The problem of heat transfer hydro magnetic Oldroyd-B fluid in vertical oscillating belt has been investigated in unsteady state. The obtained model problems are solved for the exact analytic solutions using Optimal Homotopy Asymptotic Method (OHAM). Epressions for the temperature and velocity distribution with the mass flow rate are obtained. Heat transfer rate of the fluid at the belt is also calculated. These expressions are evaluated analytically for different values of the parameters. The effect of relevant parameters like κ1 relaxation time parameter, κ2 retardation time parameter, ϒ gravitational effect, M magnetic parameter, Br Brinkman and Pr Prandtl numbers on velocity and temperature fields has been studied and presented graphically.

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