Non-linear Differential equations and Analysis of a Disturb System Using Numerical Technique (Weighted Residual Method)

Nonlinear partial differential equations governing a disturb model of magneto- hydrodynamic and heat transfer in a channel flow have been treated by the weight residual method. The stability or other wise of the disturb system is our target to the effect of a variable absorption coefficient of radiation mode of heat transfer. The results from tables, in spite of the unreliability of calculation at law Reynolds numbers indicate quite clearly that, effect of a variable absorption coefficient is to increase any tendency towards stability. The present stability analysis relates to only a simple case of flow pattern. A Further and useful development would be to consider the influence of buoyancy forces and convective heat transfer upon the stability when the channel walls are differentially and non-uniformly heated. It would also be profitable to seek to reformulate the reduction of the differential eigenvalue problem to an algebraic eigenvalue problem by use of an alternative orthogonal function expansion.