Coriolis effect on free convection in a long rotating porous box subject to uniform heat generation

The Coriolis effect on free convection in a long rotating porous box subject to uniform heat generation is investigated analytically. A three dimensional analytical solution is presented for large values of the porous media Ekman number. The convection results from internal heat generation which produces temperature gradients orthogonal to the centrifugal body force. Two types of thermal boundary conditions are considered for the top and bottom walls of the box. The first type is associated with perfectly conducting boundaries, i.e. the same temperature is imposed on both the top and bottom walls while the second type corresponds to a perfectly conducting top wall and adiabatic bottom wall. The solution to the nonlinear set of partial differential equations is obtained through an asymptotic expansion of the dependent variables in terms of two small parameters representing the reciprocal Ekman number in porous media and the aspect ratio of the domain. Secondary circulation in the form of one or two vortices is obtained in a plane orthogonal to the leading free convection plane.