Optimization of Natural Convection in Open Vertical Ducts with Heated Cores

Natural Convection in a Vertical Microannulus with Superhydrophobic Slip and Temperature Jump

“…which is also previously obtained by Wang [1]. For λ 1, the flow rate tends to the following asymptotic limit:…”

“…We may check that when both walls are no-slip surfaces, i.e., on the vanishing of both velocity slip and temperature jump: λ = γ = 0, the flow rate reduces to the one previously obtained by Wang [1]:…”

“…Again, for λ = γ = 0, we may check that Q B I (b, 0, 0) = Q A I (b, 0, 0), which as given in Eq. (14) is the flow rate previously deduced by Wang [1]. For λ 1 and γ 1, the following asymptotic limit can be obtained:…”

“…This paper aims to extend the work by Wang [1], who studied a similar problem of natural convection in an annular duct but without considering velocity slip and temperature jump.…”

“…Wang [1] found that, under each heating condition, there is an optimum size of the channel core for maximal flow and energy transport. He also investigated the singular behavior, in the form of a sharp rise from zero, of the flow when the core is very small.…”