Network method to study the transient heat transfer problem in a vertical channel with viscous dissipation

The transient problem for fully developed mixed convection considering the effect of viscous dissipation is investigated for the laminar flow in a parallel-plate vertical channel by means of the Network Simulation Method. The thermal boundary condition considered is a forced convection. The combined effects of viscous dissipation and buoyancy forces are determined in the solutions for different time intervals, being obtained in all the cases, the velocity field and the temperature field. The times taken to reach steady-state is obtained in all the cases. The numerical procedure employed, which satisfies the conservation law for the heat flux variable and the uniqueness law for temperature, also permits the direct visualisation and evolution of the local and/or integrated transport variables at any point or section of the medium.