In this paper, the problem of unsteady free convective flow of an incompressible micropolar fluid between two vertical walls is studied. The fluid motion is due to fluid density caused by temperature  gradients. Non-dimensional variables are introduced. The non-classical slip and spin boundary conditions are applied. The Laplace transform technique and state space approach method are adopted to get the solution in the Laplace domain. The inversion of the Laplace transform is acquired using standard numerical method based on Fourier series expansion. The results are discussed and illustrated graphically.

micropolar fluid, free convection, slip condition, state space approach.