## 1 Introduction
The no-slip wall condition is applicable to Newtonian fluids when the Knudsen number (Kn) is smaller than 0.001. According to [PERSON]'s kinetic theory [2], slip flow is observed when the characteristic flow length scale is within the order of the mean free path of the gas molecules. When Kn is less than 0.1 and larger than 0.01, the temperature jump and velocity slip appear, and continuum models remain valid. Therefore, Navier-Stokes equations could still be used to model the laminar flow inside circular pipes [21]. Based on this approach, [PERSON] and [PERSON] [22] utilized the CFD tool to investigate a rarefied, laminar, fully developed gaseous flow within a rhombic microchannel, taking into account temperature jump conditions. They confirmed the dependence of Nu on the microchannel geometry and Kn. [PERSON] and [PERSON] [23] investigated numerically rarefied fluid flowing in a micro-duct with an elliptical cross-section under slip flow. The steady-state, laminar, and fully developed flow under an axial uniform linear heat flux boundary condition was examined. They validated their model against published results from the literature. Their developed numerical code was reported to be capable of obtaining velocities and temperatures of the flowing fluid inside the elliptical cross-sectional pipes. [PERSON] et al. [24] conducted a numerical simulation to evaluate volume fractions of Al\({}_{2}\)O\({}_{3}\) nanoparticles and inlet velocity effects on enhancing heat transfer in slip and no-slip nanofluid flow regimes. Their findings demonstrated that the major improvement in Nu was caused by an increase in the inlet velocity rather than a rise in the volume fraction of nanoparticles. Recently, [PERSON] et al. [25] utilized Python software to study the rarefied flow with Cu-H\({}_{2}\)O nanofluid particles through a rectangular microchannel. They confirmed the significant effect of Re, Kn, and the nanoparticle volume fraction (\(\phi\)) on the heat transfer within the system. [PERSON] and [PERSON] [26] investigated heat transfer in rough wall surface microchannels with a slip flow regime. They considered incompressible gas flow for a range of Kn [0.01-0.1]. They reported that Nu is inversely proportional to Kn for both smooth and rough channels. This was confirmed by [PERSON] et al. 's [27] analytical solution of a fully developed laminar flow of gas in microtubes under constant wall heat flux conditions, in which they reported that Nu was inversely dependent on Kn and this dependence increased as a function of temperature jump. Furthermore, [PERSON] et al. [28] stressed that neglecting the temperature jump could lead to a misleading conclusion of the increase in Nu as a function of Kn. Researchers such as [PERSON] and [PERSON] [29; 30] analytically investigated the heat transfer within microtubes under laminar and fully developed gaseous flows under uniform heat flux boundary conditions. The effects of axial conduction and viscous dissipation within the fluid on the same problem were solved by [PERSON] and [PERSON] [31]. It was reported that axial conduction within the fluid was constant under constant wall heat flux boundary conditions. Consequently, Nu was not affected, and it became independent of the Peclet number (Pe = Re Pr) [29]. [PERSON] [32] highlighted the significance of shear work in the convective heat transfer of gas flowing in a microtube. He stated that shear work could be as high as the heat transfer via conduction at the upper limits of the slip flow regime. He added that the effect of shear work consists of viscous dissipation and pressure work combined effects. [PERSON] et al. [33] investigated the problem of the conjugate heat transfer of gaseous flow inside a microtube under slip flow regime. They stressed the importance of including the effects of axial diffusion and wall conjugation on the value of Nu at a low Peclet number (Pe < 20). In an earlier work, [PERSON] et al.