Korea-Australia Rheology Journal, Vol.30, No.4, 273-292, November, 2018
Effects of viscous dissipation on heat convection of viscoelastic flow lastic flow
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In the present paper, analytical solutions for thermal convection of the Finitely Extensible Nonlinear Elastic model with Peterlin’s closure (FENE-P) in isothermal slits and tubes are presented by considering the viscous dissipation effects for the first time. Temperature distributions are derived in closed form, namely the HeunT function, and Frobenius series solutions for the slit and the tube flows, respectively. The effects of fluid elasticity, the Brinkman number and the extensibility parameter on the thermal convection characteristics of FENE-P fluid flows are investigated in detail. Generally, the Brinkman number causes a fall in the Nusselt number, but a rise in the centerline temperature. The results reveal that during the cooling process the Nusselt number experiences a decrease with the Brinkman number, while the centerline temperature rises. However, during the heating process the former increases and the latter decreases. As the main innovation of this study, the results show a strong relation between the Nusselt number and the Brinkman number and also between the centerline temperature and the Brinkman number.
Keywords:FENE-P model;viscoelastic fluid;forced convection;HeunT function;isothermal tubes and slits;viscous dissipation
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