Laminar flow with temperature-dependent fluid properties between two stretching rectangular surfaces

The Navier–Stokes equations and the energy equation are used to investigate a fluid flow between two stretching rectangular surfaces subjected to a temperature difference that affects the dynamic viscosity and thermal conductivity of the fluid. The wall stretching process enhances the momentum boundary layer thickness which slows the axial motion of the fluid away from the flow boundaries. When the stretching parameter γ is equal to 1, that is the case corresponding to symmetric stretching, the minimum of the axial velocity is located at the midplane of the channel y = 0.5 if the viscosity variational parameter α equals 0. This minimum moves towards the region 0.5 < y < 1 for α > 0, but migrates towards the region 0 < y < 0.5 for α < 0. Moreover, in the case of symmetric stretching corresponding to γ = 1, the growth in Reynolds number Re tends to increase the axial velocity around the middle of the channel for α ≥ 0 in the attempt to counteract the effects of enhancing the momentum boundary layer thickness leading to the flattening of axial velocity profiles for Re ≥ 100. While the conductivity variational parameter β does not influence enough the fluid dynamics and heat transfer, the Reynolds number Re and the Péclet number Pé can increase or decrease the temperature distribution inside the channel depending on the sign of the parameter α. Practical applications related to the present study include lubrification, food manufacturing, paint industries, extrusion processes in plastic and metal industries.