A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts an the rotating surfaces art obtained at different nondimen-sional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.