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.

This content is only available via PDF.
You do not currently have access to this content.