Paradoxes of Heat Transfer on a Permeable Wall

Author(s):  
A. I. Leontiev ◽  
V. G. Lushchik ◽  
A. E. Yakubenko

Numerical modeling of a turbulent boundary layer on a permeable wall with gas injection is performed. New effects are discovered. It is shown in particular that the wall temperature in the region of the gas film may be lower than the injected gas temperature. This effect is especially essential for gas mixtures with low values of the Prandtl number.

Author(s):  
W. J. Kelnhofer

Based on n-power velocity and temperature profiles a method of computing various turbulent boundary layer thicknesses and shape factors affected by wall temperature and Prandtl number for fully developed subsonic gas flow over a flat plate is presented. Density variation in the boundary layer is given main consideration. Numerical computations include both heating and cooling of gas. Boundary layer thicknesses and shape factors are shown to be significantly affected by wall temperature and to a lesser degree by Prandtl number. An experiment is described which involved air flow up to 30 m/sec over a flat plate maintained at constant wall temperatures up to 250 C. Comparisons between theory and experiment are good.


Author(s):  
Mohammad Reza Mobinipouya

This paper addresses the laminar boundary layer flow of selected binary gas mixtures along a heated flat plate. To form the binary gas mixtures, light helium (He) is the primary gas and the heavier secondary gases are nitrogen (N2), oxygen (O2), xenon (Xe), carbon dioxide (CO2), methane (CH4), tetrafluoromethane (CF4) and sulfur hexafluoride (SF6). The central objective in the work is to investigate the potential of this group of binary gas mixtures for heat transfer intensification. From fluid physics, two thermophysical properties: viscosity η and density ρ influence the fluid flow, whereas four thermophysical properties: viscosity η, thermal conductivity λ, density ρ, and heat capacity at constant pressure Cp affect the forced convective heat transfer. The heat transfer augmentation from the flat plate is pursued by stimulating the forced convection mode as a whole. In this regard, it became necessary to construct a specific correlation equation to handle binary gas mixtures owing Prandtl number Pr ∈ (0.1, 1). The rate of heat transfer Q between a heated plate and a cold fluid is calculated with: Qmix/B=λmix0.623ρmix0.500Cp,mix0.377ηmix0.123(1) If the surface area of the plate A and the temperature difference Tw–T∞ are specified, the only possible way for intensifying the rate of heat transfer Q is by enlarging the magnitude of the average heat transfer coefficient h. This is precisely the main goal to be pursued in the present paper. The average heat transfer coefficient h in laminar boundary layer flows of incompressible, viscous fluids along heated flat plates depends on the dimensionless fluid temperature gradient at the plate θ′(0). It is given by the Prandtl number function f (Pr).


2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.


2014 ◽  
Vol 18 (4) ◽  
pp. 1079-1093 ◽  
Author(s):  
V. Singh ◽  
Shweta Agarwal

An Analysis has been carried out to study the boundary layer flow and heat transfer characteristics of second order fluid and second grade fluid with variable thermal conductivity and radiation over an exponentially stretching sheet in porous medium. The basic boundary layer equations governing the flow and heat transfer in prescribed surface temperature (PST) and prescribed heat flux (PHF) cases are in the form of partial differential equations. These equations are converted to non-linear ordinary differential equations using similarity transformations. Numerical solutions of the resulting boundary value problem are solved by using the fourth order Runge-Kutta method with shooting technique for various values of the physical parameters. The effect of variable thermal conductivity, porosity, Prandtl number, radiation parameter and viscoelastic parameters on velocity and temperature profiles (in PST and PHF cases) are analyzed and discussed through graphs. Numerical values of wall temperature gradient in PST case and wall temperature in PHF case are obtained and tabulated for various values of the governing parameters. In this study Prandtl number also treated as variable inside the boundary layer because it depends on thermal conductivity. The results are also verified by using finite difference method.


1981 ◽  
Vol 103 (1) ◽  
pp. 153-158 ◽  
Author(s):  
H. W. Coleman ◽  
R. J. Moffat ◽  
W. M. Kays

Heat transfer behavior of a fully rough turbulent boundary layer subjected to favorable pressure gradients was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Stanton numbers and profiles of mean temperature, turbulent Prandtl number, and turbulent heat flux are reported. Three equilibrium acceleration cases (one with blowing) and one non-equilibrium acceleration case were studied. For each acceleration case of this study, Stanton number increased over zero pressure gradient values at the same position or enthalpy thickness. Turbulent Prandtl number was found to be approximately constant at 0.7–0.8 across the layer, and profiles of the non-dimensional turbulent heat flux showed close agreement with those previously reported for both smooth and rough wall zero pressure gradient layers.


1961 ◽  
Vol 12 (4) ◽  
pp. 309-336 ◽  
Author(s):  
N. Curle

SummaryBy generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.


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