Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Abstract

We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is initially at a uniform temperature, and such flows are then induced by suddenly applying either a new constant temperature or a nonzero heat flux to the exterior surface. As time progresses, heat conducts inwards and this may or may not overcome the yield threshold for flow. For the constant temperature case, flow begins immediately should the parameter, Rb, which is a nondimensional yield parameter, be sufficiently large. The ultimate fate, though, is full immobility as the cylinder eventually tends towards a new constant temperature. For the constant heat flux case, the fluid remains immobile but will begin to flow eventually should Rb be sufficiently large. The two cases have different critical values for Rb.

Darcy–Bénard–Bingham convection

“…Most of these are boundary layer flows; see Rees 11 for a discussion of these works. A series of four papers by Rees and Bassom [12][13][14][15] is devoted to different aspects of onedimensional flows and it covers similar ground to works by Yang and Yeh 16 , Kleppe and Marner 17 , Patel and Ingham 18 , Bayazitoglu et al 19 and Barletta and Magyari 20 . Rees 21 has also presented nonlinear computations for convection in a sidewall-heated cavity and found that the presence of a Bingham fluid means that there is a critical value of the Darcy-Rayleigh number above which convection arises.…”

The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel

“…Much depends on the competing effects of the internal and external heating mechanisms and how these interact with the yield threshold. This work is part of a study of different aspects of porous channel and boundary layer flows involving Bingham fluids; see Rees and Bassom [9][10][11]. These earlier works consider the unsteady evolution of yield surfaces in such flows.…”