Boundary layer formations over a stretchable heated cylinder in a viscoelastic fluid with partial slip and viscous dissipation effects

Abstract

An exact similarity solution is worked out for fluid motion in the vicinity of a cylindrical surface in an electrically conducting viscoelastic fluid obeying the Jeffrey model. Cylindrical surface expands axially with linear velocity and has a prescribed surface temperature. The present analysis focuses on the partial slip assumption which gives rise to a nonlinear case Robin-type (mixed) boundary condition in axial velocity. In contrast to a previously published study (J. Mech., vol 31, pp. 69–78, 2015) which only reported local similarity solutions in no-slip case, the present work provides an exact similarity analysis by defining a quadratic surface temperature. The effects of the magnetic field and Joule heating on the momentum and thermal transport phenomena are also scrutinized. A numerical routine is used to solve the equation accurately for a wide range of fluid parameters, including ranges that could not be handled by previous approximate analytical methods that were limited to the no-slip limit. The influences of viscoelasticity and partial slip on the flow behavior are investigated, and the coefficient of skin friction for a Jeffrey fluid is calculated. Obtained results are consistent with the previously published works under special situations. The case of flat surface, which can be obtained as a limiting case of the model, is not even explored in the past.