A method for solving problems of~heat transfer during the~flow of~fluids in~a plane channel

A. V. Eremin ; I. V. Kudinov ; V. V. Zhukov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 20 (2016) no. 1, pp. 109-120.

Résumé

Using the integral method of heat-transfer with the additional boundary conditions we obtain the high precision approximate analytical solution of heat-transfer for a fluid, moving in plate-parallel channel with symmetric boundary conditions of the first kind. Because of the infinite speed of heat propagation described by a parabolic equation of heat-conduction, the temperature in the centre of channel would change immediately after the boundary conditions (of the first kind) application. We receive the approximate analytical solution of boundary value problem using the representation of this temperature in the form of additional required function and introducing the additional boundary conditions to satisfy the original differential equation in boundary points by the desired function. Using of the integral of heat balance we reduce the solving of differential equation in partial derivatives to integration of ordinary differential equation with respect to additional required function, that changes depending on longitudinal variable. We note that fulfillment of the original equation at the boundaries of the area with increasing number of approximations leads to the fulfillment of that equation inside the area. No need to integrate the differential equation on the transverse spatial variable, so we are limited only by the implementation of the integral of heat-transfer (averaged original differential equation), that allows to apply this method to boundary value problems, unsolvable using classic analytical methods.

Détail

Keywords: heat conduction in fluid, infinite speed of heat propagation, integral method of thermal balance, approximate analytical solution, additional required function, additional boundary conditions, trigonometric coordinate functions.

Bibliographie

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