Effect of time-dependent thermal boundary condition in convective heat transfer

Abstract

A numerical study is performed for the time-dependent laminar natural convection air cooling in a rectangular enclosure or in a channel. The thermal modulation is applied on each system and modeled as (1) the periodic temperature oscillation in a rectangular enclosure and (2) the variation of the heat flux of a discrete heater and (3) the modulation of the heat generation rate of a heater in a channel. (4) the heat flux modulation in a channel with porous blocks. Comprehensive time-dependent heat transfer data are obtained and averaged over a cycle of thermal modulation in a periodic steady state. Major emphasis is placed on the effect of thermal modulation on the fluid flow and heat transport in a convective system. Firstly, finite- volume numerical solutions are obtained for the buoyant convection in a square cavity which contains a horizontal baffle at mid-height. The horizontal walls of the cavity are insulated. At the cold left vertical wall, the nondimensional temperature is constant θ=0, and at the hot right vertical wall, the wall temperature is time-periodic, θ=1+εsinωτ. The length of the baffle is such that, in the basic state(ε=0), the baffle does not touch the vertical boundary layers. The flow and temperature characteristics of the basic state remain largely unaffected by the presence of the baffle. For the oscillating cases (ε≠0), the amplitude of fluctuating heat transfer rate across the cavity centerline is substantially reduced by the presence of the baffle. These changes in fluctuating flow characteristics are influenced appreciably by the thermal conductivity and the vertical location of the baffle. The oscillating flow and thermal fields are seen to be confined to the upper interior region between the top wall of cavity and the baffle. The physical interpretations, together with the prediction of the resonance frequency, are consistent with the earlier argument [2]. The transient natural convection in a vertical rectangular enclosure is al...