The thermal boundary layer on a non-isothermal surface with non-uniform free stream velocity

1958 ◽  
Vol 4 (3) ◽  
pp. 321-329 ◽  
Author(s):  
E. M. Sparrow
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Temperature Data ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Universal Functions ◽  
Isothermal Surface

A formally exact solution for the thermal boundary layer on a non-isothermal surface subjected to non-uniform free stream velocity is presented in the form of a series. It is demonstrated that the solution can be recast in terms of universal functions, which are independent of the wall temperature data of particular problems, and which depend only on a single parameter characterizing the variation of the free stream velocity.

An Aspect of Heat Transfer in Accelerating Turbulent Boundary Layers

1969 ◽  
Vol 91 (2) ◽  
pp. 229-234 ◽  
Author(s):  
B. E. Launder ◽  
F. C. Lockwood
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Free Stream ◽  
Turbulent Boundary Layers ◽  
Stanton Number ◽  
Stream Velocity ◽  
Velocity Boundary Layer ◽  
Positive Exponent

Theoretical consideration indicates that, in an accelerated turbulent flow, the thermal boundary layer may penetrate significantly beyond the edge of the velocity boundary layer. This effect may contribute in part to the marked decrease in Stanton number which has been reported in accelerated turbulent boundary layers. This paper presents theoretical solutions to turbulent velocity and thermal boundary layers in flow between converging planes where the wall temperature varies as the free-stream velocity raised to a positive exponent. The solutions clearly illustrate that, as the wall-temperature variation is made less rapid, the thermal boundary layer penetrates progressively further beyond the velocity boundary layer, causing the Stanton number to decrease.

scholarly journals Prediction of Heat Transfer From Laminar Boundary Layers, With Emphasis on Large Free-Stream Velocity Gradients and Highly Cooled Walls

1966 ◽  
Vol 88 (3) ◽  
pp. 249-256 ◽  
Author(s):  
L. H. Back ◽  
A. B. Witte
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Shear Stress ◽  
Velocity Gradient ◽  
Free Stream ◽  
Variable Density ◽  
Similarity Solutions ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Gradient Parameter

Laminar boundary-layer heat transfer and shear-stress predictions from existing similarity solutions are extended in an approximate way to perfect gas flows with a large free-stream velocity gradient parameter β and variable density-viscosity product ρμ across the boundary layer resulting from a highly cooled wall. The dimensionless enthalpy gradient at the wall gw′, to which the heat flux is related, is found not to vary appreciably with β. Thus the application of similarity solutions on a local basis to predict heat transfer from accelerated flows to an arbitrary surface may be a reasonable approximation involving a minimum amount of calculation time. Unlike gw′, the dimensionless velocity gradient at the wall fw″, to which the shear stress is related, is strongly dependent on β.

Effects of Partial Slip on Chemically Reactive Solute Distribution in MHD Boundary Layer Stagnation Point Flow Past a Stretching Permeable Sheet

2015 ◽  
Vol 13 (1) ◽  
pp. 29-36 ◽  
Author(s):  
Swati Mukhopadhyay
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Stream Velocity ◽  
Slip Parameter ◽  
Mhd Boundary Layer

Abstract This paper presents the magnetohydrodynamic (MHD) boundary layer stagnation point flow with diffusion of chemically reactive species undergoing first-order chemical reaction over a permeable stretching sheet in presence of partial slip. With the help of similarity transformations, the partial differential equations corresponding to momentum and the concentration equations are transformed into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity and the stretching velocity. Velocity decreases with the increasing magnetic parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. Due to suction, fluid velocity decreases at a particular point of the surface. With increasing velocity slip parameter, velocity increases when the free-stream velocity is greater than the stretching velocity. But the concentration decreases in this case. Concentration decreases with increasing mass slip parameter.

Skin Friction and Heat Transfer for Laminar Boundary-Layer Flow With Variable Properties and Variable Free-Stream Velocity

1953 ◽  
Vol 20 (3) ◽  
pp. 415-421
Author(s):  
S. Levy ◽  
R. A. Seban
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Layer Flow

Abstract Numerical solutions of the momentum and energy equations are presented for particular types of laminar boundary-layer flow analogous to the Hartree “wedge flows.” Variation of the viscosity and of the thermal conductivity is considered under the circumstances of no dissipation, favorable pressure gradient, and the product of conductivity and density a constant. The solution is based on approximate representations of the velocity and temperature profiles in the boundary layer and these are of such character that the labor of calculation is minimized and the accuracy of the results preserved. The differential equations are reduced to two algebraic equations which rapidly yield the skin friction and the heat transfer in terms of the wall to free-stream temperature ratio for the desired value of Prandtl number. Numerical results are given for a range of wedge flows with gases of Prandtl number 0.70 and 1.0. These results reveal that when the free-stream velocity is variable the temperature difference between the wall and the free stream exerts a substantial effect on the velocity distribution in the boundary layer and on the skin-friction coefficient. Alternatively, the heat-transfer coefficient is not affected radically. A calculation method is presented for the determination of the heat transfer and skin friction for a flow with an arbitrary variation of velocity over an isothermal surface. This method utilizes the results of the present analysis for the variable property wedge flows.

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