Transient Analysis of Slip Flow and Heat Transfer in Microchannels

Abstract

Hybrid analytical-numerical solutions for transient flow and transient convective heat transfer within microchannels are presented. Analytical solutions for flow transients in microchannels are obtained by making use of the integral transform approach. The proposed model involves the transient fully developed flow equation for laminar regime and incompressible flow with slip at the walls in simple channel geometries. The solution is constructed so as to account for any general functional form of the time variation of the pressure gradient along the duct. Then, the transient-state convection heat transfer is solved for laminar slip flow inside microchannels formed by parallel-plates, making use of the generalized integral transform technique (GITT) and the exact analytical solution of the corresponding eigenvalue problem in terms of confluent hypergeometric functions so as to eliminate the transversal coordinate. The resulting system of transformed partial differential equations in the longitudinal coordinate is numerically solved by the Method of Lines as implemented in the routine NDSolve of the Mathematica system. Mixed symbolic-numerical algorithms are developed under the Mathematica platform.