Effect of heat source/sink on MHD start-up natural convective flow in an annulus with isothermal and isoflux boundaries

Abstract

This article examines the influence of isothermal and isoflux heating/cooling with heat source/sink on unsteady hydromagnetic-free convective flow of a viscous incompressible fluid in an annulus. The flow is induced by buoyancy forces due to temperature differences as a result of the isothermal heating and constant heat flux applied on the outer surface of the inner cylinder. Our treatment of the governing energy and momentum equation is based on a two-step approach. First, the nonlinear partial differential equations are transformed to the Laplace domain using the Laplace transform method and solved analytically in the Laplace domain. The Laplace domain solution is then inverted back to time domain using a numerical scheme known as Riemann-Sum Approximation (RSA). The derived numerical values by the method of RSA exhibit an excellent conformity with PDEPE and steady-state solutions at large time. The influence of the various dimensionless controlling parameters on the flow formation is depicted graphically and in tabular form.

Keywords

• transient
• heat source/sink
• mhd
• isothermal–isoflux
• riemann-sum approximation (rsa)
• pdepe