The Effect of Inlet and Exit Losses on Free Convective Laminar Flow in the Trombe Wall Channel

Abstract

A numerical solution for two-dimensional free convective laminar flow in the Trombe wall channel has recently been presented by Akbari and Borgers [1]. Their analysis assumed no flow losses in the channel entrance and exit, other than the exit dynamic head (loss coefficient k = 1), however the actual coefficient for combined inlet and exit losses is probably 2 < k < 5. In the present study, the convective terms of the momentum and energy equations are linearized through an Oseen-type approximation. A closed-form series solution to the resulting partial differential equations is obtained. Results are presented for dimensionless temperature and velocity field, flow rate and heat transfer; in terms of loss coefficient, surface temperature ratio, and Grashof number. As expected, vent loss reduces flow rate significantly: for loss coefficient k = 5, flow rate is reduced by ∼70 percent relative to k = 1. Surprisingly, at high Grashof number, vent loss can cause a significant (∼60 percent) increase in heat transfer. Reduction in flow rate occurs entirely due to flow velocity decrease in the region near the channel center, which contributes negligibly to the total heat delivery.