We consider a system of coupled partial differential equations describing transient fluid flow and heat transfer with variable flow
properties. Classical Lie point symmetry analysis of this system resulted in admitted large Lie algebras for some special cases of
the arbitrary constants and the source term. Symmetry reductions are performed and as such the system of partial differential
equations is reduced to the system of ordinary differential equations. Some reduced ordinary differential equation could be solved
exactly with restrictions on the parameters appearing in it. In addition, shooting quadrature is employed to numerically tackle the
nonlinear model boundary value problem and pertinent results are presented graphically and discussed quantitatively