Analyzing Nano“uids Suspension Using the Porous Media Interface Heat Transfer Model

The convection of a Bingham fluid in a differentially-heated porous cavity

“…When Rb = 24 in Fig. 3, the streamlines within the nonstagnant region are mostly almost vertical or almost horizontal, apart from close to teh corners, and therefore the network model developed in Rees (2015a) is of some relevance. In that chapter, the square porous cavity was assumed to consist of narrow vertical and horizontal channels of equal width which were arranged in a square network.…”

“…where the value, G, is the threshold pressure gradient. If a porous medium were to be composed of a parallel set of identical channels of width, h, then Rees (2015a) shows that the threshold gradient is given by G = 2τ 0 /h where τ 0 is the yield stress of the fluid. An almost identical formula for G applies when the microstructure is composed of tubes of circular cross-section.…”

“…Figure 5 is concerned with a cavity having aspect ratio, A = 2 where Rb = 10. In this case a network analysis of the type given in Rees (2015a) would suggest that convection takes place whenever Ra > 6Rb, where 6 is the length of the perimeter of the cavity. This certainly appears to be consistent with the numerical results in Fig.…”

“…While a large and mature literature is associated with yield-stress fluids in general, once those fluids saturate a porous medium there are far fewer studies available. While undertaking a detailed literature review for Rees (2015a) it was found that there are only about a dozen papers dealing with convection of yield-stress fluids in a porous medium and all considered flow of boundary layer type in an otherwise unbounded region; see Rees (2015b) for comments on the realizability of the flows described in these papers. Therefore the literature is silent on the topic of cavity convection of a Bingham fluid in porous media.…”

Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium following a sudden change in surface heat flux

“…Unlike Herschel-Bulkeley and Casson fluids, they exhibit a linear stress-strain relationship once the yield stress is exceeded. They arise in a wide variety of situations both in the environment and industry, and examples of the very many natural and man-made fluids which exhibit a yield stress have been collated and prsented in the chapter [1].…”