Viscous heating effects on heat transfer characteristics of laminar compressible channel flow

The present paper investigates viscous heating effects on heat transfer characteristics of laminar Newtonian compressible channel flow. At first, incompressible Poiseuille flow case is addressed analytically by including viscous dissipation term in energy conservation equation. Temperature distributions in the channel cross-section and local Nusselt numbers are derived as functions of the Brinkman number, highlighting the role of the viscous term. The analysis is numerically supported by a set of CFD simulations. Additional CFD results are employed to extend the analysis to compressible flow case resulting in dedicated local Nusselt number correlations, function of Brinkman and Mach numbers, and expansion-altered temperature profiles. The study assumes no-slip flow and no temperature-jump boundary conditions at the channel wall (Knudsen number Kn<10−3), and addresses both fluid heating and cooling, both uniform heat flux (UHF) and uniform wall temperature (UWT) boundary condition (BC), and both circular (CR) and parallel-plate (PP) channel cross-section.