3-DIMENSIONAL FREE-CONVECTION IN A LONG ROTATING POROUS BOX - ANALYTICAL SOLUTION

A three-dimensional analytical solution to the steady-state free con v ection problem in a long rotating porous box is presented for large va lues of the porous media Ekman number. The convection results from dif ferential heating of the horizontal walls leading to temperature gradi ents orthogonal to the centrifugal body force. The solution to the non linear set of partial differential equations was obtained through an a symptotic expansion of the dependent variables in terms of two small p arameters representing the reciprocal Ekman number in porous media and the aspect ratio of the domain. The results are focused towards the C oriolis effect on the flow. Secondary circulation was obtained in a pl ane orthogonal to the leading free convection plane. The results show that the Coriolis effect on free convection is controlled by a combine d dimensionless group representing the ratio of the centrifugal Raylei gh number to the porous media Ekman number.