Exact analysis of heat convection of viscoelastic FENE-P fluids through isothermal slits and tubes

In this article, two exact analytical solutions for heat convection in viscoelastic fluid flow through isothermal tubes and slits are presented for the first time. Herein, a Peterlin type of finitely extensible nonlinear elastic (FENE-P) model is used as the nonlinear constitutive equation for the viscoelastic fluid. Due to the eigenvalue form of the heat transfer equation, the modal analysis technique has been used to determine the physical temperature distributions. The closed form solution for the temperature profile is obtained in terms of a Heun Tri-confluent function for slit flow and then the Frobenius method is used to evaluate the temperature distribution for the tube flow. Based on these solutions, the effects of extensibility parameter and Deborah number on thermal convection in FENE-P fluid flow have been studied in detail. The fractional correlations for reduced Nusselt number in terms of material modulus are also derived. Here, it is shown that by increasing the Deborah number from 0 to 100, the Nusselt number is enhanced by 8.5 and 13.5% for slit and tube flow, respectively.