Heat and mass transfer characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing velocities

The mechanical and thermal characteristics of the self-similar boundary-layer flows induced by continuous surfaces stretched with rapidly decreasing power-law velocities Uw α xm, m <-1 are considered. Comparing to the well studied cases of the increasing stretching velocities (m > 0) several new features of basic significance have been found. Thus: (i) for m < -1 the boundary layer equations admit self-similar solutions only if a lateral suction is applied; (ii) the dimensionless suction velocity fw < 0 must be strong enough, i.e. fw < fw,max(m) where fw(m) depends on m so that its absolute maximum max (fw,max(m)) = -2.279 is reached for m → ∞, while for m → -1, fw,max(m)→-∞; (iii) the case {m →- ∞, fw,max(m) = -2.279} of the flow boundary value problem is isomorphic to the stretching problems with exponentially decreasing velocities Uw α eax with arbitrary a < 0; (iv) for any fixed m < -1 and fw < fw,max(m) the flow problem admits a non-denumerable infinity of multiple solutions corresponding to the values of the dimensionless skin friction f"(0)≡ s belonging to a finite interval s  [smin(fw, m), smax (fw, m)]; (v) the solution is only unique for fw = fw,max(m) where s = smin(fw, m) = smax(fw, m) holds; (vi) to every one of the multiple solutions of the flow problem there corresponds a unique solution of the heat transfer problem with a wall temperature distribution Tw- T∞ α xn and a well defined and distinct value of the dimensionless wall temperature gradient '(0), except for the cases n =(\m \ - 1)/2 where '(0) has the same value '(0) = Pr.fw for the whole class of flow solutions with s  [smin(fw, m), smax (fw, m)]; (vii) for fw → -∞ one obtains the 'asymptotic suction profiles' corresponding to s = smin(fw, m) fw and '(0)  Pr f(w) in an explicit analytic form. The paper includes several examples which illustrate the dependence of the heat and fluid flows induced by surfaces stretching with rapidly decreasing velocities on the physical parameters fw, m, n and Pr.King Saud Universit