Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier–Stokes equations

An analytical treatment for the exact solutions of MHD flow and heat over two–three dimensional deforming bodies

“…The pioneering works of [7] on the two-dimensional pure linear stretching sheet and that of [8] (see also [9]) on the two-dimensional pure linear shrinking sheet have probably initiated ten thousands of subsequent conductions on the subject taking into account further physical properties; power-law wall stretching/shrinking [10][11][12][13][14], unsteadiness [15][16][17], stagnation-point flow [18][19][20], generalized stretching/shrinking wall [21,22], magnetohydrodynamic (MHD) effects [23][24][25][26], porosity of the media [27], wall permeability [28][29][30][31][32][33], micropolar fluids [34][35][36], three dimensional/axisymmetric flow [37][38][39]42,40,41], exponential wall stretching/shrinking [43][44][45][46], first and second order fluid wall slippage [47][48][49][50][51]…”

Entropy Generation in Boundary Layer Flow of a Micro Polar Fluid Over a Stretching Sheet Embedded in a Highly Absorbing Medium

“…Hoyt and Fabula (1964) have shown experimentally that fluids containing minute polymeric additives display a considerable reduction in the skin friction (about 30%). The theory of micro polar fluids, which display the effect of local rotary inertia and non-symmetrical stress tensor, was initially introduced and investigated by Eringen (2001), takes into account fluids consisting of randomly oriented particles suspended in a viscous medium. Extensive reviews of the theory and its applications could be found in the review article by Ariman et al (1973).…”

“…Fang et al (2011) investigated the steady momentum and heat transfer of a viscous fluid flow over a linearly stretching/shrinking sheet and then a convective boundary condition were further studied analytically. There are some analytic techniques for nonlinear problems, such as perturbation techniques (essentially based on the existence of small or large parameters) that are well known and widely applied.…”

Note on Cortell’s non-linearly stretching permeable sheet

“…For a backward flow configuration, namely the surface moving from +1 to the slot, the fluid loses any memory of the perturbation introduced by the leading edge, say the slot. Therefore, the flow induced by a shrinking sheet shows quite distinct physical phenomena from the forward stretching flow ( [13][14][15]). The shrinking sheet problem was also extended to other fluids ( [16], [17]).…”