Semi-Analytical Solution of Energy and Momentum Equations With Robin's Boundary Conditions in a Microchannel Flow

In this study, the nonlinear momentum and energy equations governing magnetohydrodynamic microchannel flow are solved under a Robin-type slip boundary condition. To impose the mixed boundary conditions directly in the semi-analytical construction, the Adomian decomposition method (ADM) is combined with the Fourier transform. The integration-by-parts operations in the Fourier domain make the boundary terms explicit and enable the Dirichlet, Neumann, and Robin-type slip conditions to be incorporated into the recursive FTADM solution. The velocity and temperature solutions are validated against fourth-order Runge–Kutta computations for the nonlinear magnetohydrodynamic Jeffery–Hamel microchannel formulation. The comparisons show excellent agreement, with maximum discrepancies of the order of 10−5 for the tested cases. The results further demonstrate the influence of the channel angle and Hartmann number on the velocity and heat-transfer behavior while retaining a compact semi-analytical representation of the solution.