Fully Developed Forced Convection Heat Transfer in a Porous Channel with Asymmetric Heat Flux Boundary Conditions

An analytical study is performed on steady, laminar, and fully developed forced convection heat transfer in a parallel plate channel with asymmetric uniform heat flux boundary conditions. The channel is filled with a saturated porous medium, and the lower and upper walls are subjected to different uniform heat fluxes. The dimensionless form of the Darcy–Brinkman momentum equation is solved to determine the dimensionless velocity profile, while the dimensionless energy equation is solved to obtain temperature profile for a hydrodynamically and thermally fully developed flow in the channel. Nusselt numbers for the lower and upper walls and an overall Nusselt number are defined. Analytical expressions for determination of the Nusselt numbers and critical heat flux ratio, at which singularities are observed for individual Nusselt numbers, are obtained. Based on the values of critical heat flux ratio and Darcy number, a diagram is provided to determine the direction of heat transfer between the lower or upper walls while the fluid is flowing in the channel.     

正弦波温度边界下多孔介质方腔内非热平衡对流传热数值模拟

采用局部非热平衡模型,在方腔左侧壁面温度正弦波变化、右侧壁面温度均一的边界条件下,通过SIM-PLER算法数值研究了固体骨架发热多孔介质方腔内的稳态非达西自然对流,主要探讨了不同正弦波波动参数N及方腔的高宽比M/L对方腔内自然对流与传热的影响规律。计算结果表明:正弦波温度边界使得方腔内的流场出现了复杂的变化,流体及固体区域左侧壁面附近出现了周期性的正负变化的温度场分布,左侧壁面局部Nusselt数出现了周期性的震荡现象;存在一个最佳温度波动参数N=1,此时多孔介质方腔内的整体散热量达到最大值;增加方腔高宽比会显著地削弱方腔内的自然对流传热过程,小高宽比也会在一定的程度上削弱多孔介质方腔内的对流传热。     

Numerical Simulation of Turbulent Flow and Heat Transfer in a Three-Dimensional Channel Coupled with Flow Through Porous Structures

This study investigates numerically the turbulent flow and heat transfer characteristics of a T-junction mixing, where a porous media flow is vertically discharged in a 3D fully developed channel flow. The fluid equations for the porous medium are solved in a pore structure level using an Speziale, Sarkar and Gatski turbulence model and validated with open literature data. Overall, two types of porous structures, consisted of square pores, are investigated over a wide range of Reynolds numbers: an in-line and a staggered pore structure arrangement. The flow patterns, including the reattachment length in the channel, the velocity field inside the porous medium as well as the fluctuation velocity at the interface, are found to be strongly affected by the velocity ratio between the transversely interacting flow streams. In addition, the heat transfer examination of the flow domain reveals that the temperature distribution in the porous structure is more uniform for the staggered array. The local heat transfer distributions inside the porous structure are also studied, and the general heat transfer rates are correlated in terms of area-averaged Nusselt number accounting for the effects of Reynolds number, velocity ratio as well as the geometrical arrangement of the porous structures.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

Numerical and experimental study of heat transfer in a tall vertical closed cavity

In this work the numerical and experimental results of heat transfer in a vertical tall closed cavity are presented. The cavity has an aspect ratio of 20, one of the vertical walls receive a constant and uniform heat flux, while the opposite wall is kept at a constant temperature. The remaining walls are assumed adiabatic. The cavity is full of air. The computational fluid dynamics software Fluent 6.3 was used for the simulation and an experimental prototype was built to obtain the heat transfer coefficients. The air temperature and the fluid velocity values are higher when emissivity (ε) is 0.03 (almost pure natural convection). The experimental total heat transfer coefficient increases between 119.9 and 159.9 % when the emissivity of the walls changes from 0.03 to 0.95.     

Combined forced and free flow in a vertical rectangular duct with prescribed wall heat flux

In this paper, combined forced and free convection is studied in a vertical rectangular duct with a prescribed uniform wall heat flux (H2 boundary condition). A different heat flux value for each plane wall is considered; the condition of a uniform wall heat flux throughout the duct results as a special case. The local momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of a Galerkin finite element method. The numerical solution gives the dimensionless velocity and temperature distributions, together with the values of the Fanning friction factor, of the Nusselt number, of the momentum flux correction factor and of the kinetic energy correction factor. These dimensionless parameters are reported as functions of the aspect ratio and of the ratio between the Grashof number, Gr, and the Reynolds number, Re. The threshold values of Gr/Re for the onset of flow reversal are evaluated.     

Analysis of Heat and Mass Transfer in a Vertical Annular Porous Cylinder Using FEM

The present study is intended to study heat and mass transfer in a vertical annular cylinder embedded with saturated porous medium. The inner surface of cylinder is maintained at uniform wall temperature and uniform wall concentration. The governing partial differential equations are non-dimensionalised and solved by using finite element method (FEM). The porous medium is discritised using triangular elements with uneven element size. Large number of smaller-sized elements are placed near the walls of the annulus to capture the smallest variation in solution parameters. The results are reported for both aiding and opposing flows. The effects of various non-dimensional numbers such as buoyancy ratio, Lewis number, Rayleigh number, aspect ratio, etc on heat and mass transfer are discussed. The temperature and concentration profiles are presented.     

An analysis on forced convection in a channel filled with a Brinkman-Darcy porous medium: Exact and approximate solutions

An analysis was made to investigate non-Darcian fully developed flow and heat transfer in a porous channel bounded by two parallel walls subjected to uniform heat flux. The Brinkmanextended Darcy model was employed to study the effect of the boundary viscous frictional drag on hydrodynamic and heat transfer characteristics. An exact expression has been derived for the Nusselt number under the uniform wall heat flux condition. Approximate results were also obtained by exploiting a momentum integral relation and an auxiliary relation implicit in the Brinkmanextended Darcy model. Excellent agreement was confirmed between the approximate and exact solutions even in details of velocity and temperature profiles.     

The effect of local thermal non-equilibrium on conduction in porous channels with a uniform heat source

We examine the effect of local thermal non-equilibrium on the steady state heat conduction in a porous layer in the presence of internal heat generation. A uniform source of heat is present in either the fluid or the solid phase. A two-temperature model is assumed and analytical solutions are presented for the resulting steady-state temperature profiles in a uniform porous slab. Attention is then focussed on deriving simple conditions which guarantee local thermal equilibrium.     

Effect of an Inserted Porous Layer Located at a Wall of a Parallel Plate Channel on Forced Convection Heat Transfer

A theoretical study is performed on heat and fluid flow in partially porous medium filled parallel plate channel. A uniform symmetrical heat flux is imposed onto the boundaries of the channel partially filled with porous medium. The dimensional forms of the governing equations are solved numerically for different permeability and effective thermal conductivity ratios. Then, the governing equations are made dimensionless and solved analytically. The results of two approaches are compared and an excellent agreement is observed, indicating correctness of the both solutions. An overall Nusselt number is defined based on overall thermal conductivity and difference between the average temperature of walls and mean temperature to compare heat transfer in different channels with different porous layer thickness, Darcy number, and thermal conductivity ratio. Moreover, individual Nusselt numbers for upper and lower walls are also defined and obtained. The obtained results show that the maximum overall Nusselt number is achieved for thermal conductivity ratio of 1. At specific values of Darcy number and thermal conductivity ratio, individual Nusselt numbers approach to infinity since the value of wall temperatures approaches to mean temperature.     

Direct contact heat transfer to a drop translating in a transverse electric field

An experimental study has been performed on heat transfer to a single drop translating in an immiscible liquid on which a steady uniform electric field is imposed perpendicular to the drop path. Particular attention has been paid to the effect of field-induced circulations inside and outside the drop. Three different combinations of liquids were tested: one for which the drop-to-medium permittivity ratio ?^* multiplied by the drop-tomedium resistivity ratio χ^* is large compared to unity and two for which ?^* χ^* ? 1. In the former a remarkable enhancement of heat transfer was obtained which could be ascribed to the induced circulations. However, a less remarkable enhancement obtained in the latter two could not be explained by the circulations which are predicted to be vanishingly weak.     

Effects of bubble size on heat transfer enhancement by sub-millimeter bubbles for laminar natural convection along a vertical plate

Injection of sub-millimeter bubbles is considered a promising technique for enhancing natural convection heat transfer for liquids. So far, we have experimentally investigated heat transfer characteristics of laminar natural convection flows with sub-millimeter bubbles. However, the effects of the bubble size on the heat transfer have not yet been understood. The purpose of this study is to clarify the effects of the bubble size on the heat transfer enhancement for the laminar natural convection of water along a vertical heated plate with uniform heat flux. Temperature and velocity measurements, in which thermocouples and a particle tracking velocimetry technique are, respectively used, are conducted to investigate heat transfer and flow characteristics for different bubble sizes. Moreover, two-dimensional numerical simulations are performed to comprehensively understand the effects of bubble injection on the flow near the heated plate. The result shows that the ratio of the heat transfer coefficient with sub-millimeter-bubble injection to that without injection ranges from 1.3 to 2.2. The result also shows that for a constant bubble flow rate, the heat transfer coefficient ratio increases with a decrease in the mean bubble diameter. It is expected from our estimation based on both experimental data and simulation results that this increase results from an increase in the advection effect due to bubbles.     

Effects of temperature-dependent viscosity variation on entropy generation,heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].     

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

Janus particle is a research hotspot due to its novelty and settlement in acid liquid during wastewater treatment. Heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion are numerically investigated based on immersed boundary lattice Boltzmann method. Chemical reaction heat ratio, Damkohler number, Peclet number, and particle number effects on temperature field, concentration field, Janus particle mass reduction, position, and velocity are investigated. The uniform particle has an equilibrium position of about 1/4 times the channel width for two corroded uniform particle settlement processes. The Janus particle horizontal position deviates from the uniform particle equilibrium position due to the force caused by nonuniform buoyancy and particle rotation. When the chemical reaction heat ratio is more than 1, the Janus particle horizontal position is closer to the channel centerline and has a positive deviation. However, the converse trend happens when the chemical reaction heat ratio is less than 1, and the Janus particle horizontal position has a negative deviation. The Janus particle horizontal position deviation magnitude increases with increasing Damkohler number and decreasing Peclet number. The horizontal position deviation phenomenon exists for the single corroded Janus particle and two corroded Janus particle settlement processes.     

Laminar forced convection with viscous dissipation in a concentric annular ductConvection laminaire forcée avec dissipation visqueuse dans un conduit annulaire concentrique

Forced convection heat transfer in fully developed flows of viscous dissipating fluids in concentric annular ducts is analyzed analytically. Special attention has been paid to the effect of the viscous dissipation. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio and the Brinkman number. The present analytical results for the case without the viscous dissipation effect are compared with those available in the literature and an excellent agreement is observed. To cite this article: M. Avc?, O. Ayd?n, C. R. Mecanique 334 (2006).     

Experimental and numerical study of developing turbulent flow and heat transfer in convergent/divergent square ducts

 The work reported in this paper is a systematic experimental and numerical study of friction and heat transfer characteristics of divergent/convergent square ducts with an inclination angle of 1^∘ in the two direction at cross section. The ratio of duct length to average hydraulic diameter is 10. For the comparison purpose, measurement and simulation are also conducted for a square duct with constant cross section area, which equals to the average cross section area of the convergent/divergent duct. In the numerical simulation the flow is modeled as being three-dimensional and fully elliptic by using the body-fitted finite volume method and the kɛ turbulence model. The uniform heat flux boundary condition is specified to simulate the electrical heating used in the experiments. The heat transfer performance of the divergent/convergent ducts is compared with the duct with uniform cross section under three constraints (identical mass flow rate, pumping power and pressure drop). The agreement of the experimental and numerical results is quite good except at the duct inlet. Results show that for the three ducts studied there is a weak secondary flow at the cross section, and the circumference distribution of the local heat transfer coefficient is not uniform, with an appreciable reduction in the four corner regions. In addition, the acceleration/deceleration caused by the cross section variation has a profound effect on the turbulent heat transfer: compared with the duct of constant cross section area, the divergent duct generally shows enhanced heat transfer behavior, while the convergent duct has an appreciable reduction in heat transfer performance. Received on 18 September 2000 / Published online: 29 November 2001     

Combined free and forced convection for developed flow in curved pipes with finite curvature ratio

Combined free and forced convection for developed flow in a curved pipe with arbitrary curvature ratio is studied numerically. The curved pipe is heated with axially uniform heat flux, while the wall temperature is maintained peripherally uniform. The buoyancy force is accounted by the Boussinesq approximation. The effects of the Dean, Prandtl, and Rayleigh numbers and especially of a wide range of curvature ratios on the flow resistance and the average heat transfer rate are presented. The significant distortion of the dividing streamline and the appearance of the secondary flow with one dominant cell for pipe flow with higher buoyancy force and curvature ratio are also discussed.     

Heat transfer enhancement through a square duct fitted with twisted tape inserts

Experimental investigations of friction factor and heat transfer characteristics of a square duct fitted with twisted tapes of different twist ratios have been reported at nearly uniform wall temperature conditions. The experimental results indicate that the friction factor and Nusselt number increases with decreasing twist ratio. The maximum heat transfer enhancement was observed for a minimum twist ratio. The thermohydraulic performance analysis is made to identify potential benefits of using a twisted tape.     

Simultaneous heat and mass transfer inside a vertical tube in evaporating a heated falling alcohols liquid film into a stream of dry air

A numerical study of the evaporation in mixed convection of a pure alcohol liquid film: ethanol and methanol was investigated. It is a turbulent liquid film falling on the internal face of a vertical tube. A laminar flow of dry air enters the vertical tube at constant temperature in the downward direction. The wall of the tube is subjected to a constant and uniform heat flux. The model solves the coupled parabolic governing equations in both phases including turbulent liquid film together with the boundary and interfacial conditions. The systems of equations obtained by using an implicit finite difference method are solved by TDMA method. A Van Driest model is adopted to simulate the turbulent liquid film flow. The influence of the inlet liquid flow, Reynolds number in the gas flow and the wall heat flux on the intensity of heat and mass transfers are examined. A comparison between the results obtained for studied alcohols and water in the same conditions is made.     

Interaction between a rigid inclusion and a line crack under uniform heat flux

The thermoelastic displacement boundary value problem for a rigid inclusion interacting with a line crack in an infinite plane subjected to a uniform heat flux is studied, in which the rigid body rotation of the inclusion is considered. To solve the prescribed problem, we use the principle of superposition to decompose it into two groups of problems, which are further reduced to several basic subproblems including Green’s functions of edge dislocation and heat source couple, as well as the problem of a plane containing the inclusion under uniform heat flux and the problem of the inclusion subjected to a small rotation. The problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips and the rigid body rotation angles with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.