A method to solve the heat transfer problem for laminar flow of Phan-Tien-Tanner fluid in a flat channel

Abstract

Abstract The paper presents a solution to the heat transfer problem for a flow of a four-mode viscoelastic linear Phan-Tien Tanner fluid in flat channels at a constant wall temperature. A special feature of this solution is the parametric representation of dependence of an axial velocity and temperature on coordinates. To obtain a solution to the energy transfer equation, we used the method of separating variables and decomposing the sought-for function into series by parameter. For a specific liquid, the profiles of dimensionless velocity and distribution of dimensionless temperature, Nusselt numbers, and other heat transfer characteristics for various Weissenberg numbers are presented.