Numerical study of the effects of variable viscosity on a fluid flow between two stretchable disks fixed at different temperatures

The flow is induced by the process of radial stretching of two parallel coaxial disks separated by an incompressible fluid layer whose viscosity varies due to the temperature difference between the two circular surfaces. Important applications of this study include food manufacturing, industrial maintenance, paint industries, lubrification, as well as extrusion processes in plastic and metal industries. The numerical shooting technique combined with the fourth-order Runge–Kutta integration scheme is employed to solve the set of ordinary differential equations derived from the similarity method used to transform the partial differential equations of the problem governed by the continuity equation, the Navier–Stokes equations and the energy equation. The results obtained contribute to a better understanding of the problem whose novelty pertains to the effects of temperature-dependent viscosity in connection with the impact of the wall stretching process on a fluid flow in a cylindrical domain. The adopted solution method enables us to go beyond previous efforts in the literature as it reveals many flow and heat transfer structures through the same investigation in terms of velocity and temperature profiles, pressure and temperature gradients, as well as streamlines consubstantial to the phenomena occurring at the fluid–structure interface characterized by the skin friction and Nusselt number which therefore deserve particular attention. Indeed, the skin friction tends to zero when the Reynolds number [Formula: see text], but exhibits important variations in the case where [Formula: see text] whatever the values of other control parameters. For the respective values of the viscosity variation parameter [Formula: see text] and [Formula: see text], the Nusselt numbers at the lower and upper disks Nu (0) and Nu (1) approach the constant value of [Formula: see text]1 as a function of the Péclet number Pé. Moreover, when Pé tends to zero, Nu (0) and Nu (1) approach the fixed value of [Formula: see text]1.