Transient three-dimensional heat transfer from rotating spheres with surface blowing

Transient heat transfer and thermal patterns around a rotating spherical particle with surface blowing are studied numerically for Reynolds numbers in the range 10?Re?300 and non-dimensional angular velocities up to Ω=1. This range of Reynolds number includes three distinct wake regimes: steady and axisymmetrical, steady but non-symmetrical, and unsteady with vortex shedding. The Navier-Stokes and energy equations for an incompressible viscous flow are solved numerically by a finite-volume method in a three-dimensional and time-accurate manner. The transient aspects of the thermal wakes associated with the aforementioned wake regimes have been explored. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that an unsteady three-dimensional flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects, and thus, the temperature distributions around the particle are significantly affected. Despite the fact that particle rotation brings about major changes locally, the surface-averaged heat transfer rates are not influenced appreciably even at high rotational speeds; consequently, it is shown that the total heat transfer rates associated with rotating spheres with surface blowing can be calculated from heat transfer correlations developed for flow over evaporating droplets.     

Effects of radiation and heat source/sink on unsteady MHD boundary layer flow and heat transfer over a shrinking sheet with suction/injection

In this paper, an investigation is made to study the effects of radiation and heat source/sink on the unsteady boundary layer flow and heat transfer past a shrinking sheet with suction/injection. The flow is permeated by an externally applied magnetic field normal to the plane of flow. The self-similar equations corresponding to the velocity and temperature fields are obtained, and then solved numerically by finite difference method using quasilinearization technique. The study reveals that the momentum boundary layer thickness increases with increasing unsteadiness and decreases with magnetic field. The thermal boundary layer thickness decreases with Prandtl number, radiation parameter and heat sink parameter, but it increases with heat source parameter. Moreover, increasing unsteadiness, magnetic field strength, radiation and heat sink strength boost the heat transfer.     

Suction, viscous dissipation and thermal radiation effects on the flow and heat transfer of a power-law fluid past an infinite porous plate

This paper presents a study of the flow and heat transfer of an incompressible Ostwald de-Waele power-law fluid past an infinite porous plate, subject to suction at the plate. The power-law index n satisfies 0 < n < 1 (shear-thinning fluid only) provided that there is suction at the plate. Three cases are studied, namely, (i) the plate with constant surface temperature (CST case), (ii) the plate with prescribed surface temperature (PST case), and (iii) the plate with prescribed heat flux (PHF case). The effects of viscous dissipation and thermal radiation are also considered in the energy equation and the variations of dimensionless surface temperature and dimensionless surface temperature gradient with various parameters are graphed and tabulated.     

HYDROMAGNETIC BOUNDARY LAYER FLOW AND HEAT TRANSFER IN VISCOELASTIC FLUID OVER A CONTINUOUSLY MOVING PERMEABLE STRETCHING SURFACE WITH NONUNIFORM HEAT SOURCE/SINK EMBEDDED IN FLUID-SATURATED POROUS MEDIUM

Analytical study for the problem of flow and heat transfer of electrically conducting viscoelastic fluid over a continuously moving permeable stretching surface with nonuniform heat source/sink in a fluid-saturated porous medium has been undertaken. The momentum and thermal boundary layer equations, which are partial differential equations, are converted into ordinary differential equations, by using suitable similarity transformation. The resulting nonlinear ordinary differential equations of momentum are solved analytically assuming exponential solution, and similarly thermal boundary layer equations are solved exactly by using power series method, with the solution obtained in terms of Kummer's function. The results are shown with graphs and tables. The effect of various physical parameters like viscoelastic parameter, porosity parameter, Eckert number, space, and temperature-dependent heat source/sink parameters enhances the temperature profile, whereas increasing the values of the suction parameter and Prandtl number decreases the temperature profile. The results have technological applications in liquid-based system involving stretchable materials.     

NONSIMILAR SOLUTIONS FOR HEAT TRANSFER IN WALL JET FLOWS

An analysis is presented to investigate the flow and heat transfer characteristics of a laminar plane wall jet with non-isothermal wall as well as uniform suction and blowing at the surface and a laminar cylindrical wall jet. The approach used is local nonsimilarity method, wherein, the nonsimilanty terms appearing in the momentum and energy equations are retained and simplifications are introduced only in the auxiliary system of equations. To insure the accuracy of the results, solutions are obtained for three levels of truncation of the governing equations. For the case of plane wall jet problem, both a series solution as well as local nonsimilarity solution have been given and the agreement between the two is found to be very good. For the cylindrical wall jet problem, the results obtained by the local nonsimilarity approach in the present paper have been compared with the series solution results. Numerical results for the wall shear stress, velocity distribution, wall heat transfer rate and temperature field are presented.     

On the Prandtl or Schmidt number dependence of the turbulent heat or mass transfer coefficient

Numerical experiments using a direct numerical simulation (DNS) of turbulent flow between two parallel plates in conjunction with Lagrangian scalar tracking (LST) of trajectories of thermal markers in the flow field are conducted for Prandtl or Schmidt numbers between 0.01 and 50,000. The LST methodology is used to generate mean temperature profiles as a function of the entry distance in the case of a step change in heat or mass flux at the walls of the channel. The heat transfer coefficient and the Nusselt number ratio, Nu(x)/Nu(x→∞), downstream from the step change in the wall flux are determined for the range of Pr or Sc fluids examined. Relations between the heat or mass transfer coefficient at the fully developed part of the channel and Pr or Sc are proposed for low and high Pr or Sc cases. Finally, unified correlations, which provide the heat or mass transfer coefficient for all Pr or Sc, in the Reynolds number range examined, are proposed. Also, the exponent of the asymptotic dependence of the eddy diffusivity close to the wall is obtained.     

UNSTEADY MHD BOUNDARY LAYER FLOW WITH DIFFUSION AND FIRST-ORDER CHEMICAL REACTION OVER A PERMEABLE STRETCHING SHEET WITH SUCTION OR BLOWING

In this study, unsteady MHD boundary layer flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet with suction or blowing and also with power-law variation in wall concentration is investigated. Using similarity transformation, the governing partial differential equations are converted into nonlinear self-similar ordinary differential equations. The transformed equations are then solved by the finite difference method using the quasi-linearization technique. Due to the increase in the unsteadiness parameter, the velocity initially decreases, but after a certain point it increases. A similar effect is also observed in case of concentration distribution. The increase in magnetic parameter causes a decrease in velocity and an increase in concentration. For increasing strength of applied suction both momentum and concentration boundary layer thicknesses decrease. On the other hand, applied blowing has reverse effects. Moreover, the mass transfer from the sheet is enhanced with increasing values of Schmidt number, reaction rate parameter, and also power-law exponent (related to wall concentration distribution). For high negative values of the power-law exponent, mass absorption at the sheet occurs. Moreover, due to increase of unsteadiness, this mass absorption is prevented.     

Effect of blockage on heat transfer from a cylinder to power law liquids

The influence of planar confining walls on the steady forced convection heat transfer from a cylinder to power-law fluids has been investigated numerically by solving the field equations using FLUENT (version 6.2). Extensive results highlighting the effects of the Reynolds number (1?Re?40), power-law index (0.2?n?1.8), Prandtl number (1?Pr?100) and the blockage ratio (β=4 and 1.6) on the average Nusselt number have been presented. For a fixed value of the blockage ratio, the heat transfer is enhanced with the increasing degree of shear-thinning behaviour of the fluid, while an opposite trend was observed in shear-thickening fluids. Due to the modifications of the flow and temperature fields close to the cylinder, the closely placed walls (i.e., decreasing value of the blockage ratio) further enhance the rate of heat transfer as the fluid behaviour changes from Newtonian to shear-thickening fluids (n>1), the opposite influence is seen with the decreasing value of the flow behaviour index (n) in shear-thinning (n<1) fluids. Finally, the functional dependence of the present numerical results on the relevant dimensionless parameters has been presented in the form of closure relationships for their easy use in a new application.     

HEAT TRANSFER DUE TO MHD SLIP FLOW OF A SECOND-GRADE LIQUID OVER A STRETCHING SHEET THROUGH A POROUS MEDIUM WITH NONUNIFORM HEAT SOURCE/SINK

An analysis is carried out to study the heat transfer characteristics of a second-grade non-Newtonian liquid due to a stretching sheet through a porous medium under the influence of external magnetic field. The stretching sheet is assumed to be impermeable. Partial slip condition is used to study the flow behavior of the liquid. The effects of viscous dissipation, nonuniform heat source/sink on the heat transfer are addressed. The nonlinear partial differential equations governing momentum and heat transfer in the boundary layer are converted into nonlinear ordinary differential equations using similarity transformation. Analytical solutions are obtained for the resulting boundary value problems in the case of two types of boundary heating, namely, constant surface temperature (CST) and prescribed surface temperature (PST). The effects of slip parameter, second-grade liquid parameter, combined (magnetic and porous) parameter, Prandtl number, Eckert number, and nonuniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and wall temperature gradient are obtained.     

Stagnation slip flow and heat transfer on a moving plate

A two-dimensional or axisymmetric stagnation flow impinges on a plate moving in its own plane. The no slip condition on the solid boundary is replaced by the partial slip condition. The Navier-Stokes and energy equations admit exact similarity solutions. The resulting nonlinear differential equations are solved asymptotically and numerically. The flow depends heavily on the velocity slip factor λ. We find drag decreases as 1/λ and heat transfer increases with λ, the Prandtl number, and decreased thermal slip.     

Free convective flow over a vertical plate in a doubly stratified medium with electrophoresis, heat source/sink and chemical reaction effects

We analyzed the problem of unsteady, incompressible free convective doubly stratified flow past a semiinfinite vertical plate with the influence of electrophoresis, heat source/sink and chemical reaction. The partial differential equations governing the flow are solved by employing an implicit finite difference scheme of Crank-Nicolson type. The effect of heat generation and absorption in stratified and unstratified flow are examined and hence the influence of stratification on velocity, temperature and concentration are investigated and presented graphically. Further, the impact of the electrophoresis on particle concentration in the presence of generative and destructive reaction is analyzed. As well, the effects of the physical parameters on local and average values of skin friction, Nusselt number and Sherwood number are also investigated and illustrated graphically. The particular solutions of the present results are compared with the existing solution in literature and are found to be in good agreement.     

MHD flow of a micropolar fluid towards a vertical permeable plate with prescribed surface heat flux

The problem of a steady mixed convection stagnation point flow towards a permeable vertical plate with prescribed surface heat flux immersed in an incompressible micropolar fluid is studied numerically. The governing partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by a finite-difference scheme known as the Keller-box method and the Runge–Kutta–Fehlberg method with shooting technique. The effects of the material parameter, buoyancy parameter, suction/injection parameter and the Prandtl number on the fluid flow and heat transfer characteristics are discussed. It is found that dual solutions exist for both assisting and opposing flows. The skin friction coefficient and the local Nusselt number increase in the presence of suction and magnetic field. Moreover, suction as well as fluids with larger Prandtl number widens the range of the buoyancy parameter for which the solution exists.     

Radiation-absorption,chemical reaction,Hall and ion slip impacts on magnetohydrodynamic free convective flow over semi-infinite moving absorbent surface

The investigation of radiation-absorption,chemical reaction,Hall and ion-slip impacts on unsteady MHD free convective laminar flow of an incompressible viscous,electrically conducting and heat generation/absorbing fluid enclosed with a semi-infinite porous plate within a rotating frame has been premeditated.The plate is assumed to be moving with a constant velocity in the direction of fluid movement.A uniform transverse magnetic field is applied at right angles to the porous surface,which is absorbing the fluid with a suction velocity changing with time.The non-dimensional governing equations for present inves-tigation are solved analytically making use of two term harmonic and non-harmonic functions.The graphical results of velocity,temperature and concentration distributions on the analytical solutions are displayed and discussed with reference to pertinent parameters.It is found that the velocity profiles decreased with an increasing in Hartmann number,rotation parameter,the Schmidt number,heat source parameter,while it increased due to an increase in permeability parameter,radiation-absorption param-eter,Hall and ion slip parameters.However,the temperature profile is an increasing function of radiation-absorption parameter,whereas an increase in chemical reaction parameter,the Schmidt num-ber Sc or frequency of oscillations decrease the temperature profile on cooling.Also,it is found that the concentration profile is decreased with an escalating in the Schmidt number or the chemical reaction parameter.     

The heat transfer coefficient between a particle and a bed (packed or fluidised) of much larger particles

The heat transfer coefficient has been measured for a heated phosphor-bronze sphere (diam. 2.0, 3.0 or 5.56 mm) added to a bed of larger particles, through which air at room temperature was passed. The bronze heat transfer sphere was attached to a very thin, flexible thermocouple and was heated in a flame to before being immersed in the bed. The cooling of the bronze sphere enabled the heat transfer coefficient, h, to be measured for a variety of U/U_mf, as well as diameters of both the particles in the bed and the heat transfer sphere. It was found that before the onset of fluidisation, h rose with U, but h reached a constant value for U?U_mf. These measurements indicate that in this situation (of a relatively small particle in a bed of larger particles) all the heat transfer is between the hot bronze sphere and the gas flowing over it. Consequently, a Nusselt number, based on the thermal conductivity of the gas, is easy to define and for U?U_mf (i.e. a packed bed), Nu is given by

     

一种新型受热面传热和流动特性的数值模拟及实验研究

针对余热利用过程中低温热源的含尘量高、不连续及不稳定等特点, 提出了一种新型菱形受热面结构。在传热过程中, 该受热面表现出管束叉排布置的特征, 传热过能力较强, 流动阻力较大, 壳侧对流换热表面传热系数较高。在实施吹灰过程中, 该受热面呈现出管束顺排布置的特征, 易清洗, 吹灰效率高。采用数值模拟和实验方法研究了新型受热面结构的传热和流动特性, 给出了壳侧的Nusselt数和摩擦因子随Reynolds数的变化规律。实验结果和数值分析均表明, 该受热面能够适应现有余热利用过程的基本要求, 在便于清灰和除垢的同时实现高效传热。     

Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds

Computational fluid dynamics as a simulation tool allows obtaining a more detailed view of the fluid flow and heat transfer mechanisms in fixed-bed reactors, through the resolution of 3D Reynolds averaged transport equations, together with a turbulence model when needed. In this way, this tool permits obtaining of mean and fluctuating flow and temperature values in any point of the bed. An important problem when modeling a turbulent flow fixed-bed reactor is to decide which turbulence model is the most accurate for this situation. To gain insight into this subject, this study presents a comparison between the performance in flow and heat transfer estimation of five different RANS turbulence models in a fixed bed composed of 44 homogeneous stacked spheres in a maximum space-occupying arrangement in a cylindrical container by solving the 3D Navier-Stokes and energy equations by means of a commercial finite volume code, Fluent 6.0^®. Air is chosen as flowing fluid. Numerical pressure drop, velocity and thermal fields within the bed are obtained. In order to judge the capabilities of these turbulence models, heat transfer parameters (Nu_w, k_r/k_f) are estimated from numerical data and together with the pressure drop are compared to commonly used correlations for parameter estimations in fixed-bed reactors.     

Heat transfer and pressure drop in a ZrB2 microchannel heat sink: A numerical approach

Advances in micro-electro-mechanical systems (MEMS) resulted in the fabrication of electronic and optic devices which generate high amounts of heat in a small space. Microchannel heat sinks are a new type of heat exchangers which are capable to absorb such ultrahigh heat fluxes and ensure the proper function of such devices. In the present work, a microchannel heat sink made of ZrB₂ ceramic is investigated numerically to evaluate its feasibility to operate at such harsh conditions. The governing equations of the liquid domain (water) and solid domain (ZrB₂) were solved by the finite element method. The obtained results showed a considerable heat transfer rate from the heated surface. For example, at an ultra-high heat flux of 3.6 MW/m², the maximum temperature didn't exceed ~360 K. The high heat transfer area per volume of the applied microchannel, as well as the remarkable thermal conductivity of ZrB₂, are the main reasons for such a high heat transfer rate.     

Radiation effect on viscous flow of a nanofluid and heat transfer over a nonlinearly stretching sheet

In this work, we study the flow and heat transfer characteristics of a viscous nanofluid over a nonlinearly stretching sheet in the presence of thermal radiation, included in the energy equation, and variable wall temperature. A similarity transformation was used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge-Kutta scheme was used to obtain the solution of the boundary value problem. The variations of dimensionless surface temperature, as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include the nanoparticle volume fraction ϕ, the nonlinearly stretching sheet parameter n, the thermal radiation parameter N_R, and the viscous dissipation parameter Ec, were graphed and tabulated. Excellent validation of the present numerical results has been achieved with the earlier nonlinearly stretching sheet problem of Cortell for local Nusselt number without taking the effect of nanoparticles.     

Successive linearisation analysis of unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and thermal radiation effects

In this study, we investigate the application of the new successive linearisation method (SLM) to the problem of unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and thermal radiation effects. The governing nonlinear momentum, energy and mass transfer equations are successfully solved numerically using the SLM approach coupled with the spectral collocation method for iteratively solving the governing linearised equations. Comparison of the SLM results for various flow parameters against numerical results and other published results, obtained using the homotopy analysis method (HAM) and Runge–Kutta methods, for related problems indicates that the SLM is a very powerful tool which is much more accurate and efficient than other methods. The SLM converges much faster than the traditional methods like the HAM and is very easy to implement. © 2011 Canadian Society for Chemical Engineering     

Radiation cooling for heat sinks with high emissivity lanthanum aluminate ceramic coating

The increasing miniaturization and densification of electronic components have increased the demands for efficient heat sinks to dissipate the dense heat generated by these small components. However, owing to the limitations of the substrate material of heat sinks, optimizing the fin structure and its arrangement to enhance heat conduction and convection remains a challenge. In this study, the temperature change of hot water in a 304 steel barrel with and without a La_0.9Ca_0.1Al_0.9Fe_0.1O₃ (LAF) coating was studied. The results demonstrated that the cooling rate of hot water in the barrel coated with LAF coating increased by 28%. Furthermore, a high-emissivity LAF ceramic coating (0.91) was applied to an aluminum heat sink, and the heat transfer performance of the heat sink with and without the LAF coating was studied. The experimental results showed that the equilibrium temperature of the LAF-coated heat sink was reduced by ∼8 °C. Additionally, the LAF coating increased the total heat transfer coefficient by 20% and reduced the thermal resistance by 18%. The proportion of radiation heat transfer on the surface of the heat sink increased with the LAF coating, which accounted for 44% of the total heat transfer coefficient. Thus, LAF coatings have the potential to effectively improve the heat-transfer performance of thermal devices with different metals.