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Analytic solutions of the temperature distribution in Blasius viscous flow problems. (English) Zbl 1007.76014
Summary: We apply an analytic technique, namely the homotopy method, to obtain an analytic approximation of temperature distribution in a laminar viscous flow over semi-infinite plate. An explicit analytic solution for temperature distributions is obtained in general cases, and recurrence formulae are given for the corresponding constant coefficients. In the cases of constant plate temperature distribution and constant plate heat flux, we calculate the first-order derivative of temperature on the plate at the 30th order of approximation. The convergence regions of these two formulae are greatly enlarged by Padé technique. The analytical results agree well with numerical results in a very large region of Prandtl number $1\le \text{Pr}\le 50$, and therefore can be applied without interpolations.
##### MSC:
 76D10 Boundary-layer theory, separation and reattachment, etc. (incompressible viscous fluids) 76M25 Other numerical methods (fluid mechanics) 80A20 Heat and mass transfer, heat flow 68W30 Symbolic computation and algebraic computation