Slip Flow in Elliptic Microducts with Constant Heat Flux

Abstract

This paper outlines a numerical model for determining the dynamic and thermal performances of a rarefied fluid flowing in a microduct with elliptical cross-section. A slip flow is considered, in laminar steady state condition, in fully developed forced convection, with Knudsen number in the range 0.001−0.1, in H1 boundary conditions. The velocity and temperature distributions are determined in the elliptic cross-section, for different values of both aspect ratio γ and Knudsen number, resorting to the Comsol Multiphysics software, to solve the momentum and energy equations. The friction factors (or Poiseuille numbers) and the convective heat transfer coefficients (or Nusselt numbers) are calculated and presented in graphs and tables. The numerical solution is validated resorting to data available in literature for continuum flow in elliptic cross-sections (Kn = 0) and for slip flow in circular ducts ([Formula: see text]). A further benchmark is carried out for the velocity profile for slip flow in ellipticalcross-sections, thanks to a recent analytical solution obtained using elliptic cylinder coordinates and the separation of variables method. The Poiseuille and Nusselt numbers for elliptic cross-sections are discussed. The results may be used to predict pressure drop and heat transfer performance in metallic microducts with elliptic cross-section, produced by microfabrication for microelectromechanical systems (MEMS).

Ritz method for slip flow in curved micro-ducts and application to the elliptic duct

“…The difference is \0.1 %. Other sources include Spiga and Vocale [10] who used finite elements, and Duan and Muzychka [11] found an exact series solution in elliptic coordinates, but only three analytic terms are obtained. Table 3 shows a comparison of the average velocity.…”

“…Table 3 shows a comparison of the average velocity. The results of Refs [10,11]., which are in terms of Knudsen number and accommodation coefficient, are condensed into a single slip factor through Eq. (4).…”

Asymmetrical Heating in Rarefied Flows Through Circular Microchannels

“…The equation of motion is solved by considering the usual firstorder slip boundary condition for the velocity at the wall [18]:…”

“…By means of Eq. (18), the wall temperature as a function of cylindrical coordinate 4> can be obtained. Obviously for a = 7t the wall temperature is uniform along the perimeter of the cross section, instead for a = n/2 the wall temperature varies reaching its maxi mum value in the point < /> = 0 and the minimum one at (f> = n, due to the symmetry.…”

Slip Flow and Constant Flux Heat Transfer in Isosceles Triangular Ducts

“…Finite elements were used for semicircular [34] or elliptic [35,36] channels. An eigenfunction expansion and boundary collocation was applied to a variety of cross sections [37][38][39].…”