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O. K. Onanuga, M. A. C. Chendo and N. E. Erusiafe

**keywords:** Darcy-forchheimer, heat transfer, hydromagnetic, Joule heating, variable electric conductivity

In this study, analysis of transient free convective Joule heating flow of viscous dissipation and radiative heat transfer in an inclined Darcy-forchhemier porous cylinder medium with the constant uniform source or sink and variable electric conductivity is considered. The Rosseland approximation is adopted for the expression of thick radiation heat flux in the heat equation with gray radiating liquid, non-scattering but with absorbing-emitting depending on wavelength. The boundary layer coupled nonlinear governing system of partial differential equations are non-dimensional and solved using unconditionally stable, compatible and convergence implicit finite difference scheme of Crank-Nicolson type. The computational results are obtained and presented graphically to illustrate all the embedded parameters in the transient momentum and energy equations. The flowing liquid and heat transfer characteristics at the plate which are of engineering interest are examined and discussed for the skin-friction coefficient and thermal gradient as shown graphically.

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