Consideration is given to the buoyancy effects on fully developed gaseous slip flow in vertical microducts of constant but arbitrary geometry. The thermal boundary condition is assumed to be the constant wall heat flux of the first kind, H1. The rarefaction effects are treated using the first order slip velocity and temperature jump boundary conditions. The method of solution being considered is mainly analytical in which the governing equations in cylindrical coordinates and three of the boundary conditions are exactly satisfied. The remaining slip boundary conditions on the duct wall are applied to the solution through the least squares matching method. As an application of the method, the hydrodynamic and thermal features are obtained for five duct geometries including trapezoid, double-trapezoid, isosceles triangle, rhombus, and ellipse. A complete parametric study indicates that both Poiseuille and Nusselt numbers are decreasing functions of Knudsen number and increasing functions of mixed convection parameter. It is also observed that the functionality of these parameters on the duct aspect ratio is generally non-monotonic and dependent upon the Knudsen number.
