Summary: In the present investigation a theoretical analysis is performed to study the unsteady mixed convection flow and heat transfer between two infinite coaxial isothermal disks. One disk rotated at a constant rate and another one at a time-dependent rate. Two modes of the time-dependent rotation, asymptotic and torsionally oscillatory, are studied. Governing equations are formulated with respect to a rotating frame of reference. The density variation in the centrifugal force term is considered to explore the rotation-induced buoyancy effect. By using proper transformations, a simple model of spatial similarity for a Boussinesq fluid is developed and then solved by a finite-difference method. Effects of rotation, centrifugal buoyancy, unsteadiness, oscillation amplitude and frequency on the flow and heat transfer characteristics are discussed.