MODELING OF CONJUGATE HEAT TRANSFER BETWEEN PARALLEL PLATES SEPARATED BY A HYDRODYNAMICALLY DEVELOPED LAMINAR FLOW BY THE QUADRUPOLE METHOD

The thermal quadrupole method allows the quasi-analytical modeling of heat transfer through a hydrodynamically developed laminar flow between two parallel plates. It is a meshless method based on an integral transform technique. The principle consists of calculating the transfer matrix linking temperature and flux density between the two walls of the channel. The convection-diffusion equation which governs heat transfer in the flow is solved analytically. The interest of this “fluid quadrupole” is to allow the modeling of the conjugate heat transfer between the channel and thick walls through the analytical formalism of the quadrupole method. It is cheked, in the case of mini-microchannels, that the local convective heat transfer coefficient h is rather strongly dependent on the wall nature.     

Heat transfer enhancement in self-sustained oscillatory flow in a grooved channel with oblique plates

The aim of this work is to investigate the conjugate heat transfer in periodic mounted obstacles channel with oblique plates as vortex generators installed at the rear obstacles on the opposite wall. Special attention will be paid to the analysis of flow evolution and heat transfer enhancement in the intermediate and low Reynolds number range without recourse to turbulent flow. Various physical arrangements are considered as plate length, tilt angle and Reynolds number in order to investigate their influence on the thermal and flow characteristics in the steady state as well as in the self-sustained oscillatory flow.     

Effect of Conjugate Heat Transfer on MEMS-Based Thermal Shear Stress Sensor

ABSTRACT

The effect of conjugate heat transfer resulting from a microelectromechanical systems (MEMS)-based thermal shear stress is investigated. Due to the length-scale disparity and large solid–fluid thermal conductivity ratio, a two-level computation is used to examine the relevant physical mechanisms and their influences on wall shear stress. The substantial variations in transport properties between the fluid and solid phases and their interplay with regard to heat transfer and near-wall fluid flow structures are investigated. It is demonstrated that for state-of-the-art sensor design, the buoyancy effect can noticeably affect the accuracy of the shear stress measurement.     

Numerical investigation on conjugate heat transfer to supercritical CO2 in membrane helical coiled tube heat exchangers

ABSTRACT

Conjugate heat transfer to supercritical CO₂ in membrane helical coiled tube heat exchangers has been numerically investigated in the present study. The purpose is to provide detailed information on the conjugate heat transfer behavior for a better understanding of the abnormal heat transfer mechanism of supercritical fluid. It could be concluded that the supercritical fluid mass flux and vertical/horizontal placement would significantly affect the abnormal heat transfer phenomenon in the tube side. The flow field of supercritical fluid is affected by both the buoyancy and centrifugal force in the conjugate heat transfer process. The local wall temperature and heat transfer coefficient in the tube side would rise and fall periodically for the horizontal heat exchanger, but this phenomenon will gradually disappear with the increase of the mass flow rate or fluid temperature in the tube side. The dual effects of buoyancy force and centrifugal force lead to the deflection of the second flow direction for the vertical placement, which further results in the heat transfer deterioration region on the top-generatrix wall for the downward flow being larger than that for the upward flow.     

Simulation of Conjugate Heat Transfer Using the Lattice Boltzmann Method

The Lattice Boltzmann Method (LBM) is utilized to investigate conjugate heat transfer. Hot and cold streams enter the computational domain, and heat transfer takes place between the two streams through a finite thickness and finite thermal conductivity wall. The main objective of the work is to demonstrate that LBM can solve conjugate heat transfer by using one energy equation for solid and fluid phases. The flux continuity insures automatically. Furthermore, the effects of extended surfaces were investigated on the rate of heat transfer and pressure drop.     

Thermal Interaction between Two Forced‐Convection Boundary Layers across a Conductive Solid Wall

This paper presents an analytical model to the problem of thermal interaction between two forced convection layers of parallel flow on opposite wall sides. The problem is formulated in dimensionless terms to generalize the solution. The two convection layers are analyzed separately by employing the integral technique. The two analyses are then coupled by applying the solid–fluid interfacial conditions. The study indicates that the thermal interaction process is governed mainly by two dimensionless parameters relating the heat transfer effectiveness of two interactive convection modes and wall conduction. The effects of governing parameters on the flow and heat transfer characteristics of two coupled convection layers are documented. Results regarding mean conjugate Nusselt number are obtained for wide ranges of governing parameters.     

Heat transfer characteristics of a partially insulated tube with an impulsive temperature rise

The heat transfer for a laminar forced convection inside a two dimensional planar symmetric duct is analyzed. The fluid passage is formed by two parallel plates, and flow is fully developed and incompressible. Flow is isothermal to a position x_o = 0, where the wall temperature jumps impulsively to T₁ > T₀ and remains at this value up to the position x₁, where it jumps back T₀. The problem is considerably simplified by introducing a transformation to reduce the heat transfer problem to the standard thermal entrance region problem for flow between parallel plates. Various heat transfer characteristics for different values of Prandtl and Nusselt numbers are analyzed and found to be physically realistic.     

Computation of the flow and thermal fields in a thermoacoustic refrigerator

The hydro- and thermodynamic processes near and within two-dimensional stack plates are simulated by numerical solution of the unsteady compressible Navier–Stokes, continuity, energy equations, and the equation of state (for air as the working fluid). The stack is assumed to consist of flat plates of equal thickness. The second order mean velocity field is computed in the neighborhood of the stack plates. In the stack plate extremities the vortical mean flow is observed which is due to the abrupt change of a slip condition to a no-slip velocity boundary condition. The temperature of the stack is governed by the energy equation; therefore the entire problem is treated as a conjugate heat transfer problem. The temperature fields in the neighborhood of the solid stack plate are also observed. From the location of the heat exchangers in Fig. 1(a), it is obvious that knowledge of the flow and thermal fields at the edges of the stack plates is the key for the development of a systematic design methodology for heat exchangers in thermoacoustic devices.     

Local effects of longitudinal heat conduction in plate heat exchangers

In a plate heat exchanger, heat transfer from the hot to the cold fluid is a multi-dimensional conjugate problem, in which longitudinal heat conduction (LHC) along the dividing walls often plays some role and can not be neglected. Large-scale, or end-to-end, LHC is always detrimental to the exchanger’s effectiveness. On the contrary, if significant non-uniformities exist in the distribution of either convective heat transfer coefficient, small-scale, or local, LHC may actually enhance the exchanger’s performance by improving the thermal coupling between high heat transfer spots located on the opposite sides of the dividing wall.     

Monitoring of transient 3D temperature distribution and thermal stress in pressure elements based on the wall temperature measurement

Abstract

Two methods for monitoring the thermal stresses in pressure components of thermal power plants are presented. In the first method, the transient temperature distribution in the pressure component is determined by measuring the transient wall temperature at several points located on the outer insulated surface of the component. The transient temperature distribution in the pressure component, including the temperature of the inner surface is determined from the solution of the inverse heat conduction problem (IHCP). In the first method, there is no need to know the temperature of the fluid and the heat transfer coefficient. In the second method, thermal stresses in a pressure component with a complicated shape are computed using the finite element method (FEM) based on experimentally estimated fluid temperature and known heat transfer coefficient. A new thermometer with good dynamic properties has been developed and applied in practice, providing a much more accurate measurement of the temperature of the flowing fluid in comparison with standard thermometers. The heat transfer coefficient on the inner surface of a pressure element can be determined from the empirical relationships available in the literature. A numerical-experimental method of determination of the transient heat transfer coefficient based on the solution of the 3D-inverse heat conduction problem has also been proposed. The heat transfer coefficient on the internal surface of a pressure element is determined based on an experimentally determined local transient temperature distribution on the external surface of the element or the basis of wall temperature measurement at six points located near the internal surface if fluid temperature changes are fast. Examples of determining thermal and pressure stresses in the thick-walled horizontal superheater header and the horizontal header of the steam cooler in a power boiler with the use of real measurement data are presented.     

Liquid cooling of a microprocessor: experimentation and simulation of a sub-millimeter channel heat exchanger

Abstract

A heat exchanger dedicated to the cooling of a microprocessor has been designed and realized. It consists of a bottom wall in contact with the processor and a cover that has been dug to a depth of 200?μm on one side and 1?mm on the other. Thus, by turning the cover, the hydraulic diameter of the channel can be changed. Both hydraulic and thermal performances of this heat exchanger have been experimentally tested. Three-dimensional numerical simulations were simultaneously carried out and good agreement was obtained. The influence of the distributor and the collector on the distribution of fluid flow and heat fluxes is emphasized. A new concept of micro-heat exchanger is proposed for the cooling of electronics devices for which wall to fluid heat exchange quality and pumping effect are critical. The ability of a liquid heat exchanger involving a dynamic deformation of one of its walls to cool a microprocessor is investigated. Three-dimensional transient numerical simulations of fluid flow and conjugate heat transfer were performed using commercial software. Effect of geometrical and actuation parameters has been explored, demonstrating the ability of such heat exchanger to simultaneously pump the fluid and enhance the heat transfer.     

The analysis of conjugate problems of conduction and convection for non-Newtonian fluids past a flat plate

In this paper, the conjugate problems of laminar forced convection in non-Newtonian fluid flow and heat conduction inside a heated flat plate is studied. A conjugate parameter ζ is proposed to reflect the characteristics of the conjugate problems. The value of the conjugate parameter lies among 0 and 1 and the two limiting values correspond to the ordinary convection problem with boundary condition of constant wall heat flux (ζ = 0) and constant wall temperature (ζ = 1), respectively. In addition, the power-law model is used for non-Newtonian fluids with exponent n < 1 for pseudoplastics, n = 1 for Newtonian fluids and n > 1 for dilatant fluids. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of conjugate problems and the whole regime of the non-Newtonian fluids. The effects of the conjugate parameter, the power-law viscosity index and the generalized Prandtl number on the temperature profiles, as well as on the local heat transfer rate are clearly illustrated.     

Steady Conjugate Heat Transfer from X-Ray or Laser-Heated Sphere in External Flow at Low Reynolds Number

ABSTRACT

A laser or an X-ray beam is used to heat a sphere that is immersed in uniform external flow. Temperature distributions as well as local and average convective heat transfer coefficients are calculated in order to evaluate the efficacy of cooling the solid sphere. The present work extends previous studies by: (1) applying a unique heat source imposed by irradiating the sphere with an intense X-ray energy beam; (2) performing the conjugate heat transfer analysis in fluid and solid domain; and (3) calculating the internal and surface temperature distribution. Absorption of the irradiation results in nonuniform heat generation, having an exponential spatial distribution of heat source. The limiting cases of heat source distribution are localized surface “laser” heating and near-uniform heat generation throughout the sphere. Key results are reported for two different source beam sizes (small and large) striking the sphere, with comparison to the solution for the isothermal wall boundary condition.     

Hybrid formulation and solution for transient conjugated conduction–external convection

This work presents a hybrid numerical–analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid–solid interface. This conjugated conduction–convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid–fluid interface. From the available steady velocity distributions, a hybrid numerical–analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

CONJUGATE HEAT AND MASS TRANSFER IN CONVECTIVE DRYING OF POROUS MEDIA

Abstract

A methodology for the analysis of conjugate problems in the convective drying of porous media is presented. In this study, the interface between porous medium and external convective flow is treated as an internal boundary within a two-phase system rather than a geometric limit. The problems of solid drying and convection boundary layer are connected by expressing the continuity of the state variables and their respective fluxes through the interface. The performance of the proposed methodology is evaluated by applying it to wood-drying problems. The analysis of the drying of porous media as a conjugate problem allows the assessment of the effect of the heat and mass transfer within the solid on the transfer in the adjacent fluid, providing good insight on the complexity of the transfer mechanisms.     

Recent Studies on Fluid Flow and Heat Transfer in Thermal Microdevices

Control and measurement of fluid flow and heat transfer in microdevices is of great importance to the development and application of MEMS and Bio-MEMS such as thermal inkjet printer heads, microchemical reactors, and PCR. Thus, the detailed flow behavior, in particular the two-phase flow in microdevices, has attracted much attention in recent years. Several types of thermal micropumps have been developed, although there is still room for further development. Various techniques for measuring the temperature, which are applicable to microscale devices, have also been proposed. As the cooling problem in microdevices becomes increasingly significant, a prospective view on integrated heat and mass transfer is quite necessary. Thus, in this work, some issues and future prospects for fluid dynamics and heat transfer of thermal microdevices are presented and discussed, in terms of thermocapillary pump, temperature measurement in microdevices, and flow near an evaporating meniscus.     

Effects of thermal radiation on micropolar fluid flow and heat transfer over a porous shrinking sheet

The effects of thermal radiation on the flow of micropolar fluid and heat transfer past a porous shrinking sheet is investigated. The self-similar ODEs are obtained using similarity transformations from the governing PDEs and are then solved numerically by very efficient shooting method. The analysis reveals that for the steady flow of micropolar fluid, the wall mass suction needs to be increased. Dual solutions of velocity and temperature are obtained for several values of the each parameter involved. For increasing values of the material parameter K, the velocity decreases for first solution, whereas, for second solution it increases. Due to increase of thermal radiation, the temperature and thermal boundary layer thickness reduce in both solutions and also the heat transfer from the sheet enhances with thermal radiation.     

Improvement of the heat transfer quality by air cooling of three-heated obstacles in a horizontal channel using the lattice Boltzmann method

This study focuses on the cooling of three heated obstacles with different heights mounted on the bottom of the channel wall using different aspects that influence the enhancement of the heat exchange, as is known in the concept of cooling electronic devices. The lattice Boltzmann method associated with multiple relaxation times (LBM-MRT) was adopted to simulate the physical configurations of the studied system. In this context, the D2Q9 and D2Q5 models are applied to describe the fluid flow behavior and conjugate heat transfer, respectively. The evaluation of heat exchange between the cold fluid and three-heated obstacles has been accurately analyzed under the effect of several parameters such as Reynolds number, obstacle spacing, and thermal conductivity ratio. In addition, the setting of two and three fluids flow inlets were also studied. The results are presented in terms of streamlines, isotherms, and local Nusselt curves. The heat transfer increases with increasing solid-fluid thermal conductivity. It is also more pronounced for large Reynolds numbers. Moreover, the heat transfer significantly enhances for the second and third obstacles when obstacle spacing increases. The improvement of the heat transfer is performed by the implementation of several jet flows in the studied system.     

Effects of heat absorption and thermal radiation on heat transfer in a fluid–particle flow past a surface in the presence of a gravity field

A continuum two-phase fluid–particle model accounting for fluid-phase heat generation or absorption and thermal radiation is developed and applied to the problem of heat transfer in a particulate suspension flow over a horizontal heated surface in the presence of a gravity field. Analytical solutions for the temperature distributions and the wall heat fluxes for both phases are obtained. Two cases of wall thermal conditions corresponding to stationary and periodic temperature distributions are considered. Numerical evaluations of the analytical solutions are performed and the results are reported graphically to elucidate special features of the solutions. The effects of heat absorption and thermal radiation are illustrated through representative results for the temperature distributions and heat fluxes of both phases for various fluid–particle suspensions. It is found that heat absorption increases the total heat transfer rate for various particulate volume fraction levels while thermal radiation decreases it.