• FLOW AND THERMAL CONVECTION OF THIRD GRADE VISCOELASTIC FLUID FROM A VERTICAL POROUS PLATE WITH BIOT NUMBER EFFECTS

Abstract

A mathematical model is developed to analyse the nonlinear, non-isothermal, steady-state, laminar boundary layer flow and heat transfer of an incompressible third grade viscoelastic non-Newtonian fluid past a vertical porous plate with Biot number effects. The transformed conservation equations of mass, linear momentum and heat equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller-Box method (KBM). The influence of a number of emerging non-dimensional parameters, namely the third grade fluid parameter (f), material fluid parameters (ε₁, ε₂), Prandtl number (Pr), Biot number (g) and dimensionless tangential coordinate (x) on velocity and temperature evolution in the boundary layer regime are examined in detail.  Furthermore, the effects of these parameters on surface heat transfer rate and local skin friction are also investigated. It is observed that velocity, skin friction and heat transfer rate are reduced with increasing third-grade fluid parameter (f), whereas the temperature is increased. An increase in the material fluid parameter (ε₁) reduces the velocity, skin friction and heat transfer rate but increases temperature. And increasing material fluid parameter (ε₂) accelerates velocity, skin friction and heat transfer rate but decelerates the temperature. Detailed interpretation of the computations is included. The present simulations are of interest in chemical engineering systems and solvent and low density polymer materials processing.