Periodic Flow of Non-Newtonian Fluid Over a Uniformly Heated Block With Thermal Plates: A Hybrid Mesh-Based Study

Abstract

In this work, we analyze the characteristics of periodic flows in non-isothermal viscous fluid over a heated block in the presence of thermal plates at Reynolds number (Formula presented.). The unsteady, incompressible Navier–Stokes (NS) equations with suitable initial and boundary data in 2D are executed by the finite element technique using a highly refined hybrid mesh. The temporal discretization is performed by an implicit stable backward differencing in time and a stable choice of finite elements from the finite element library for spatial discretization. The discrete nonlinear system arising from this discretization is linearized by Newton’s method and then solved through a direct linear solver PARDISO. For this forced convective study, the range of dimensionless parameters, namely, the Prandtl number (Formula presented.) and power law index (Formula presented.), are varied from 1 to 10 and 0.6 to 1.4 with a low Grashof number varying as (Formula presented.) to produce a forced convection regime, respectively. For the authentication, we have compared our results with the literature at a similar configuration. After simulation, the results accomplished in the velocity profile, pressure, isotherm contours, drag and lift coefficients (trajectory motion), average Nusselt number (Formula presented.), etc. are considered. For convergence of solution at low shear rate (Formula presented.), crosswind stabilization (CWS) function has been incorporated. It is observed that (Formula presented.) becomes oscillatory for the shear-thinning case (Formula presented.), while for the shear-thickening cases (Formula presented.), it converges to a single value. Furthermore, the drag (Formula presented.) and lift (Formula presented.) coefficients are more pronounced for shear-thinning cases (Formula presented.) as compared with shear-thickening cases (Formula presented.).