**Abstract**

An unsteady MHD flow of a temperature dependent heat source/sink in an annulus due to ramped motion and ramped temperature of the boundaries has been analyzed. The partial differential equations of the fluid flow are formulated taking into account the ramped temperature and ramped velocity of the inner cylinder. The closed form solution are obtained for three cases of the magnetic field being fixed relative the fluid, cylinder and when the velocity of the magnetic field is less than the velocity of the moving cylinder. The problem is solved using Laplace transform technique to obtain the Laplace domain solution and Riemann sum approximation to obtain the time domain solution. The effect of the governing parameters on the fluid flow are illustrated graphically. It is found that, Hartmann number has a retarding effect on the skin friction at the outer surface of the inner cylinder and mass flow rate. It also decreases fluid velocity for cases ð Þ *K* ¼ 0*:*0 *and K* ¼ 0*:*5 the reverse effect is noticed for case ð Þ *K* ¼ 1*:*0 . Increase in Hartmann number lead to an increase in skin friction at the inner surface of the outer cylinder for case ð Þ *K* ¼ 0*:*0 but decreases it for cases ð Þ *K* ¼ 0*:*0 *and K* ¼ 0*:*5 .

**Keywords:** ramped temperature, ramped motion, magneto-hydrodynamic, natural convection, annulus, heat source/sink
