A Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium
KAUST DepartmentPhysical Sciences and Engineering (PSE) Division
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AbstractThe problem of thermal dispersion effects on unsteady free convection from an isothermal horizontal circular cylinder to a non-Newtonian fluid saturating a porous medium is examined numerically. The Darcy-Brinkman-Forchheimer model is employed to describe the flow field. The thermal diffusivity coefficient has been assumed to be the sum of the molecular diffusivity and the dynamic diffusivity due to mechanical dispersion. The simultaneous development of the momentum and thermal boundary layers are obtained by using finite difference method. The stability conditions are determined for each difference equation. Using an explicit finite difference scheme, solutions at each time-step have been found and then stepped forward in time until reaching steady state solution. Velocity and temperature profiles are shown graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficient approach the steady state values.
CitationA Conditionally Stable Scheme for a Transient Flow of a Non-Newtonian Fluid Saturating a Porous Medium 2012, 9:651 Procedia Computer Science
JournalProcedia Computer Science
Conference/Event name12th Annual International Conference on Computational Science, ICCS 2012