Home – Home – Jornals – Journal of Applied Mechanics and Technical Physics 2026 number 4

For a power-law temperature dependence of the viscosity coefficient, the problem of steady Poiseuille flow in a channel with nonuniformly heated walls is reduced to a three-parameter boundary-value problem for a system of third-order ordinary differential equations. In the absence of a pressure drop, the problem admits a solution describing the temperature distribution in a fluid at rest. This solution exists over a finite interval between the negative and positive critical values of the dimensionless temperature gradient at the channel walls. At small values of the Péclet number (based on the pressure drop), the first solution branch bifurcates from the quiescent state. Two additional branches are found when the wall temperature gradient exceeds the critical values. Thus, in the region of negative gradients, two solutions exist for the same parameter values, differing in flow rate and wall heat flux. For wall temperature gradients exceeding the positive critical value, the third branch is a continuation of the first. A distinctive feature of the second and third branches is that, as the Péclet number tends to zero, the flow rate tends to a nonzero value.