Analytical Velocity and Temperature Distributions for Flow in Microchannels of Various Cross-Sections

Abstract

Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels for a wide variety of cross-sections. The considered geometries include hyper-elliptical channels and regular polygon ducts, which covers several common shapes. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. The boundary conditions are applied using a linear least-squares point matching technique to minimize the residual between the actual and the modeled values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical solutions from literature for a variety of channel cross-sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.