Effect of variable thermal conductivity and viscosity on single phase convective heat transfer in slip flow

For a variety of fields in which micro-mechanical systems and electronic components are used, fluid flow and heat transfer at the microscale needs to be understood and modeled with an acceptable reliability. In general, models are prepared by making some extensions to the conventional theories by including the scaling effects that become important for microscale. Some of these effects are; axial conduction, viscous dissipation, and rarefaction. In addition to these effects, temperature variable thermal conductivity and viscosity may become important in microscale gas flows due to the high temperature gradients that may exist in the fluid. For this purpose, simultaneously developing, single phase, laminar and incompressible air flow in a microtube and in the micro gap between parallel plates is numerically analyzed. Navier–Stokes and energy equations are solved and the variation of Nusselt number along the channel is presented in tabular and graphical forms as a function of Knudsen, Peclet, and Brinkman numbers, including temperature variable thermal conductivity and viscosity.     

Film cooling and heat transfer with air injection through two rows of compound angle holes.

This paper describes the results of an experimental investigation into the film cooling effectiveness and the heat transfer characteristics of two staggered rows of compound angle holes. The effects of hole spacings and turbulence intensity on film cooling and heat transfer characteristic are investigated for three blowing rates; 0.5, 1.0 and 1.7. An attempt has been made to correlate the film cooling effectiveness results using a two dimensional correlation group. The increase of spanwise hole spacing results in a reduction in the film cooling effectiveness and an increase in the Stanton number. Increasing the freestream turbulence intensity has caused a significant reduction in the local film cooling effectiveness but increased the Stanton number, especially at blowing rate of 0.5.     

Effect of heat transfer on the plane-channel poiseuille flow of a thermo-viscous fluid

A steady-state plane channel flow of viscous incompressible fluid with no-slip and heat transfer boundary conditions is considered. The flow is induced by a fixed pressure difference and the fluid viscosity depends on the temperature in accordance with a power law. It is shown numerically that the dependence of the Peclet number on the nondimensional pressure difference is not single-valued. An investigation of the solution’s dependence on the Biot number shows that for Biot numbers greater than unity the velocity profile has a point of inflection. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–80, March–April, 2000. The work received financial support from the Russian Foundation for Basic Research (project N97-01-00063).     

Non-Darcy Mixed Convection in a Vertical Porous Channel with Boundary Conditions of Third Kind

Combined free and forced convection flow in a parallel plate vertical channel filled with porous matrix is analyzed in the fully developed region with boundary conditions of third kind. The flow is modeled using the Brinkman?CForchheimer-extended Darcy equations. The plates exchange heat with an external fluid. Both conditions of equal and different reference temperatures of the external fluid are considered. Governing equations are solved numerically by shooting technique that uses classical explicit Runge?CKutta scheme and Newton?CRaphson method as a correction scheme and analytically using perturbation series method for Darcy model. The velocity field, the temperature field and Nusselt numbers are obtained for governing parameters such as porous parameter, inertia term and perturbation parameter for equal and unequal Biot numbers and are displayed graphically. The dimensionless mean velocity and bulk temperature are also determined. It is found that the numerical solutions agree for small values of the perturbation parameter in the absence of the inertial forces.     

Forced convection heat transfer of Giesekus viscoelastic fluid in pipes and channels

A theoretical solution is presented for the convective heat transfer of Giesekus viscoelastic fluid in pipes and channels, under fully developed thermal and hydrodynamic flow conditions, for an imposed constant heat flux at the wall. The fluid properties are taken as constant and axial conduction is negligible. The effect of Weissenberg number (We), mobility parameter (α) and Brinkman number (Br) on the temperature profile and Nusselt number are investigated. The results emphasize the significant effect of viscous dissipation and fluid elasticity on the Nusselt number in all circumstances. For wall cooling and the Brinkman number exceeds a critical value (Br ₁), the heat generated by viscous dissipation overcomes the heat removed at the wall and fluid heats up longitudinally. Fluid elasticity shifts this critical Brinkman number to higher values.     

Transient heat transfer from a solid sphere translating at low reynolds number

In this paper the heat transfer from a solid spherical particle translating at low Reynolds number is analytically examined for the limit of vanishing Peclet number. The temperature distribution within the solid sphere is treated as fully transient while the fluid phase is considered to be quasisteady. The temperature field in the dispersed phase is obtained by a singular perturbation expansion of the Acrivos-Taylor type. The time-dependence in the solid phase is handled by means of the Laplace transform. This approach allows the temperature and heat flux continuity conditions at the solid-liquid interface to be exactly satisfied. The solution in the time domain appears in the form of infinite series which have associated with them a set of eigenvalues for every order of the perturbation expansion. The Nusselt number to orderPe, however, depends only on the leading order eigenvalues. An analytical limit of the Nusselt number for large values of time is also obtained.     

Influence of temperature dependent conductivity of a nanofluid in a vertical rectangular duct

Natural convective heat transfer and fluid flow in a vertical rectangular duct filled with a nanofluid is studied numerically assuming the thermal conductivity to be dependent on the fluid temperature. The transport equations for mass, momentum and energy formulated in dimensionless form are solved numerically using finite difference method. Particular efforts have been focused on the effects of the thermal conductivity variation parameter, Grashof number, Brinkman number, nanoparticles volume fraction, aspect ratio and type of nanoparticles on the fluid flow and heat transfer inside the cavity. It is found that the flow was enhanced for the increase in Grashof number, Brinkman number and aspect ratio for any values of conductivity variation parameter and for regular fluid and nanofluid. The heat transfer rate for regular fluid is less than that for the nanofluid for all governing parameters.     

Analysis of heat transfer in a partially wet radial fin assembly during dehumidification

This paper presents the analysis of heat transfer in a partially wet annular fin assembly during the process of dehumidification. In past studies, both fully dry and fully wet fins have been analyzed. New analytical formulation leading to a closed-form solution has been developed for a partially wet fin, which is most common in dehumidifier coil operation during air conditioning. The parameters that influenced the heat transfer rate in the finned tube structure are ratio of fin and wall thermal conductivities, ratio of fin thickness to fin pitch, ratio of wall thickness to fin pitch, ratio of fin length to fin pitch, cold fluid Biot number, ambient Biot number, the relative humidity and dry bulb temperature of the incoming air, and the cold fluid temperature inside the coil. Calculations were carried out to study the performance of the heat exchanger. The computed results included the temperature distribution in the wall and the fin and the fin efficiency.     

Axisymmetric Powell-Eyring fluid flow with convective boundary condition: optimal analysis

The effects of axisymmetric flow of a Powell-Eyring fluid over an impermeable radially stretching surface are presented. Characteristics of the heat transfer process are analyzed with a more realistic condition named the convective boundary condition. Governing equations for the flow problem are derived by the boundary layer approximations. The modeled highly coupled partial differential system is converted into a system of ordinary differential equations with acceptable similarity transformations. The convergent series solutions for the resulting system are constructed and analyzed. Optimal values are obtained and presented in a numerical form using an optimal homotopy analysis method (OHAM). The rheological characteristics of different parameters of the velocity and temperature profiles are presented graphically. Tabular variations of the skin friction coefficient and the Nusselt number are also calculated. It is observed that the temperature distribution shows opposite behavior for Prandtl and Biot numbers. Furthermore, the rate of heating/cooling is higher for both the Prandtl and Biot numbers.     

Experimental study of convective heat transfer from a rotating finned tube in transverse air flow

 The convective heat transfer from fins to air has been evaluated using rotating annular fins subjected to an air flow parallel to the fins. The fin cooling is studied using infrared thermography. The thermal balance in a fin during its cooling process allows us to obtain the heat transfer coefficient from the temperature time evolution of the fin. Moreover, Particle Image Velocimetry allows us to obtain the flow field in the mid-plane between two fins. The influence of the fin spacing on the convective heat transfer is studied for various velocities of the superposed air flow and various fin rotational speeds. These tests were carried out for air flow Reynolds numbers (based on the shaft diameter and the velocity of the superposed air flow) between 2550 and 18200 and rotational Reynolds numbers (based on the shaft diameter and the peripheral speed) between 800 and 2.9 × 10⁴, for different fin spacings. Received: 14 May 1999/Accepted: 8 October 1999     

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.     

Mixed convection flow in vertical channel with boundary conditions of third kind in presence of heat source/sink

The effects of viscous dissipation and heat source/sink on fully developed mixed convection for the laminar flow in a parallel-plate vertical channel are investigated.The plate exchanges heat with an external fluid.Both conditions of equal and different reference temperatures of the external fluid are considered.First,the simple cases of the negligible Brinkman number or the negligible Grashof number are solved analytically.Then,the combined effects of buoyancy forces and viscous dissipation in the presence of heat source/sink are analyzed by a perturbation series method valid for small values of the perturbation parameter.To relax the conditions on the perturbation parameter,the velocity and temperature fields are solved by using the Runge-Kutta fourth-order method with the shooting technique.The velocity,temperature,skin friction,and Nusselt numbers at the plates are discussed numerically and presented through graphs.     

Heat transfer in magnetohydrodynamic laminar radial channel flow

Heat transfer in the steady axisymetrical laminar source flow of an incompressible electrically conducting fluid between two parallel disks in the presence of a transverse applied magnetic field is analyzed. The energy equation is solved numerically for the temperature distribution, where both Joulean and viscous heating are included. Both local and average Nusselt numbers for the case of constant wall temperature are evaluated. For fluids of moderate and high Prandtl numbers, Nusselt number is seen to be a strong function of both Hartmann number and a heat generation parameter together with a modified Peclet number. However, for fluids of small Prandtl number, Joulean heating and viscous dissipation can be neglected without appreciable error.     

Heat transfer in laminar entrance region of a flat channel for the temperature boundary condition of the third kind

To explore the influence of the developing flow in a flat channel on the laminar forced convection heat transfer, the non-linear momentum and the linear energy equation are solved successively by employing the Galerkin-Kantorowich method of variational calculus. Assuming constant fluid properties, negligible axial diffusion and temperature boundary condition of the third kind, semi analytic solution for velocity and temperature is derived. The local Nusselt numbers are tabulated for various values of Biot and Prandtl number.     

Rewetting analysis of hot surfaces with internal heat source by the heat balance integral method

A two region conduction-controlled rewetting model of hot vertical surfaces with internal heat generation and boundary heat flux subjected to constant but different heat transfer coefficient in both wet and dry region is solved by the Heat Balance Integral Method (HBIM). The HBIM yields the temperature field and quench front temperature as a function of various model parameters such as Peclet number, Biot number and internal heat source parameter of the hot surface. Further, the critical (dry out) internal heat source parameter is obtained by setting Peclet number equal to zero, which yields the minimum internal heat source parameter to prevent the hot surface from being rewetted. Using this method, it has been possible to derive a unified relationship for a two-dimensional slab and tube with both internal heat generation and boundary heat flux. The solutions are found to be in good agreement with other analytical results reported in literature.     

波纹竖板层流降膜蒸发传热的分析

对高粘度液体在等温正弦形波纹壁面上的自由降落与蒸发建立了摄动分析模型。得到了流动的分析解和蒸发传热的数值解。考察了壁面波纹的波幅和波数、液膜表面张力及贝克利数对流动与传热的影响,结果表明,加大波纹的波幅、适当选择波数、减小贝克利数可增强传热,而表面张力对蒸发传热的影响较小。     

Turbulent heat transfer to dilute aqueous suspensions of titanium dioxide in pipes

An experimental investigation into turbulent heat transfer to pseudoplastic titanium dioxide suspensions in pipes has been carried out. Existing heat transfer correlations, including the analogy equations between heat and momentum transfer, generally predict higher Nusselt and Stanton numbers than those observed experimentally. However, a simplified heat transfer model based on the consideration of the laminar sub-layer at the wall and the turbulent core correlates the heat transfer results for heating as well as cooling. The limitations of the existing analogy equations between heat and momentum transfer are discussed.     

Viscous dissipation effects of power-law fluid flow within parallel plates with constant heat fluxes

Both hydro-dynamically and thermally fully developed laminar heat transfer of non-Newtonian fluids between fixed parallel plates has been analyzed taking into account the effect of viscous dissipation of the flowing fluid. Thermal boundary condition considered is that both the plates kept at different constant heat fluxes. The energy equation, and in turn the Nusselt number, were solved analytically in terms of Brinkman number and power-law index. The findings show that the heat transfer depends on the power-law index of the flowing fluid. Pseudo-plastic and dilatant fluids manifest themselves differently in the heat transfer characteristics under the influence of viscous dissipation. Under certain conditions, the viscous dissipation effects on heat transfer between parallel plates are significant and should not be neglected.     

Wiener–Hopf solution of rewetting of an infinite cylinder with internal heat generation

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite cylinder with heat generation has been solved by Wiener–Hopf technique. The analytical solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat generation rate. Also, the dry out heat generation rate is obtained by setting the Peclet number equal to zero, which gives the maximum permissible heat generation so as to prevent the dry out of the coolant.     

Effects of temperature-dependence of viscosity and viscous dissipation on laminar flow heat transfer in circular tubes

Heat transfer effects of variable viscosity and viscous dissipation for heated developing laminar flows in circular tubes have been investigated. Three studies are reported covering a comprehensive range of input data for the case of constant wall heat flux. Initially the program was used to predict the effect on heat transfer of temperature-dependent viscosity via a general temperature power relation. In addition, predictions were made for nine particular fluids covering a range of Prandtl numbers from 0.025 to 12 500, and a range of Brinkman numbers from 1.8 × 10^?10 to 6.8 × 10³. A more detailed study was made for two particular oils covering a range of practical interest. For the liquids considered their viscosity temperature-dependence resulted in enhancement of heat transfer, whereas for fluids with a Prandtl number <200 the effect of viscous dissipation was negligible, and for fluids of a Brinkman number > × 10^?2 the outcome was a reduction of heat transfer. A numerical instability problem occurred for situations of very high viscous dissipation which limited the length of duct that could be examined.