This is a theoretical study that extends a classical method of treating the convection heat transfer in complex geometries to gaseous slip flow forced convection in microchannels with H1 thermal boundary condition. Through this line, the momentum and energy equations in cylindrical coordinates are made dimensionless. Afterward, solutions are presented that exactly satisfy the dimensionless differential equations along with the symmetry condition and finiteness of the flow parameter at the origin. The first-order slip boundary conditions are then applied to the solution utilizing the least squares matching method. Though the method is general enough to be applied to almost any arbitrary cross section, four differ- ent cross sections of polygonal, trapezoidal, rhombic, and elliptic shape are considered for presentation. The accuracy of the method is proven by comparing the results against avail- able literature data. Finally, after a complete discussion of the results, the tabulated data of Nusselt number are presented for each geometry by covering the entire slip flow range of the Knudsen number.
