle and a larger inclination angle if the baffle is close to the cold main stream. In contrast, the average Nusselt number is slightly smaller if the baffle is surrounded by the recirculation than it is without the baffle. An accurate correlation is proposed for calculating the average Nusselt number over the investigated range of the baffle position and the inclination angle for a fixed baffle height (0.75).     

Turbulent Opposing Mixed Convection Heat Transfer in a Vertical Flat Channel with One-Side Heating

The paper presents experimental data on turbulent local heat transfer in a flat vertical channel with one-side heating for opposing mixed convection in wide ranges of airflow parameters (Re = 4 × 10³–4 × 10⁴; Gr_q = 1.7 × 10⁸–1.4 × 10¹⁰; pressures p = 0.2, 0.4, 0.6 MPa). Analysis has been performed by application of different buoyancy parameters. General correlation was suggested to predict the heat transfer rate. The experimental data were compared with the available correlations for vertical tubes.     

Radiation Effects on Turbulent Mixed Convection in an Asymmetrically Heated Vertical Channel

The purpose of present study is to numerically investigate the radiation effects on turbulent mixed convection flow between two differentially heated vertical parallel plates. Two flow situations known as aiding and opposing flow are considered. Frictional Reynolds number and Grashof number are assumed to be 150 and 1.6 × 10⁶, respectively. Both hydrodynamically and thermally developing and fully developed regions in the channel are investigated. Three Reynolds-averaged Navier–Stokes-based low Reynolds turbulence models are evaluated and the model with better overall performance is applied to the simulations. The radiative transfer equation for the gray and participating fluid is solved using the discrete-ordinates method, adopting its eighth-order quadrature scheme. The effects of two radiative parameters, namely, wall emissivity and optical thickness, on the flow and thermal fields, Nusselt number, and friction factor are addressed. Present results indicate that the presence of thermal radiation has a significant influence on flow and thermal fields. With an increase in wall emissivity and optical thickness, influence of radiation on the mean velocity, mean temperature, and turbulence kinetic energy profiles grows in both aiding and opposing regions. This results in an increase in bulk temperature, centerline velocity, and Nusselt number and a decrease in friction factor on both sides.     

变物性对有凸出热源通道换热计算的影响

本文基于一侧含有三个均匀分布的凸出热源竖壁、另一侧为绝热竖壁的二维垂直换热通道,研究了物性变化相比于常物性和Boussinesq假设对通道内最大温度和平均Nu数的影响。通过网格无关性验证,证实了计算程序的有效性,并修正了无量纲最大温度的公式为幂函数形式。计算结果验证了,在Gr〉7．5×10。时,变物性对非对称通道换热的必要性。     

MHD Mixed Convection in a Channel with a Triangular Cavity

A numerical study has been carried out in an open channel, which have a heated triangular cavity at the bottom wall. The remaining walls of the channel are adiabatic. Flow inlets to the channel with uniform velocity and fully developed flow are accepted at the exit of the channel. Steady state mixed convection by laminar flow has been studied by numerically solving governing equations to obtain flow field and temperature distribution under the magnetic field and Joule effect. Equations are solved via the Galerkin weighted residual finite element technique. Calculations are performed for different governing parameters such as Hartmann number (10 ≤ Ha ≤ 100), Reynolds number (100 ≤ Re ≤ 2,000), Rayleigh number (10³ ≤Ra ≤ 10⁵), Joule parameter (0 ≤ J ≤ 5), and Prandtl number (1 ≤ Pr ≤ 10). It is found that heat transfer decreases with an increasing of the Hartmann number especially at higher values of Rayleigh number. Fluid temperature at the exit of the channel also decreases with increasing of Hartmann number. Fluid temperature at the outlet of the channel becomes higher at low Reynolds number and higher Rayleigh number. However, it decreases with the decreasing of the Reynolds number.     

Simulation Studies on Multimode Heat Transfer from a Square-Shaped Electronic Device with Multiple Discrete Heat Sources

ABSTRACT

The results of a numerical study of the problem of multimode heat transfer from a square-shaped electronic device provided with three identical flush-mounted discrete heat sources are presented here. Air, a radiatively nonparticipating fluid, is taken to be the cooling medium. The heat generated in the discrete heat sources is first conducted through the device, before ultimately being dissipated by convection and surface radiation. The governing partial differential equations for temperature distribution are converted into algebraic form using a finite-volume based finite difference method, and the resulting algebraic equations are subsequently solved using Gauss-Seidel iterative procedure. A grid size of 151 × 91 is used for discretizing the computational domain. The effects of all relevant parameters, including volumetric heat generation, thermal conductivity, convection heat transfer coefficient, and surface emissivity, on various important results, such as the local temperature distribution, the peak temperature of the device, and the relative contributions of convection and surface radiation to heat dissipation from the device, are studied in sufficient detail. The exclusive effect of surface radiation on pertinent results of the present problem is also brought out.     

Three-Dimensional Study of Natural Convection in a Horizontal Channel With Discrete Heaters on One of Its Vertical Walls

Three-dimensional natural convection in a horizontal channel with an array of discrete flush-mounted heaters on one of its vertical walls is numerically studied. Effects of thermal conductivities of substrate and heaters and convection on outer sides of the channel walls on heat transfer are examined. The substrate affects heat transfer in a wider range of thermal conductivities than do the heaters. At lower heater thermal conductivities a higher heat portion is transferred by direct convection from the heaters to the adjacent coolant. However, higher substrate conductivity is associated with higher heat portion transferred through the substrate. The innermost heater column is found to become the hottest heater column due to the lower coolant accessibility. The heat transfer in the channel is strongly influenced by convection on the outer sides of the channel walls. Correlations are presented for dimensionless temperature maximum and average Nusselt number.     

Inverse Natural Convection Problem with Radiation in Rectangular Enclosure

Inverse thermal problem is applied to natural convective flow with radiative heat transfer. The bottom wall temperature in the 2-D cavity domain is estimated by using gas temperature measurements in the flow field. The inverse problem is solved through a minimization of an objective function using the conjugate gradient method with adjoint problem. The effects of functional form of bottom wall temperature profile, the number and the position of measurement points, and the measurement errors are investigated and discussed. The conjugate gradient method is found to work well in estimating the bottom wall temperature, even when natural convection with radiation phenomena is involved.     

Combined Effect of Mixed Convection and Surface Radiation Heat Transfer for Thermally Developing Flow in Vertical Channels

Combined effect of laminar flow mixed convection and surface radiation heat transfer for thermally developing airflow in a vertical channel heated from a side has been experimentally examined with different thermal and geometric parameters. The channel boundary is made of two isothermal walls and two adiabatic walls, the isothermal parallel wall is heated uniformly and the opposite cold wall temperature is maintained equal to the inlet conditions. The heated wall temperature ranged from 55 to 100°C, Reynolds number ranged from 800 to 2900 and the heat flux was varied from 250 to 870 W/m². To cover the wide range of Reynolds numbers, two aspect ratios of square and rectangular section were used. Surface radiation from the internal walls is considered through two emissivities i.e. 0.05 and 0.85, to represent weak and strong radiation effects, respectively. From the experiments, surface temperature and Nusselt number distributions of convection and radiation heat transfer are obtained for different heat flux values. Flow structure inside the channel is visualized to observe the flow pattern. The results show the combined effect of laminar flow mixed convection and surface radiation on the total heat transfer rate within the channel. The accumulating buoyancy force and airflow moves together vertically in the upward direction to give significant heat transfer enhancement in the vertical orientation of the channel.     

Natural Convection Flow with Surface Radiation Along a Vertical Wavy Surface

In this study, natural convection boundary layer flow of thermally radiating fluid along a heated vertical wavy surface is analyzed. Here, the radiative component of heat flux emulates the surface temperature. Governing equations are reduced to dimensionless form, subject to the appropriate transformation. Resulting dimensionless equations are transformed to a set of parabolic partial differential equations by using primitive variable formulation, which are then integrated numerically via iterative finite difference scheme. Emphasis has been given to low Prandtl number fluid. The numerical results obtained for the physical parameters, such as, surface radiation parameter, R, and radiative length parameter, ξ, are discussed in terms of local skin friction and Nusselt number coefficients. Comprehensive interpretation of velocity distribution is also given in the form of streamlines.     

Mixed Convection Heat Transfer from Tandem Square Cylinders in a Vertical Channel at Low Reynolds Numbers

The fluid flow and heat transfer characteristics around two isothermal square cylinders arranged in a tandem configuration with respect to the incoming flow within an insulated vertical channel at low Reynolds number range (1 ≤ Re ≤ 30) are estimated in this article. Spacing between the cylinders (S) is fixed at four widths of the cylinder dimension (d) and, the blockage parameter (B) is set to 0.25. The buoyancy-aided/opposed convection is examined for the Richardson number (Ri) ranges from ?1 to 1 with a fixed Prandtl number (Pr) of 0.7. The transient numerical simulation for this two-dimensional, incompressible, laminar flow and heat transfer problem is carried out by a finite volume code based on the PISO algorithm in a collocated grid system. The results suggest that the flow remains steady for the entire range of parameters chosen in this study. The representative streamlines, vorticity, and isotherm patterns are presented to interpret the flow and thermal transport visualization. Additionally, the time average drag coefficient (C _D ) as well as time and surface average Nusselt number (Nu) for the upstream and downstream cylinders are determined to elucidate the effects of Re and Ri on flow and heat transfer phenomena.     

Developing Flow of Mixed Convection in a Vertical Rectangular Duct with One Heating Wall

Heat transfer and flow patterns of laminar mixed confection in the developing region of a vertical rectangular duct with one heating wall have been investigated numerically in this study. The parabolic boundary layer model is adopted to predict the three-dimensional buoyancy-assisted flow field. Governing equations art solved by using the SIMPI.KC method coupled with a forward marching, implicit finite difference scheme. The velocity and temperature distributions as well as the stream wise variations of local heat flux and fluid pressure are calculated under various geometric parameters. Results show that the flow characteristics are significantly dependent on the buoyancy effect (Gr / Re), the aspect ratio of cross section of duct (H). and the Prandtl number (Pr). The numerical solutions obtained have been compared and verified with existing studies. Meanwhile, the analytical solutions of fully developed flaw recently reported 181 are found to exactly portray the behavior of flow far downstream.     

Wall Shape Effects on Convection Heat Transfer Over a Corrugated Channel

This study investigates the effects of the wall waviness on forced convection and its fluid flow in a channel bound by two wavy walls. The lattice Boltzmann method based on the boundary fitting method is used to simulate flow and thermal fields in the corrugated channel. The problem is investigated for different Reynolds numbers (50 to 150), wall amplitudes (0 to 0.35), number of wall wavelength (2 to 8), and phase difference of the walls (0 to 270) when the Prandtl number is equal to 0.71 for air flow. The study represents the significant effects of wavy walls on flow and thermal fields in a two‐dimensional channel. It is found when the phase difference between the channel walls has a value equal to 90°; the best heat transfer rate can be achieved in comparison with other geometrical conditions and the flow is likely to be periodically unsteady at lower Reynolds numbers.     

Natural Convection Heat Transfer of a Rectangular Block within a Vertical Enclosure

A numerical solution of the natural convection heat transfer between two cold and hot isolated vertical plates is presented for different horizontal and vertical location ratios of an enclosure. Results show that: a) flow configurations of cold and hot plates are different; b) the increase of vertical location ratio, toward that corresponding to the enclosure middle value, is considerably diminishing the temperature differences between heating and cooling conditions; c) the effect of vertical location ratio variation is more prominent on heat transfer for cold and hot plates than that of the horizontal location ratio variation; d) the average Nusselt number, obtained from the hot isolated plate, is 20–39% larger than that of the cold plate under the same conditions when the isolated plate varies horizontally; e) for a narrow distance between the inner plate and the bounding wall, the inner plate Nusselt number is enhanced, but aside from this, the plate average Nusselt number is insensitive to the plate position; and f) different trends are found to affect heat transfer for cold and hot plates when the isolated plate varies vertically. The optimal vertical location can be found at specific Rayleigh number for the hot plate and cold plate.