The similarity solutions of unsteady mixed convection boundary layer equations over a flat porous vertical plate has been investigated by repeated applications of the method of one parameter continuous Group Theory. By applying group theory we have converted the governing partial differential equations into a pair of ordinary differential equations with appropriate boundary conditions. We have analyzed six possible cases for which similarity solutions exist. Out of six cases two cases Were derived by Z3kerullah
(2001) without suction. It is found that our solutions arc consistent with some of tbe published results in the literature. One set of the coupled nonlinear equation~ are ~olved numerically. This set is a purely steady one. In most practical purposes steady cases are generally dealt with.
The heat transfer and skin friction factors
{q.
(O),T~(O)}are displayed and shown graphically for some values of the parameter F" .. It is shown that both the skin friction and heat transfer coefficient increases with suction and the effect of injection is just reverse.It is desirable to solve certain classes of problem (bur not all) by Group TIleory method. Each problem has its own special features. So it requires a thorough knowledge of the happenings of the problem. The method of Group Theory may also be applied to certain classes of the boundary value problems for which the governing partial differential equations are expressed in ~phericill or cylindrica I cOQrdinates.
If a number of dependent and independent variable are present in the problem, first a group of independent similarity variables '11,'12,'1]>'" are sought from the original independent variables and are one kss in number. The17, are absolute invarianl.
For each dependent variable, an absolute invariant Ii. is sought which involve the
,
dependent variable.
A good choice is gj =uih,Ix,x ,. ",X
I,
where u.is the dependent variable.,\1 2 n I
The function gj is then equated to a function F(17l"12" ",17m_t).
71
r
If gj
~Ujh'\Xl'X2""'X,)
then~F;\rI
,l/y"',l/m1)
Uj ~ h.
X ,x~,...,x =f-
I 1"
mJ
is the dependent variable transformation. Substituting V;l1;OUS transformations into the original system of equations, the new system stands mth numher of independent variable reduced by one.
Thus the reductions of variables in the problem carry more and more restrictions to develop various types of possible cases. It would be quite simple to investigate these possibilities. Finally, we may reach 10 a po~ilion to give the analytical solution of the problem under restricted conditions.
72
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