An attempt has been done to study the dual solutions (steady and unsteady solutions) of free convective micropolar fluid flow near the stagnation point of a sphere. Governing equations are solved numerically using suitable similarity transformations and MATLAB built-in bvp4c solver technique. The results are discussed graphically for various values of conjugate parameter (corresponds to convective boundary condition) and material parameter for micropolar fluid. Numerical results of wall temperature and skin friction coefficient are represented by tables. During time-dependent case, skin friction coefficient is controlled by material parameter, but the conjugate parameter enhances skin friction coefficient.KeywordsConvective boundary conditionLower stagnation pointMicropolar fluidSolid sphereSteady and unsteady flow