Numerical Simulation of Heat Transfer in an Enclosure with Time-Periodic Heat Generation Using Finite-Difference Method

Abstract

This paper reports a numerical investigation of highly coupled system of partial differential equations, simulating the fluid flow and heat transfer in a large-scale enclosure with time-periodic heat generation. The bottom wall of the enclosure is insulated, and heat exchange with the environment is modeled at other external boundaries. The heater with time-periodic heat generation is located at the bottom of the enclosure. The internal surfaces of both the heater and walls are assumed to be gray. Air is the working fluid and the Rayleigh number is 109. To solve the governing equations with dimensionless vorticity – stream function – temperature variables, the finite difference method has been used. The developed model has been validated through a comparison with data of other authors. The effect of surface emissivity and periodic heat generation on Nusselt numbers and both stream function and temperature distributions has been investigated. The results showed that the influence of the thermal radiation on total thermal transmission increases with surface emissivity of walls and heater surfaces. The present numerical method can be applied in several engineering problems, such as designing passive cooling systems and the simulation of heat transfer in building constructions.