Translation groups of the boundary-layer flows induced by continuous moving surfaces

被引:9
作者
Magyari, Eugen [1 ]
机构
[1] Swiss Fed Inst Technol, Inst Hochbautech, CH-8093 Zurich, Switzerland
关键词
HEAT-TRANSFER CHARACTERISTICS; DARCY FREE-CONVECTION; ENTRAINMENT THEOREM; STRETCHING SHEET; VERTICAL PLATE; MASS-TRANSFER; EQUATIONS; SUCTION; BEHAVIOR; WALL;
D O I
10.1017/S0022112010000911
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
The steady plane boundary-layer flows of velocity field {u(x, y), v(x, y)} induced by continuous moving surfaces are revisited in this paper. It is shown that the governing balance equations, as well as the asymptotic condition u(x, infinity) = 0 at the outer edge of the boundary layer are invariant under arbitrary translations y -> y + y(0)(x) of the transverse coordinate y. The wall conditions, i.e. the prescribed stretching velocity u(x, 0) equivalent to U-w(x) and the transpiration velocity v(x, 0) equivalent to V-w(x) distributions, however, undergo in general substantial changes. The consequences of this basic symmetry property on the structure of the solution space are investigated. It is found that starting with a primary solution which describes the boundary-layer flow induced by an impermeable surface, infinitely many translated solutions can be generated which form a continuous group, the translation group of the given primary solution. The elements of this group describe boundary-layer flows induced by permeable surfaces stretching under transformed wall conditions, U-w(x) -> (U) over tilde (m)(x) = u[x, y(0)(x)] and V-w(x) -> (V) over tilde (w)(x) = v[x, y(0)(x)] - y(0)'(x)u[x, y(0)(x)], respectively. In this way, starting with a known solution {u(x, y), v(x, y)} so that the inverse y(0)(x) = u(-1)(x, (U) over tilde (m)) of u[x, y(0)(x)] exists, a new solution {(u) over tilde (x, y), (v) over tilde (x, y)} corresponding to any desired stretching velocity distribution (U) over tilde (m)(x) can be prepared. It also turns out that several exact solutions discovered during the latter decades are not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.
引用
收藏
页码:327 / 343
页数:17
相关论文
共 39 条