Thermal analysis of a flow of immiscible couple stress fluids in a channel

An analytical study of the entropy generation rate and heat transfer in a flow of immiscible couple stress fluids between two horizontal parallel plates under a constant pressure gradient is performed. Both plates are kept at different and constant temperatures higher than that of the fluid. The Stokes couple stress flow model is employed. The classical no-slip condition is prescribed at the plates, and continuity of the velocity, rotation, couple stress, shear stress, temperature, and heat flux is imposed at the interfaces. The velocity and temperature distributions are found analytically, and they are used to compute the entropy generation number and Bejan number. The effects of the couple stress parameter and Reynolds number on the velocity, temperature, entropy generation number, and Bejan number are investigated. It is observed that the friction near the plates in couple stress fluids decreases as the couple stress increases.     

An experimental analysis of the flow pattern in heat exchangers with an egg carton configuration (parallel,convergent and divergent cases)

An experimental analysis about the flow patterns that appear in the channel formed between two corrugated plates with an egg carton configuration is reported. The types of flow instabilities caused by the corrugated plates are identified and described by means of flow visualization experiments, and photographic sequences illustrate the flow features present for each case. The influence on flow instabilities of Reynolds number, phase angle, convergence/divergence angle and spacing between corrugated plates is investigated. The corrugated plates are set divergent and convergent in order to investigate if recirculations are broken by chaotic advection. The improvement of heat transfer in the laminar regime has become an essential task in many applications and therefore the experiments are conducted in this regime.The corrugated plates geometry provides two main advantages over the conventional plane plates: the recirculation zones observed in the longitudinal direction and the three-dimensionality of the flow, i.e. the recirculations reduce the thermal resistances while the three-dimensionality of flow generates a better mixing and a more uniform temperature distribution.This experimental study contributes to the general knowledge on the subject being the first that addresses the analysis of convergent and divergent egg carton plates. It is expected that the results presented here will shed some light as to advantageously use these geometries in the near-future heat exchangers. (Because of the improve chaotic mixing in divergent corrugated plates, this configuration may be a good option to improve heat exchangers performance, because a better mixing is always related to the presence of core fluid near exchange surfaces, and consequently an increase in temperature gradients and heat transfer.)     

Simultaneous convection and radiation in flow between two parallel plates

A numerical solution is described for simultaneous forced convection and radiation in flow between two parallel plates forming ahannel. The front plate is transparent to thermal radiation while the back one is thermally insulated. Analyses for both flow and heat are presented for the case of a non-emitting ‘blackened’ fluid. The governing equations of the stream function and the temperature together with their boundary conditions are presented in non-dimensional expressions. The solution is found to depend on eight dimensionless parameters, namely the ratio of the height of the channel to the distance between the plates, the initial dimensionless temperature, the optical thickness, the absorptivities of both plates, the Reynolds number, the Prandtl number and the heat transfer coefficient from the front plate to the surroundings. The numerical solution is obtained using a finite-difference technique. A study has been made of the effect of the initial temperature of the flow at the channel inlet, the dimensionless loss coefficient from the front plate, the absorptivity of the back plate and the optical thickness, on the temperature distribution in the channel, the heat collection efficiency and the average temperature rise in the channel. Results showed that increasing the optical thickness increases the temperature of the front plate and decreases the temperature of the back plate. Also, increasing the optical thickness increases the efficiency of heat collection, which reaches its maximum asymptotic value at an optical thickness of about 1.5. Moreover, the location of the maximum temperature is found to depend on both the optical thickness and the dimensionless heat loss coefficient from the front plate.     

Unsteady natural convection Couette flow of heat generating/absorbing fluid between vertical parallel plates filled with porous material

The extended Brinkman Darcy model for momentum equations and an energy equation is used to calculate the unsteady natural convection Couette flow of a viscous incompressible heat generating/absorbing fluid in a vertical channel(formed by two infinite vertical and parallel plates) filled with the fluid-saturated porous medium.The flow is triggered by the asymmetric heating and the accelerated motion of one of the bounding plates.The governing equations are simplified by the reasonable dimensionless parameters and solved analytically by the Laplace transform techniques to obtain the closed form solutions of the velocity and temperature profiles.Then,the skin friction and the rate of heat transfer are consequently derived.It is noticed that,at different sections within the vertical channel,the fluid flow and the temperature profiles increase with time,which are both higher near the moving plate.In particular,increasing the gap between the plates increases the velocity and the temperature of the fluid,however,reduces the skin friction and the rate of heat transfer.     

Comparison of different kinetic models for the heat transfer problem

The steady-state heat transfer problem between two parallel plates is investigated using kinetic models of the Boltzmann equation: BGK, S-model and ES-model. The discrete velocity method is used to determine the values of physical parameters: density, bulk velocity, temperature and heat flux. The obtained results are compared with the analytical expressions and some experimental data.     

Stochastic thermoelastic problem of a functionally graded plate under random temperature load

This study attempts to derive the statistics of temperature and thermal stress in functionally graded material (FGM) plates exposed to random external temperatures. The thermomechanical properties of the FGM plates are assumed to vary arbitrarily only in the plate thickness direction. The external temperatures are expressed as random functions with respect to time. The transient temperature field in the FGM plate is determined by solving a nonhomogeneous heat conduction problem for a multilayered plate with linear nonhomogeneous thermal conductivity and different homogeneous heat capacity in each layer. The autocorrelations and power spectrum densities (PSDs) of temperature and thermal stress are derived analytically. These statistics for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304) are computed under the condition that the fluctuation in the external temperature can be considered as white noise or a stationary Markov process.     

Dissipative effect on convective MHD channel flow

By means of a numerical analysis viscous and Joulean dissipations are considered in a combined forced and free convective MHD flow between two vertical plates that are subjected simultaneously to a pressure and a temperature gradient. It is shown that the dissipations tend to increase the flow rate and decrease the heat transfer, and they destabilize the system when the high temperature is at the lower side.     

Convective heat and mass transfer from a falling film to a laminar gas stream

A numerical study has been made of convective heat and mass transfer from a falling film to a laminar gas stream between vertical parallel plates. The effects of gas-liquid phase coupling, variable thermophysical properties, and film vaporization have been considered. Simultaneous mass, momentum and heat transfer between liquid film and gas stream is numerically studied by solving the respective governing equations for the liquid film and gas stream together. The influences of the inlet liquid temperature and liquid flowrate on the cooling of liquid film are examined for air-water and air-ethanol systems. Results show that the heat transfer from the gas-liquid interface to the gas stream is predominantly determined by the latent heat transfer connected with film evaporation. Additionally, better liquid film cooling is noticed for the system having a higher inlet liquid temperature or a lower liquid flowrate.     

Optimum separation of asymmetrically heated sub-channels forming a bundle: influence of simultaneous flow and temperature

This paper focuses on laminar heat and fluid flow in an array of sub-channels placed in an uniform stream, which is characterized by a fixed pressure difference and a developing velocity and temperature. The dominant feature of the study deals with the optimal selection of the plate-to-plate separation between subchannels placed in a specified volume that renders maximum heat transmission from the heated plates to the moving fluid. Asymmetric heating from one plate in a typical sub-channel to either air or water is produced by uniform temperature in one case and uniform heat flux in the other case. Upon relaxing the vital condition of developing velocity, the numerical computations for the optimal separation and the maximum heat transmission incurred in little error for both cooling fluids.     

Natural convection with surface radiation from a planar heat generating element mounted freely in a vertical channel

Experiments and numerical simulations have been conducted to study the conjugate heat transfer by natural convection and surface radiation from a planar heat generating element placed centrally between two adiabatic vertical plates. The relevant problem dependent parameters considered in this study are modified Rayleigh number, channel aspect ratio, stream-wise location of the heat generating element, and surface emissivities of the heat generating element and the adiabatic side plates. Experiments are conducted for different values of modified Rayleigh number ranging from 3.2 × 10⁵ to 1.6 × 10⁷ and surface emissivities 0.05, 0.55, 0.75 and 0.85. The interdependence between the heat transfer mechanism and the flow field under the influence of surface radiation on natural convection is explored and discussed. Experimental correlations for total and convective Nusselt number, and dimensionless temperature in terms of relevant parameters have been developed. The mathematical model governing the problem has been numerically solved using a commercial computational fluid dynamics package FLUENT 6.3 and the numerical predictions substantiate the experimental observations.     

Heat transfer between infinite parallel plates in a rarefied gas

The problem of heat transfer between two infinite parallel plates is investigated on the basis of equations obtained by averaging the Boltzmann kinetic equation with respect to the transverse velocity. A numerical solution of the problem is accomplished for a temperature ratio between the plates of T₀/T₁=1/4 and for various Knudsen numbers.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 87–91, January–February, 1972.     

Effect of ion slip on the time-varying Hartmann flow of a non-Newtonian viscoelastic fluid with heat transfer

Ion slip in a time-varying Hartmann flow of a conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal insulating porous plates is studied with allowance for heat transfer. A uniform and constant pressure gradient is applied in the axial direction. An external uniform magnetic field and uniform suction and injection through the surface of the plates are applied in the normal direction. The two plates are maintained at different but constant temperatures; the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained with the use of finite differences, and the effect of various physical parameters on both the velocity and temperature fields is discussed.     

Natural convection heat transfer from sinusoidal wavy surfaces

This paper presents the results of an experimental study of the natural convection heat transfer characteristics of sinusoidal wavy surfaces on vertical plates maintained at a constant temperature. Local heat transfer coefficients were obtained with a Mach-Zehnder interferometer. The heat transfer from the wavy surfaces, compared to a plane plate of equal projected area, increased with increasing amplitude-to-wavelength ratio. The heat transfer was increased by about 15 percent at an amplitude-to-wavelength ratio of 0.3; for this case a flow instability was detected. A quantitative comparison with a previously published numerical investigation is also presented. In general, there is agreement between the two studies.     

轴对称自由振动功能梯度材料微圆板中的热弹性阻尼

基于经典弹性薄板理论和单向耦合热传导理论,研究了材料性质沿厚度连续变化的功能梯度微圆板的热弹性阻尼特性．首先,考虑热力耦合效应,建立了功能梯度微圆板轴对称横向自由振动微分方程．然后,忽略温度梯度在面内的变化,建立了单向耦合变系数一维热传导方程．采用分层均匀化近似方法,将变系数热传导方程转化为一系列常系数的微分方程,利用上下表面的热边界条件和层间连续性条件获得了微圆板温度场解析解．将所得温度场代入微圆板的自由振动微分方程,得到了包含热弹性阻尼的复频率,从而获得了反映热弹性阻尼水平的逆品质因子．最后,针对材料性质沿板厚按幂函数变化的陶瓷-金属功能梯度微圆板,定量地分析材料梯度指数、几何尺寸、边界条件、温度环境等对微圆板热弹性阻尼的影响．     

A numerical study of unsteady gas-solid flow between parallel porous plates submitted to a magnetic field

This paper studies unsteady laminar flow of dusty conducting fluid between parallel porous plates with temperature dependent viscosity and the Network Simulation Method (NSM) is used to solve the governing nonlinear partial differential equations. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates that are assumed to be porous. The NSM is applied to solve the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. With this method, only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. The velocity and temperature are studied for different values of the viscosity and magnetic field parameters.     

Asymptotic Nusselt numbers for dissipative non-Newtonian flow through ducts

General expressions for fully developed temperature profiles and Nusselt numbers are obtained for heat transfer to non-Newtonian fluid flow between parallel plates and through circular pipes subjected to a uniform wall heat flux. The effect of viscous dissipation is taken into account since it may often be significant in the flow of non-Newtonian fluids. Asymptotic Nusselt numbers for three widely used models, i.e. the power law fluid, the Bingham plastic, and the Ellis fluid are obtained as specific results.     

Magnetic Heat Transfer Enhancements on Fin-Tube Heat Exchangers

通过DNS方法解耦合的三维非稳态流动和固流体能量方程组,本文研究了两平行磁质平板和圆管所组成的肋片式圆管换热器单元与震荡流体间的传热过程.对不同的磁场频率和振幅的三维动态流热场的模拟结果表明增强磁场频率和振幅能很有效地增加周期平均传热强度达到强化传热的目的.     

Exact solutions of incompressible Couette flow with porous walls for slightly rarefied gases

In this work, the transient incompressible Couette flow and steady-state temperature profiles between two porous parallel plates for slightly rarefied gases are solved exactly. The first-order approximation of slip velocity at the boundaries is used in the formulation. The solution is also applicable for Couette flow in micro-channels under certain circumstances. The influences of mass transfer and a nondimensional slip parameter on slip velocities are discussed. It is also found that the transient slip velocities at the walls are greatly different from the steady-state velocity slips. The influences of velocity slip and temperature slip parameters on the temperature distribution and heat transfer at the walls are analyzed and discussed. It is shown that the slip parameters can greatly change the temperature profiles and heat transfer characteristics at the walls.     

Anisotropic conduction of heat caused by molecular orientation in a flowing polymeric liquid

To demonstrate the influence of molecular orientation on the heat conduction in a flowing polymeric liquid, we consider a variant of the Graetz-Nusselt problem. A polymeric liquid is flowing between two flat, parallel plates with a sudden change in the wall temperature. The temperature distribution in the entrance region is calculated numerically taking viscous dissipation into account. It is assumed that the material properties are independent of the temperature. It is shown that the change in the temperature distribution in the fluid caused by molecular orientation is large enough to affect polymer processing significantly.     

Some analytical solutions for viscometric flows of power-law fluids with heat generation and temperature dependent viscosity

Exact solutions are given for flows of power-law fluids, with heat generation and temperature dependent viscosity, in three situations, namely pressure flow through a circular tube, shear flow between rotating concentric cylinders and shear flow between parallel plates. The application of the results to the experimental determination of the material parameters is discussed and it is shown that the method usually adopted in practice, does in fact lead to accurate estimates.