Canadian Journal of Chemical Engineering, Vol.72, No.3, 457-467, 1994
A Bifurcation Study of Convective Heat-Transfer in a Hele-Shaw Cell
Steady-state multiplicity characteristics of convective heat transfer within a Hele-Shaw cell are investigated. The Navier-Stokes equations and the energy equation are averaged across the narrow gap, d, of the cell. The resulting two-dimensional, stationary equations depend on the following parameters : (i) the length to height aspect ratio gamma, (ii) the tilt angle phi (iii) the Prandtl number Pr, (iv) an inertia parameter xi = d2/12a2, and (v) the Grashof number, Gr = Q(g)betaga5/kv2. Here a is the height of the cell and Q(g) is the heat generation rate per unit volume. The complete structure of symmetric and asymmetric stationary solutions are traced using recent algorithms from bifurcation theory. In the double limit of xi --> 0 and Gr --> infinity such that Ra = 4GrPrxi remains finite (where Ra is the Rayleigh number for the Darcy model) the Hele-Shaw model reduces to that of the Darcy model.