Consider natural convection between two infinite parallel plates like the system discussed in section 5.5.2. Instead of using a Newtonian fluid between the heated walls, what would happen if a Bingham plastic were used?

a. Determine the velocity profile assuming a yield stress, \(\tau_{o}\), and viscosity, \(\mu_{o}\), for the fluid.

b. Where does the fluid stop flowing?

Transcribed Image Text:

5.5.2 SIMULTANEOUS HEAT AND MOMENTUM TRANSPORT-NATURAL CONVECTION The previous section showed how mass transfer and heat transfer could be coupled via a generation term. The current problem shows a common example of the same phenomenon serving to couple momentum and heat transfer. We refer to this coupling as natural or free convection since a tem- perature difference drives the inherent motion of a fluid. Natural convection is responsible for the wind, the cellular surface patterns observed on the sun, the great red spot of Jupiter, the hexagon on the north pole of Saturn, and what is called radiant heat in most homes and apartments. The problem we consider is an idealization of flow between two vertical walls, one heated and the other cooled as in Figure 5.14. A fluid with density, p, and viscosity, , is placed between the