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.

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.

Darryl E. Metzger Memorial Session Paper: The Streamwise Development of Go¨rtler Vortices in a Favorable Pressure Gradient

1996 ◽  
Vol 118 (1) ◽  
pp. 162-171 ◽  
Author(s):  
M. V. Finnis ◽  
A. Brown
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Velocity Gradient ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Velocity Variation ◽  
Radius Of Curvature ◽  
Stream Velocity ◽  
Mean Flow ◽  
Favorable Pressure Gradient

Measurements are presented of the streamwise velocity variation within a laminar boundary layer on a concave surface of 4 m radius of curvature for which the free-stream velocity gradient factor (ν/U02)dU0/dx was approximately 1 × 10−6. The stream velocity variation was consistent with the presence of counterrotating vortices resulting from the Go¨rtler instability. The vortices exhibited exponential growth over the streamwise extent of the measurements to a disturbance amplitude of approximately 13 percent of the local free-stream velocity. The vortex growth rates were found to be less than those for a zero velocity gradient factor, indicating that a favorable pressure gradient stabilizes the flow with respect to the Go¨rtler instability. Boundary layer profiles at local upwash and downwash positions are compared with the linear theory for which the mean flow was modeled using the Pohlhausen approximation to the solution of the boundary layer equations. The agreement between the measured and predicted profiles indicates that the linear stability theory can provide a fair approximation to the small amplitude growth of the Go¨rtler instability.

Effectiveness and Heat Transfer for a Turbulent Boundary Layer With Tangential Injection and Variable Free-Stream Velocity

1962 ◽  
Vol 84 (3) ◽  
pp. 235-242 ◽  
Author(s):  
R. A. Seban ◽  
L. H. Back
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Free Stream ◽  
Free Stream Velocity ◽  
Stream Velocity ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Air Stream ◽  
External Stream

The effectiveness and the heat transfer have been measured in a system involving the tangential injection of air from a single spanwise slot into the turbulent boundary layer of an external air stream, with the velocity of the external stream increasing in a way that concentrated the acceleration in a region downstream of the initial mixing zone. The effectiveness was changed but little from the value that would have existed had the free-stream velocity remained at its initial value and both temperature profiles and analytical considerations show that this invariability of the effectiveness is associated with thermal boundary-layer thicknesses that are much larger than the hydrodynamic thicknesses. Heat-transfer coefficients are shown to be predictable from existing information provided that the momentum thickness Reynolds number is large enough.

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