Effect of viscous dissipation on natural convection flow between vertical parallel plates with time-periodic boundary conditions

This article investigates the natural convection flow of viscous incompressible fluid in a channel formed by two infinite vertical parallel plates. Fully developed laminar flow is considered in a vertical channel with steady–periodic temperature regime on the boundaries. The effect of internal heating by viscous dissipation is taken into consideration. Separating the velocity and temperature fields into steady and periodic parts, the resulting second order ordinary differential equations are solved to obtain the expressions for velocity, and temperature. The amplitudes and phases of temperature and velocity are also obtained as well as the rate of heat transfer and the skin-friction on the plates. In presence of viscous dissipation, fluids of relatively small Prandtl number has higher temperature than the channel plates and as such, heat is being transferred from the fluid to the plate.

► We investigate the influence of viscous dissipation on natural convection flow in a vertical channel.
► Consideration of viscous dissipation term results in nonlinearity of the energy equation.
► Viscous dissipation and convection terms lead to coupling of the momentum and energy equations.
► Perturbation technique is used to deal with the nonlinearity and the coupling.
► Influence of the governing parameters is discussed on the periodic solutions obtained from the equations of motion.