Unsteady flow and heat transfer of three immiscible fluids

The problem of unsteady flow and heat transfer of three immiscible viscous fluids has been studied in a horizontal channel. The fluids in all the three regions are assumed to be incompressible with different viscosities and thermal conductivities. The channel walls are maintained at two different constant temperatures. The partial differential equations governing the flow are transformed to ordinary differential equations using the exponential function of periodic frequency parameter and exact solutions are found. The expressions for velocity and temperature distributions are computed numerically for different values of physical parameters governing the flow and the results are presented graphically. It is found that the flow can be controlled choosing suitable values of ratios of viscosities, height ratios, pressure, conductivity ratios, the Eckert number, frequency parameter and periodic frequency parameters. In addition, closed form expression for the rate of heat transfer at the top and bottom walls are derived and are tabulated.