Viscous flow due to non-uniform cylinder with non-uniform stretching (shrinking) and porous velocities

A theoretical investigation is accomplished by considering a viscous flow over a porous and stretching (shrinking) cylinder of non-uniform radius. The stretching (shrinking) and injection (suction) velocities are dependent upon the axial coordinate (z). Moreover, the circular porous duct has a non-uniform shape whose surface geometry is such that R(z) = (delta(0) + delta(1)z)(delta 2). The current model is the generalization of all such models, which describe the fluid flow over a stretching (shrinking), porous (uniform/variable, both injection and suction can take place) and non-uniform (uniform) cylinder. More precisely, the classical simulations can be retrieved easily from the modeled problem. If we adjust and manipulate the parameters of the modeled problem accordingly, then we may convert the current model into all previous cases of flow problems on the above title. By means of generalized and unusual similarity transformations for the velocity components and similarity variables, the governing equations along with boundary conditions are converted into a set of differential equations (DEs). The last DEs have variable coefficients of arbitrary and multiple degrees and their significant contribution is replicated in the solutions of the modeled equations. The final problem involves a set of parameters and their properties are directly associated with the different physical mechanisms taken into account. The closed form solutions (exponential and rational functions) of the problem are found for fixed and special values of the parameters. On the other hand, curvature effects are examined on flow properties. The modeled equations are solved numerically and new results are found.