Analytical and numerical investigations of slip flow in a Jeffery-Hamel configuration within a converging microchannel incorporating a step variation in wall temperature and the effects of radial heat conduction

This study presents analytical and numerical solutions for steady, laminar, thermally developing slip flow through a converging microchannel of the Jeffery-Hamel family with an abrupt change in wall temperature. The analysis includes the effects, not previously explored, of radial conduction and rarefaction. The elliptic energy equation is analytically solved using functional analysis method by decomposing it into two first-order partial differential equations. Numerical validation is performed using a second-order finite difference method, showing a high agreement with a maximum deviation error <0.2 %, confirming the accuracy of both methodologies in efficiently resolving the singularity. Radial conduction is influenced by the ratio of the aperture angle ψ to the Péclet number, becoming significant as this ratio increases and diminishes with higher Knudsen numbers Kn. Additionally, heat transfer is enhanced with a larger aperture angle but decreases with rising Kn due to the temperature jump at the wall. Key findings reveal optimum regime of heating characterized by a linear variation of bulk temperature and uniform heat flux, for a fixed Reynolds number and at an optimal value around ψ_opt = 21° in no-slip flow, decreasing to ψ_opt = 8.8° as the flow becomes more rarefied at Kn = 0.1. These insights are crucial for optimizing the thermal performance of converging microchannel flows and microfluidic device design.