Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the heat transfer to constant-property laminar boundary layer with power-function free-stream velocity and wall-temperature distributions


Author: Isao Imai
Journal: Quart. Appl. Math. 16 (1958), 33-45
MSC: Primary 76.00
DOI: https://doi.org/10.1090/qam/103000
MathSciNet review: 103000
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Abstract: The heat transfer to constant-property laminar boundary layer with power-function variations of free stream velocity $ ({u_1} = c{x^m})$ and of temperature difference between wall and free stream $ ({T_0} - {T_1} = b{x^n})$ is studied by means of an improved version of the WKB method developed by the author. It is found that the local heat-transfer coefficient $ h$ can be approximately given in the form

$\displaystyle \frac{{hx/k}}{{{{\left( {{u_1}x/v} \right)}^{1/2}}}} = \frac{1}{{... ...{\left( {\sigma \alpha } \right)}^{1/3}} - \frac{\beta }{{10\alpha }}} \right],$

where $ \beta = 2m/(m + 1)$, $ \alpha $ is the non-dimensional velocity gradient at the wall (usually expressed as $ \alpha = f''(0)$), $ \sigma $ is the Prandtl number, $ k$ is the thermal conductivity, and $ v$ is the kinematic viscosity.

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DOI: https://doi.org/10.1090/qam/103000
Article copyright: © Copyright 1958 American Mathematical Society

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