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-lay er flows induced by continuous surfaces stretched with rapidly decreasing p ower-law velocities U-w proportional to x(m), m < -1 are considered. Compar ing to the well studied cases of the increasing stretching velocities (m > 0) several new features of basic significance have been found. Thus: (i) fo r m < -1 the boundary layer equations admit self-similar solutions only if a lateral suction is applied; (ii) the dimensionless suction velocity f(w) < 0 must be strong enough, i.e. f(w) < f(w,max) (m) where f(w,max)(m) depen ds on m so that its absolute maximum max (f(w,max)(m)) = -2.279 is reached for m <right arrow> -infinity, while for m --> -1, f(w,max) (m) --> -infini ty; (iii) the case {m --> -infinity, f(w,max)(m) = -2.279} of the flow boun dary value problem is isomorphic to the stretching problems with exponentia lly decreasing velocities U-w proportional to e(ax) with arbitrary a < 0; ( iv) for any fixed m < -1 and f(w) < f(w,max) (m) the flow problem admits a non-denumerable infinity of multiple solutions corresponding to the values of the dimensionless skin friction f " (0) drop s belonging to a finite int erval s epsilon [s(min) (f(w), m), s(max) (f(w), m)]; (v) the solution is o nly unique for f(w) = f(w,max) (m) where s = s(min) (f(w), m) = s(max) (f(w ), m) holds; (vi) to every one of the multiple solutions of the flow proble m there corresponds a unique solution of the heat transfer problem with a w all temperature distribution T-w - T infinity proportional to x(n) and a we ll defined and distinct value of the dimensionless wall temperature gradien t I'(0), except for the cases n (\m \ - 1)/2 where I'(0) has the same value I'(0) = Pr for the whole class of flow solutions with s epsilon [s(min)(f( w), m), s(max)(F-w, m)]; (vii) for f(w) --> -infinity one obtains the 'asym ptotic suction profiles' corresponding to s = s(min)(f(w), m) congruent to f(w) and I'(0) congruent to Pr(.)f(w) in an explicit analytic form. The pap er includes several examples which illustrate the dependence of the heat an d fluid flows induced by surfaces stretching with rapidly decreasing veloci ties on the physical parameters f(w), m, n and Pr.