Viscous flow over a stretching (shrinking) and porous cylinder of non-uniform radius

The classical models of viscous flows and heat transfer are reformulated in this article. The physical problem describes flow and heat transfer over a stretching (shrinking) and porous cylinder of non-uniform radius. The mathematical model is presented in the form of new equations and dimensionless parameters by means of reframing techniques. A porous and heated cylinder of a non-uniform diameter is stretched (shrunk) with variable stretching (shrinking) velocities. The governing equations and their physical geometrical perspectives are summarized into simplest boundary value ordinary differential equations. A set of unseen, generalized, and convenient transformations are used to solve the complex problem. The current formulation accumulates all the previous models of axisymmetric flow and heat transfer toward stretching (shrinking) and porous cylinder presented in the literature and prevails over all such models. The current model can be easily transformed into classical simulations for particular values of the parameters. The problem is solved numerically and the results were compared with the benchmark solutions. Velocity, temperature, skin friction coefficient, and Nusselt number profiles are plotted and analyzed for different values of the parameters. Moreover, coupling effects of all parameters are seen on flow and heat transfer characteristics and new results are explored and discussed.