A Numerical Study of Natural Convective Flow Through a Vertical Symmetrically Heated Channel With an Unheated Upper Section

Abstract

Natural convective flow through a vertical plane channel has been considered. The walls of the lower portion of the channel are heated to a uniform temperature, both of the heated walls being at the same temperature. The walls of the upper part of the channel are unheated, i.e., are adiabatic. The reason for undertaking the study arose from the fact that using an adiabatic upper wall section can, through the so-called chimney effect, increase the flow rate through the channel and therefore increase the heat transfer rate from the lower heated wall section. However if the upper adiabatic wall section is too long the increased pressure drop due to viscous effects can lead to a reduced flow rate through the channel and to a reduced heat transfer rate. Therefore a need existed to examine in more detail the effect that the height of the upper adiabatic wall section has on the heat transfer rate. The flow has been assumed to be steady and the Boussinesq approximation has been adopted. The solutions have been obtained using the commercial CFD code FLUENT©. The solution has the Rayleigh number, the Prandtl number, the ratio of the channel width to the height of the heated channel wall section, and the ratio of the height of the adiabatic channel wall section to the height of the heated wall section as parameters. Results have only been obtained for a Prandtl number of 0.74 (the value for air at temperatures near ambient temperature). Results have been obtained for a wide range of values of the remaining parameters and the effects of these parameters on the mean Nusselt number have been studied.