Numerical Computation of MHD Thermal Flow of Cross Model over an Elliptic Cylinder: Reduction of Forces via Thickness Ratio

Abstract

The present work is concerned with a comprehensive analysis of hydrodynamic forces, under MHD and forced convection thermal flow over a heated cylinder in presence of insulated plates installed at walls. The magnetic field is imposed in the transverse direction of flow. The Galerkin finite element (GFE) scheme has been used to discretize the two-dimensional system of nonlinear partial different equations. The study is executed for the varying range of flow behavior index n from 0.4 to 1.6, Hartmann number Ha from 0 to 100, Reynolds number Re from 10 to 50, Grashof number Gr from 1 to 10, thickness ratio e from 0.5 to 1.0, and Prandtl number Pr from 1 to 10, respectively. A coarse hybrid computational grid is developed, and further refinement is carried out for obtaining the highly accurate solution. The optimum case selection is based on flow patterns, drag and lift coefficients, and pressure drop reduction against cylinder thickness ratios and average Nusselt numbers. Drag coefficient increases with an increase in thickness ratio e . The drag force reduction for e = 0.5 and e = 0.75 is also observed for a range of the power law index as compared with e = 1.0 cylinder. Maximum pressure drop over the back and front points of cylinder is reported at Ha = 100 .

Computational Analysis of Fluid Forces on an Obstacle in a Channel Driven Cavity: Viscoplastic Material Based Characteristics

“…In this direction, the conforming element pair P 2 − P 1 is selected for the velocity and pressure approximations. This element is a stable pair satisfying the inf-sup condition [40][41][42][43]. Newton's method is applied to solve discrete nonlinear algebraic systems, and the inner linear subproblems are solved using a direct solver.…”

“…Due to the high nonlinearity of the model, exact solutions to such problems are rare; therefore, we apply FEM computation for the numerical approximation of the governing equations. In this direction, the conforming element pair ℙ 2 − ℙ 1 is selected for the velocity and pressure approximations This element is a stable pair satisfying the inf-sup condition [40][41][42][43]. Newton's method is applied to solve discrete nonlinear algebraic systems, and the inner linear subproblems are solved using a direct solver.…”

Statistical Analysis of Hydrodynamic Forces in Power-Law Fluid Flow in a Channel: Circular Versus Semi-Circular Cylinder

“…Among many numerical tools reported in the literature to deal with the mechanics of fluid flow, the finite element method (FEM) is the prominent one. The functionality of the finite element method and the mathematical modeling for our problem is described in references [36][37][38][39][40][41][42].…”

Numerical Computations of Entropy Generation and MHD Ferrofluid Filled in a Closed Wavy Configuration: Finite Element Based Study

“…The discrete systems of nonlinear algebraic equations are computed by utilizing the Newton method and the linearized inner system with a direct solver PARDISO. There are many benefits of using the PARDISO solver (see [27][28][29][30][31][32][33][34] for further information).…”