Abstract
The problem of unsteady oscillatory flow and heat transfer in a horizontal composite porous medium is performed. The flow is modeled using the Darcy-Brinkman equation. The viscous and Darcian dissipation terms are also included in the energy equation. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both regions of the channel. Effect of the physical parameters such as the porous medium parameter, ratio of viscosity, oscillation amplitude, conductivity ratio, Prandtl number and the Eckert number on the velocity and/or temperature fields are shown graphically. It is observed that both the velocity and temperature fields in the channel decrease as either of the porous medium parameter or the viscosity ratio increases while they increase with increases in the oscillation amplitude. Also, increasing the thermal conductivity ratio is found to suppress the temperature in both regions of the channel. The effects of the Prandtl and Eckert numbers are found to decrease the thermal state in the channel as well.
Highlights
In recent years considerable interest has been evidenced in the study of flow past a porous medium because of its natural occurrence and importance in both geophysical and engineering environments
The closed-form solutions are reported for small such that oscillation amplitude εA ≤ 1
It was concluded that the temperature field decreased as either of the Prandtl number, the Eckert number or the thermal conductivity ratio increased
Summary
In recent years considerable interest has been evidenced in the study of flow past a porous medium because of its natural occurrence and importance in both geophysical and engineering environments. Research on thermal interaction between heat generating porous bed and overlying fluid layer was largely motivated by the nuclear reactor severe accident problems. Another area of nuclear engineering applications is the design of pebble bed reactor which requires a proper understanding of forced convection through packed beds under normal operating conditions and of free convection either in the case of loss of coolant or during cold shut down. The surfaces of the joint are articular cartilage, a smooth rubbery material which is attached to the solid bone. It has been suggested that because of the porous nature of the articular cartilage, other lubricating material is squeezed into the joint when it is under stress. King and Cox [10] performed an asymptotic analysis of the steady-state and time-dependent laminar porous channel flows
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