Numerical modeling of non-affine viscoelastic fluid flow including viscous dissipation through a square cross section duct: heat transfer enhancement due to the inertia and the elastic effects

Fouad Hagani, M'Hamed Boutaous, Ronnie Knikker, Shihe Xin, Dennis Siginer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Non-isothermal laminar flow of a viscoelastic fluid including viscous dissipation through a square cross section duct is analyzed. Viscoelastic stresses are described by Giesekus modele orthe Phan-Thien Tanner model and the solvent shear stress is given by the linear Newtonian constitutive relationship. The flow through the tube is governed by the conservation equations of energy, mass, momentum associated with to one non affine rheological model mentioned above. The mixed type of the governing system of equations (elliptic parabolic hyperbolic) requires coupling between discretisation methods designed for elliptic type equations and techniques adapted to transport equations. To allow appropriate spatial discretisation of the convection terms, the system is rewritten in a quasi-linear first-order and homogeneous form without the continuity and energy equations. With the rheological models of the Giesekus type, the conformation tensor is by definition symmetrical and positivedefinite, with the PTT model the hyperbolicity condition is subject to restrictions related to the rheological parameters. Based on this hyperbolicity condition, the contribution of the hyperbolic part is approximated by applying the characteristic method to extract pure advection terms which are then discretized by high ordre schemes WENO and HOUC. The algorithm thus developed makes it possible, to avoid the problems of instabilities related to the high Weissenberg number without the use of any stabilization method. Finally, a Nusselt number analysis is given as a function of inertia, elasticity, viscous dissipation, for constant solvent viscosity ratio and constant material and rheological parameters.

Original languageEnglish
Title of host publicationFluids Engineering
PublisherAmerican Society of Mechanical Engineers(ASME)
ISBN (Electronic)9780791884584
DOIs
Publication statusPublished - 2020
EventASME 2020 International Mechanical Engineering Congress and Exposition, IMECE 2020 - Virtual, Online
Duration: Nov 16 2020Nov 19 2020

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)
Volume10

Conference

ConferenceASME 2020 International Mechanical Engineering Congress and Exposition, IMECE 2020
CityVirtual, Online
Period11/16/2011/19/20

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

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