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.
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The problem of steady, laminar, fully developed flow and heat transfer of viscous and couple stress fluids in a vertical channel is investigated. The transport properties of the fluids in both the regions are assumed to be constant. The walls of the channel are considered to be isothermaI. The goveming momentum and energy equations are coupled and nonlinear due to the buoyancy effects. The basic equations are solved analytically using the regular perturbation method and numerically using the Runge-Kutta-GiII method. The results are represented graphically for different vaIues of the couple stress parameter, viscosity ratio, width ratio, coefficient of thermaI expansion ratio, density ratio, conductivity ratio, ratio of the Grashof number and Reynolds number and Eckert number on velocity and temperature distributions. In addition, results for the Nusselt number are computed for different values of the physical parameters and presented in a tabular form. It is found that the effect of the couple stress parameter is to promote the motion of the fluid.
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