Natural convection on a vertical stretching cylinder

The flow and natural (or mixed) convection due to a vertical stretching cylinder is studied. Using similarity transforms, the Navier–Stokes and energy equations reduce to a set of nonlinear ordinary differential equations. Asymptotic analysis for large Reynolds numbers shows the relation between axisymmetric flow and two-dimensional flow. Due to the algebraic decay of the similarity functions, numerical integration is performed using a compressed coordinate. The axial velocity is composed of forced convection due to stretching and natural convection from the heated cylinder. The heat transfer increases with both the Reynolds number and the Prandtl number. The result is also a rare similarity solution of the free convection and Navier–Stokes equations.

► New stretching similarity solution for axisymmetric natural convection and Navier–Stokes equations is presented.
► The effect of cylinder curvature is of order R−1/2, where R is a Reynolds number.
► Due to algebraic decay, numerical integration is performed on a compressed radial variable.
► Thermal boundary layers exist for large Prandtl and Reynolds numbers.