Consider a laminar flow past an arbitrarily shaped surface for which the distribution of wall shear...
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Consider a laminar flow past an arbitrarily shaped surface for which the distribution of wall shear stress To(x) is known. The thermal boundary condition is an unheated starting length followed by specified wall temperature, i.e. T(x,0)= T for 0≤x≤x, and T(x,0) = T₁, for x ≤x. Assuming that the fluid Prandtl number is high, i.e. Pr»1, (a) write the governing differential energy equation and boundary conditions assuming self- similarity: 0(n) = T-T Tw-Too where n = yg (x), (b) determine g(x), (c) solve for (n) and determine the distribution of heat transfer coefficient h(x,x), Note: For Pr>>>1, the distribution of u across the thermal boundary layer is approximately linear with the distance from the wall y, i.e. u= y. To (x) μl T=T= constant x=0\ T = Tw TT (unheated) X = constant Consider a laminar flow past an arbitrarily shaped surface for which the distribution of wall shear stress To(x) is known. The thermal boundary condition is an unheated starting length followed by specified wall temperature, i.e. T(x,0)= T for 0≤x≤x, and T(x,0) = T₁, for x ≤x. Assuming that the fluid Prandtl number is high, i.e. Pr»1, (a) write the governing differential energy equation and boundary conditions assuming self- similarity: 0(n) = T-T Tw-Too where n = yg (x), (b) determine g(x), (c) solve for (n) and determine the distribution of heat transfer coefficient h(x,x), Note: For Pr>>>1, the distribution of u across the thermal boundary layer is approximately linear with the distance from the wall y, i.e. u= y. To (x) μl T=T= constant x=0\ T = Tw TT (unheated) X = constant
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Related Book For
Fundamentals of Heat and Mass Transfer
ISBN: 978-0471457282
6th Edition
Authors: Incropera, Dewitt, Bergman, Lavine
Posted Date:
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