A Class of Similarity Solutions to the Boundary-Layer Energy Equation

1963 ◽  
Vol 85 (1) ◽  
pp. 78-79 ◽  
Author(s):  
R. H. Edgerton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Energy Equation ◽  
Transfer Problem ◽  
Similarity Solutions ◽  
Simple Solution ◽  
Heat Transfer Problem ◽  
Incompressible Boundary ◽  
The Subject

This note presents a class of simple similarity solutions to the incompressible boundary-layer energy equation which appear to have been overlooked in papers on the subject. It is shown that one simple solution is particulary applicable to the axisymmetric stagnation point heat-transfer problem.

Uncoupling the Conjugate Heat Transfer Problem in a Horizontal Plate Under the Influence of a Laminar Flow

2003 ◽  
Author(s):  
Ricardo S. Va´squez ◽  
Antonio J. Bula
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Conjugate Heat Transfer ◽  
Energy Equation ◽  
Transfer Problem ◽  
Heat Transfer Problem ◽  
Interface Temperature ◽  
Horizontal Plate ◽  
Steady State Condition ◽  
Heated Body

The conjugate heat transfer process of cooling a horizontal plate in steady state condition is studied. The model considers both solid and fluid regions in Cartesian coordinates. The problem was solved analytically, considering the fluid flowing in a laminar condition and hydrodynamically developed before any interaction with the heated body. The height of the fluid considered was enough to allow the generation of a thermal boundary layer without any restriction. The conservation of mass, momentum and energy equations were considered to turn the problem into a non dimensional form. The heated body presented a constant heat flux at the bottom side, and convective heat transfer at the top side in contact with the fluid. The other two boundary conditions are adiabatic. The energy equation was considered in the solid to turn it into a non dimensional form. The interface temperature was obtained from a regression using the Chebyshev polynomial approximation. As the problem deals with the cooling of a electronics components, the solution presents the mathematical solution of the energy equation for the solid, including the isothermal lines. The non dimensional form allows a thorough analysis of the problem, considering the influence of the different parameters in the conjugate heat transfer problem. The solution is compared with numerical solution of different problems, and the parameters considered are Reynolds number, plate thickness, Prandtl number, and solid thermal conductivity. The results obtained present isothermal lines, local Nusselt number, and average Nusselt number.

Vorticity amplification in stagnation-point flow and its effect on heat transfer

1965 ◽  
Vol 21 (3) ◽  
pp. 513-534 ◽  
Author(s):  
S. P. Sutera
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Transfer Problem ◽  
Analogue Computer ◽  
Wall Heat Transfer ◽  
Free Stream Turbulence ◽  
The Mean

Recently a mathematical model was proposed (Sutera, Maeder & Kestin 1963) to demonstrate that vorticity amplification by stretching was an important mechanism underlying the sensitivity of stagnation-point heat transfer on cylinders to free-stream turbulence. According to the model, vorticity of a scale larger than a certain neutral scale and appropriately oriented can undergo amplification as it is convected towards the boundary layer. Such vorticity, present in the oncoming flow with small intensity, can reach the boundary layer with a greatly magnified intensity and induce substantial three-dimensional effects therein. The mean temperature profile was shown to be much more responsive to these effects than the mean velocity profile and very large increases in the wall-heat-transfer rate were calculated for Prandtl numbers 0·74 and 7·0.In this work a second, more general, case is treated in which the approaching flow carries vorticity of scale 1·5 times the neutral. By means of iterative procedures applied on an electronic analogue computer, an approximate solution to the full Navier–Stokes equation is generated. The heat-transfer problem is solved simultaneously for Pr = 0·70, 7·0 and 100. It is found that a vorticity input which increases the wall-shear rate by less than 3% is capable of increasing the wall-heat-transfer rate by as much as 40%. The sensitivity of the thermal boundary layer depends on Prandtl number. In the three cases investigated it is greatest for Pr = 7·0 and least for Pr = 100.

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