Network numerical analysis of magneto-micropolar convection through a vertical circular non-Darcian porous medium conduit

Abstract

Abstract The fully developed, mixed convection heat transfer of a magneto-micropolar fluid in a Darcy–Forchheimer porous medium containing heat sources contained in a vertical circular conduit is investigated in this article. The conservation equations for mass, linear momentum, micro-inertia, angular momentum (micro-rotation) and energy are presented in a cylindrical coordinate system (r, θ, z) with appropriate boundary conditions. A Darcy–Forchheimer drag force model is employed to simulate the effects of bulk linear porous impedance and second order porous resistance. The governing partial differential equations are non-dimensionalized into a set of ordinary differential equations in a single independent variable (η) and solved using the Network Simulation Method. Benchmark solutions are compared with earlier computations using the finite element method, showing excellent agreement. The influence of Darcy number, Forchheimer number, Grashof number, Hartmann number, geometric scale ratio (conduit radius to length ratio), Eringen parameter (ratio of vortex viscosity to Newtonian viscosity) and heat source/sink parameter on the linear velocity, angular velocity (micro-rotation) and temperature functions are studied in detail. Flow i.e. linear (translational) velocity, f, is seen to be inhibited with increasing magnetic field (Hartmann number), Forchheimer number and Eringen parameter, but accelerated with increasing Darcy number. Micro-rotation (g) is decreased with increasing Forchheimer number and Hartmann number, but increased with a rise in Grashof number, Darcy number, geometric scale ratio and Eringen parameter. Both velocity (f) and micro-rotation (g) are increased in the presence of a heat source but decreased with a heat sink. Several special cases of the flow regime are also documented. Applications of the problem include the cooling of porous combustion chambers, geophysical transport in electrically-conducting zones, exhaust nozzles of porous walled flow reactors, hydromagnetic control processes in nuclear engineering and magnetic materials processing (ceramic foams).