A bivariate spectral homotopy analysis method (BSHAM) is extended to solutions of systems of nonlinear coupled partial\ndifferential equations (PDEs). The method has been used successfully to solve a nonlinear PDE and is now tested with systems. The\nmethod is based on a new idea of finding solutions that obey a rule of solution expression that is defined in terms of the bivariate\nLagrange interpolation polynomials. The BSHAM is used to solve a system of coupled nonlinear partial differential equations\nmodeling the unsteady mixed convection boundary layer flow, heat, and mass transfer due to a stretching surface in a rotating\nfluid, taking into consideration the effect of buoyancy forces. Convergence of the numerical solutions was monitored using the\nresidual error of the PDEs. The effects of the flow parameters on the local skin-friction coefficient, the Nusselt number, and the\nSherwood number were presented in graphs.
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