Thermally Developing Heat Transfer with Non-Linear Viscoelastic and Newtonian Fluids with Pressure Dependent Viscosity

[+] Author and Article Information
Dennis A. Siginer

Centro de Investigación en Creatividad y Educación Superior & Departamento de Ingeniería Mecánica Universidad de Santiago de Chile, Santiago, Chile; Department of Mathematics and Statistical Sciences & Department of Mechanical, Energy and Industrial Engineering, Bostwana International University of Science and Technology, Palapye, Bostwana

F.Talay Akyildiz

Department of Mathematics and Statistics, Al-Imam University, Riyadh, Saudi Arabia

M'hamed Boutaous

Université de Lyon, CNRS, INSA-Lyon, CETHIL, UMR5008, F-69621, Villeurbanne, France

1Corresponding author.

ASME doi:10.1115/1.4040153 History: Received March 01, 2018; Revised April 29, 2018


A semi-analytical solution of the thermal entrance problem with constant wall temperature for channel flow of Maxwell type viscoelastic fluids and Newtonian fluids, both with pressure dependent viscosity, is derived. A Fourier - Gauss Pseudo Spectral scheme is developed and used to solve the variable coefficient parabolic partial differential energy equation. The dependence of the Nusselt number and the bulk temperature on the pressure coefficient is investigated for the Newtonian case including viscous dissipation. These effects are found to be closely interactive. The effect of the Weissenberg number on the local Nusselt number is explored for the Maxwell fluid with pressure dependent viscosity. Local Nusselt number decreases with increasing pressure coefficient for both fluids.

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