Heat and Mass Transfer From a Film Into Steady Shear Flow

Steady advection–diffusion around finite absorbers in two-dimensional potential flows

“…A similar overlapping accuracy was found for a three-dimensional problem of heat or mass transfer in a steady shear flow by Phillips (1990), who combined high-and low-Pe expansions only for the Nusselt number, Nu, using singular perturbation. The dependence of the flux σ on Pe can be described heuristically by a formula of the form…”

“…The classical approach, therefore, has been to employ asymptotic analysis to obtain approximate solutions, usually relating the total integrated flux, or Nusselt number, Nu, to the Péclet number, Pe. Early studies of this type focused on spheres (Acrivos & Taylor, 1962) and more complicated shapes (Brenner, 1963) in Stokes flows, and later studies dealt with heat or mass transfer in steady shear flow (Phillips, 1990). Related work continues to the present day, e.g.…”

Effect of Radiation on the Unsteady Hydro magnetic Heat Transfer Flow in a Vertical Wavy Channel with Oscillating Flux

“…The combined effect of thermal and mass diffusion in channel flows has been studied by a few authors in recent times [1]. The problem of combined buoyancy driven thermal and mass diffusion has been studied in parallel plate geometries by a few authors, notably, Lai [2], Chen and Mont Sogol [3], Poulikakos [4] and Angirasa et.…”

Convective diffusion from strip-like micro-probes into colloidal suspensions

“…The trailing-edge analyses [13,14,20,23] take account of the second square-root singularity, due to analogous step change in boundary conditions (1d), (1e) at x = h. Dependence of the concentration field in the trailing-edge region on the upstream conditions results in essential structural difference from the leading-edge analysis. The edge effects due to spatial diffusion were studied extensively only for the simple shear flow, p = 1, [11][12][13][14][15][16][17][18][19][20][21]. The early numerical studies [11,16,17] failed to give correct estimate of the edge effects because of use of the rectangular mesh in original coordinates (x, z).…”

“…For each of the edge regions, he used the rectangular mesh in the regularized coordinates, obtained by a suitable square-root conformal mapping. The idea of singular asymptotic matching was also used in analytic studies based on the Wiener-Hopf method [12,13,15,20]. As intuitively taken by Newman [14] and explicitly pronounced by Phillips [20], the concept of localized trailing-edge effect is limited to estimating just the leading term in the corresponding singular asymptotic matching for high H. The correct higher-order terms in such expansions [20] unavoidably include secondary changes of the overall concentration field, caused by the effect of longitudinal diffusion in the leading-edge region.…”