HEAT TRANSFER IN A LAMINAR CYLINDRICAL WALL JET WITH UNIFORM SURFACE HEAT FLUX

The steady state flow and heat transfer characteristics of a laminar cylindrical wall jet are obtained for uniform surface heat flux conditions. Local nonsimilarity solutions as well as series solutions are presented for the velocity and thermal fields. Numerical results are given for the wall shear stress, surface temperature variation and temperature field for a Prandtl number of 0.73.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

COMBINED HEAT AND MASS TRANSFER IN FREE CONVECTION ALONG A ROTATING PLATE UNDER UNIFORM HEAT AND UNIFORM MASS FLUXES

The problem of combined heat and mass transfer in laminar free convection along a vertically rotating plate subjected to a uniform heat flux and/or a uniform mass flux is studied analytically. The governing non-dimensional nonlinear coupled partial differential equations are solved by local similarity and local nonsimilarity approach. Numerical results for the local Nusselt number, the local Sherwood number and the local wall shear stress for the convective-diffusion of hydrogen, water vapor and naphthalene into the air are presented in tabular forms. The analysis extends the range both when the concentration buoyancy force assists as well as opposes the thermal buoyancy force.     

COMBINED FORCED AND FREE CONVECTION IN BOUNDARY LAYER FLOW OF NON-NEWTONIAN FLUID ON A HORIZONTAL PLATE

An analysis is presented to study the effects of buoyancy-induced streamwise pressure gradients on laminar forced convection heat transfer to non-Newtonian fluids from a horizontal plate. Numerical solution of the transformed boundary layer equations has been carried out for different values of the flow behavior index and the buoyancy parameter by means of the local nonsimilarity method. A discussion is provided for the effect of the buoyancy force on the friction factor, the dimensionless heat transfer rate and the details of the velocity as well as temperature fields.     

Thermophoresis and chemical reaction effects on non-Darcy MHD mixed convective heat and mass transfer past a porous wedge in the presence of variable stream condition

An analysis is presented to investigate the effect of thermophoresis particle deposition and variable viscosity on non-Darcy MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations are carried out for different values of dimensionless parameter in the problem and an analysis of the results obtained show that the flow field is influenced appreciably by the applied magnetic field. The results are compared with those known from the literature and excellent agreement between the results is obtained.     

CHEMICAL REACTION ON NON-LINEAR BOUNDARY LAYER FLOW OVER A POROUS WEDGE WITH VARIABLE STREAM CONDITIONS

An analysis is presented to investigate the effects of variable viscosity and thermal stratification on non-Darcy MHD mixed convective heat and mass transfer of a viscous, incompressible, and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations up to third-order level of truncation are carried out for different values of dimensionless parameters. The results are presented graphically, and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters. The results are compared with those known from the literature, and excellent agreement between the results is obtained.     

Evaporation under an impinging jet: A numerical model

A numerical model is presented to predict the flow and coupled heat and mass transfer characteristics under a round laminar jet impinging normally on a plane wall maintained at a constant wet-bulb temperature. The full Navier-Stokes energy and conservation of species equations in their primitive form are solved using a finite difference technique for the case of a jet of hot humid air impinging on an isothermal wet surface. It is found that a modified Sherwood number defined in terms of a log-mean, mole fraction driving potential renders the former insensitive to the evaporation rate.     

ANALYTICAL STUDY OF HEAT TRANSFER TO LAMINAR FLOW OF NON-NEWTONIAN FLUIDS IN ANNULUS

An analytical study is made of the problem of laminar flow heat transfer to pseudoplastic fluids in a concentric circular tube annulus. The solution is obtained for simultaneously developing velocity and temperature profiles and constant wall heat flux. Constant property results are presented for different values of flow behavior index, n, and several inner to outer tube radius ratios and Prandtl numbers. Variable property solutions, with strongly temperature-dependent consistency index are obtained. The effect of viscous dissipation on the results of heat transfer is also presented.     

MASS TRANSFER THROUGH PERMEABLE WALLS: A NEW INTEGRAL EQUATION APPROACH FOR CYLINDRICAL TUBES WITH LAMINAR FLOW

Mass transfer through cylindrical semipermeable walls is analyzed. The solution is obtained in terms of integral equations. Despite the existence of a non-homogeneous boundary condition on the semipermeable wall, the solution thus obtained is particularly advantageous since the associated eigenvalue problem is independent of the Sherwood number. This parameter takes into account the main conductances at the tube wall.

The approach is applied to the case of mass transfer from the interior of a capillary tube with semipermeable walls to an external fluid. The flow in the tube is laminar, and the external flow is assumed turbulent.

The mathematical methodology employed provides a framework to develop numerical schemes of fast and sure convergence.     

高粘变物性流体垂直管内流动传热

对高粘变物性流体管内传热进行了计算机仿真计算.结果表明,高粘流体传热时径向温差很大,采用较小的加热管径可以有效地减小径向温差.     

STEADY LAMINAR FLOW THROUGH TWISTED PIPES: FLUID FLOW AND HEAT TRANSFER IN RECTANGULAR TUBES

Fluid flow and heat transfer characteristics in a twisted rectangular tube having an aspect ratio of two were studied using a numerical solution to the momentum and energy equations. Fluid flow solutions are presented for a fully developed laminar flow of a Newtonian fluid. Heat transfer results are presented for the case of axially uniform wall temperature. For the case of peripherally uniform wall temperature, the overall Nusselt number in a twisted rectangular tube was found to be higher than a straight tube by up to 30 percent over certain ranges of twist lengths. However, for the case of non-uniform wall temperature, the overall absolute Nusselt number increased very rapidly with decrease in the twist length     

Impingement Heat Transfer for a Cluster of Laminar Impinging Jets Issuing from Noncircular Nozzles

Abstract:

Results of numerical simulation of the flow and heat transfer characteristics for a semi-confined cluster of laminar air jets impinging normally on a plane wall are presented. A central jet is surrounded by four equally spaced jets of the same configuration. Both circular and noncircular nozzles are considered. The nozzle footprint is displayed in the static pressure, temperature, and local Nusselt number contours on the impingement surface only for relatively short nozzle-to-surface distances. The heat transfer characteristics and performance of circular and noncircular nozzles are compared. It is observed that the Nusselt number based on property values at the jet temperature is relatively insensitive to the temperature difference between the jet and the impingement surface. Also, the local Nusselt numbers are independent of the thermal boundary condition; i.e., the values are nearly the same for both isothermal and uniform heat flux conditions at the target surface. Finally, Nusselt numbers for a single equivalent jet viz. one with the same area as the five nozzles in the cluster combined, are compared for the case of the circular jet.     

UNSTEADY MHD HEAT AND MASS TRANSFER BY MIXED CONVECTION FLOW IN THE FORWARD STAGNATION REGION OF A ROTATING SPHERE AT DIFFERENT WALL CONDITIONS

This study is focused on the problem of MHD heat and mass transfer by mixed convection flow in the forward stagnation region of a rotating sphere in the presence of heat generation and chemical reaction effects. The surface of the sphere is maintained at constant fluid temperature and species concentration. The governing equations of the problem are converted into ordinary differential equations by using suitable similarity transformations. Two cases are considered, namely, constant wall temperature and mass (CWTM) and constant heat and mass fluxes (CHMF). The obtained self-similar equations for both cases are solved numerically using an efficient iterative implicit finite-difference method. The numerical results are compared with previously published results on special cases of the problem and found to be in excellent agreement. The obtained results are displayed graphically to illustrate the influence of the different physical parameters on the velocity components in x- and y-directions, temperature, and concentration profiles as well as the local surface shear stresses and local heat and mass transfer coefficients.     

多孔介质中受限层流冲击射流的流动与换热特性

基于两区(two-domain)模型采用基于预处理的时间推进法对铺设有多孔介质层的恒温平板在受限层流冲击射流作用下的流动与换热特性进行了研究,其中多孔区域动量方程采用Brinkman-Forchheimer拓展Darcy模型,能量方程则采用局部热平衡(LTE)模型,并对porous/fluid交界面切应力跳跃条件对多孔介质冲击射流的影响进行了分析。流体的控制方程采用基于密度的有限体积法来求解,并针对于多孔区域低速流动特点采用相对应的预处理矩阵来消除控制方程的刚性。还对Reynolds数、孔隙率、Darcy数、热导率比、多孔介质层厚度等参数的变化对流动结构及换热特性的影响进行了分析。研究结果表明,在目前的计算条件下,在其他参数一定时,Reynolds数、孔隙率对通道内流动结构的影响有限;Darcy数、多孔介质层厚度则对流动结构的影响很大;上述参数对受冲击平板的总体换热性能均有明显的影响。在受冲击平板上铺设适当厚度的高渗透率、高热导率的多孔材料能有效地增强换热性能。     

ANALYTICAL/NUMERICAL PREDICTION OF THE TOTAL MASS TRANSFER NEAR THE ENTRANCE TO THE MASS TRANSFER SECTION OF ROUND TUBES

The underlying idea behind the classical Lévêque problem was to provide a simple asymptotic solution for the incipient development of the mass (heat) boundary layer flow in a round tube. Inspired by physical concepts, Lévêque assumed that the hydrodynamic boundary layer was confined to a thin annular region near the tube wall so that the fluid velocity varied linearly with y = R ? r, y being the distance measured from the wall. The present article addresses the Lévêque problem from a mathematical perspective, adhering to the original concentration conservation equation in cylindrical coordinates continually without making any hydrodynamic assumptions a priori. The approximate solution procedure to be pursued here combines the transversal method of lines (TMOL) with the Fröbenius power series method. The quality of the local and global mass transfer results obtained with the new TMOL/Fröbenius methodology surpasses the quality of the counterpart results determined by the traditional Lévêque approach.     

Parametric sensitivity of the ignition process to mass transfer in adiabatic tubular reactors with exothermic heterogeneous reactions

The alternative effects of reaction kinetics, mass, heat and momentum transport on mass conversion by chemical reactions are examined theoretically for a reacot tube with laminar flow. The reaction enthalpy is considered. A heterogeneous reaction between several gaseous components takes place at the inner surface of this reactor tube. Strongly exothermic reactions lead to self-acceleration of the reaction, unless reaction enthalpy is removed through the tube wall. Under certain conditions, there will be a sudden change from mass transfer controlled by the reaction to that controlled by diffusion. This phenomenon is known as ignition of the reaction. The effect of ignition and its sensitivity to reaction enthalpy, thermal conductivity and diffusivity of the fluid as well as activation energy of the first order heterogeneous wall reaction are investigated by a numerical solution of the transport equations. Axial conduction of heat and mass is neglected both in the fluid and in the tube wall. Non-stoichiometric wall reactions of first order, with temperature dependent reaction rates and equilibrium constants, are considered. The results are presented in graphical form, as plots of the local mass flux at the reacting wall as functions of the dimensionless tube length.     

Unidirectional transport of heat and salt in free convection of water with variable physical properties along a vertical plate with uniform temperature and salinity

The steady laminar boundary layer flow of saline water along an isothermal vertical plate is studied in this paper. The results are obtained with the numerical solution of the boundary layer equations taking into account the variation of all water thermophysical properties with temperature and salinity. The combination of different temperatures and salinities at the boundary conditions results in a large number of upward, downward or bidirectional flows. The present study concerns the wall heat transfer, wall salinity transfer, wall shear stress and velocity and temperature profiles across the boundary layer for unidirectional upward or downward flow.     

LAMINAR FILM BOILING ON A VERTICAL SURFACE WITH THERMAL LEAKAGE AT ITS ENDS

The analysis presented is for laminar film boiling on a vertical surface treating the test section as a fin with the heat leakage from its ends. The formulation of the problem is accomplished as a conjugate between the thermal conduction in the test section and the phenomenon of film boiling on its lateral face. This approach revealed that the film boiling heat transfer coefficients, both local and average values, are profoundly influenced by the fin parameter. An explicit form of the equation is provided from the computer results to evaluate the film boiling heat transfer coefficient.     

Experimental and Numerical Simulation Study of Heat Transfer Due to Confined Impinging Circular Jet

An experimental and numerical simulation study of heat transfer due to a confined impinging circular jet is presented. In this research, a stainless steel foil heated disk was used as the heat transfer surface of a simulated chip, and the thermocouples were mounted symmetrically along the diameter of the foil to measure the temperature distribution on the surface. Driven by a small pump, a circular air jet (1.5 mm and 1 mm in diameter) impinged on the heat‐transfer surface with middle and low Reynolds numbers. The parameters, such as Reynolds number and ratio of height‐to‐diameter, were changed to investigate the radial distribution of the Nusselt number and the characteristics of heat transfer in the stagnation region. Numerical computations were performed by using several different turbulence models. In wall bounded turbulent flows, near‐wall modeling is crucial. Therefore, the turbulence models enhanced wall treatment, such as the RNG κ‐? model, may be superior for modeling impingement flows. The numerical results showed reasonable agreement with the experimental data for local heat transfer coefficient distributions. The impinging jet may be an effective method to solve the cooling problem of high power density electronic packaging.     

Holographic determination of mass transfer due to impinging square jet

Local mass transfer from a flat plate under the influence of an impinging laminar air jet, issuing from a square tube, has been studied using laser holographic interferometry. No angular variation in mass transfer was found to exist near the jet centre. However, in regions far from the jet centre a periodic angular variation in mass transfer was shown to exist. Regression equations for the local mass transfer coefficient are presented for Re = 710, 980, 1325 and 1810.