Journal of Fluid Mechanics

Analytic solutions of the temperature distribution in Blasius viscous flow problems

a1 School of Naval Architecture & Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200030, China
a2 College of Engineering, Idaho State University, Campus Box 808, Pocatello, ID 83209-8060, USA


We apply a new analytic technique, namely the homotopy analysis method, to give an analytic approximation of temperature distributions for a laminar viscous flow over a semi-infinite plate. An explicit analytic solution of the temperature distributions is obtained in general cases and recurrence formulae of the corresponding constant coefficients are given. In the cases of constant plate temperature distribution and constant plate heat flux, the first-order derivative of the temperature on the plate at the 30th order of approximation is given. The convergence regions of these two formulae are greatly enlarged by the Padé technique. They agree well with numerical results in a very large region of Prandtl number 1[less-than-or-eq, slant]Pr[less-than-or-eq, slant]50 and therefore can be applied without interpolations.

(Received December 17 1999)
(Revised May 6 2001)