Effect of temperature-dependent viscosity on entropy generation in transient viscoelastic polymeric fluid flow from an isothermal vertical plate

A numerical investigation of the viscosity variation effect upon entropy generation in time-dependent viscoelastic polymeric fluid flow and natural convection from a semi-infinite vertical plate is described. The Reiner-Rivlin second order differential model is utilized which can predict normal stress differences in dilute polymers. The conservation equations for heat, momentum and mass are normalized with appropriate transformations and the resulting unsteady nonlinear coupled partial differential equations are elucidated with the well-organized unconditionally stable implicit Crank-Nicolson finite difference method subject to suitable initial and boundary conditions. Average values of wall shear stress and Nusselt number, second-grade fluid flow variables conferred for distinct values of physical parameters. Numerical solutions are presented to examine the entropy generation and Bejan number along with their contours. The outcomes show that entropy generation parameter and Bejan number both increase with increasing values of group parameter and Grashof number. The present study finds applications in geothermal engineering, petroleum recovery, oil extraction and thermal insulation, etc

Natural convection flow of a viscous fluid about a truncated cone with temperature dependent viscosity

The two-dimensional natural convection flow of a viscous incompressible fluid with temperature dependent viscosity about a truncated cone is considered. The governing equations for the flow are obtained by using suitable transformations and solved by using an implicit finite difference method. Perturbation solutions are obtained near the leading edge and in the downstream regime, and the results are obtained in terms of the local skin friction coefficient and the local Nusselt number. Perturbation solutions are compared with the finite difference solutions and are found to be in excellent agreement. The dimensionless velocity profiles and viscosity distribution are also presented graphically for various values of the viscosity variation parameter, Ɛ, for small values of the Prandtl number appropriate for liquid metals