Thermal visualization of Ostwald-de Waele liquid in wavy trapezoidal cavity: Effect of undulation and amplitude

Abstract

The present study is concerned with the numerical simulations of Ostwald-de Waele fluid flow in a wavy trapezoidal cavity in the presence of a heated cylinder situated at the center of the cavity. The work consists in characterizing the mixed convection as a function of the intensity of heat flow. The flow behaviour and temperature distribution in a cavity are the main focus of this study. The lower wall of the cavity is fixed and heated while the wavy surface is insulated and moves with a constant speed. The sloping walls are kept cold and are subject to zero no-slip conditions for velocity components. The whole setup is modeled as a set of coupled partial differential equations and is solved by the Finite Element Method. For pressure and velocity approximations, we use the stable finite element pair P2−P1, while for temperature approximation we use the space of linear polynomial as P1. The ranges of the parameters involved in the study are the Ostwald-de Wale index (0.5≤n≤1.5), Prandlt number (1≤Pr≤10), Grashof number (100≤Gr≤1000), the number of undulation (0≤λ≤4), and the non-dimensional amplitude of the wavy surface (0.02≤A≤0.06). The major findings of the study are shown using velocity profile, streamlines, and isotherms. Moreover, the kinetic energy and average (Nuavg) Nusselt number is determined for various values of the parameters involved.