The similarity solution of unsteady, incompressible MHD thermal boundary layer flow in natural convection has been investigated using group-theoretic transformations. Two parameter group transformations is applied for simultaneous elimination of more than one independent variable. Consequently the system of governing highly non-linear partial differential equations with auxiliary conditions reduces to a non-linear ordinary differential equation with appropriate auxiliary conditions. Effects of all emerging physical parameters are demonstrated with the help of graphs for both velocity and temperature distribution. The numerical solution is derived systematically in dimensionless form as an application of engineering with MATLAB.

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MHD thermal flow two parameter group–theoretic method similarity solution