An efficient numerical method is presented in this study to discuss the
effects of variable heat flux, viscous dissipation and the slip velocity
on the viscous Casson flow and heat transfer due to an unsteady
stretching sheet taking into account the influence of heat generation or
absorption. Industrially, this type of fluid can describe the flow of
blood in an industrial artery, which can be polished by a material
governing the blood flow. The spectral collocation method based on
Chebyshev polynomials of the third-kind is employed to solve the
resulting system of ordinary differential equations which describe the
problem. Influence of the parameters governing the flow and heat
transfer such as unsteadiness parameter, slip velocity parameter, Casson
parameter, local Eckert number, heat generation parameter and the
Prandtl number are discussed and presented through tables and graphs.
Also, the local skin-friction coefficient and the local Nusselt number
at the stretching sheet are computed and discussed. Finally, the results
show that the given procedure is an easy and efficient tool to
investigate the solution of such fluid models.