An approximate method for calculating laminar natural convective motion in a trombe-wall channel

Laminar natural convective motion in a channel formed by differentially heated vertical plates is analyzed. The proposed model combines the momentum-integral equation with the Oseen approximation for convective terms in the energy equation to predict the volumetric flow rate as a function of channel height. A second-order ordinary differential equation for pressure defect in the channel is derived by approximating the axial velocity profile with a fourth-order polynomial. Results obtained from the present model are in good agreement with previously reported results. Consideration of a second-order axial velocity profile in the momentum-integral model leads to closed form solutions that are in good agreement with previously reported results only in the mid to high flowrate regime. In the low flow-rate regime, the second-order model gives results that deviate significantly from results obtained for other models. Neglect of inertia terms in the momentum-integral model leads to a first-order differential equation for the pressure and a closed form solution of the problem. However, this approximation yields results that are good only in the mid to high flowrate regime, while showing deviations from other models in the low flowrate regime. Finally, the present model is also shown to be capable of application to fluids with widely ranging Prandtl numbers.