A concentric micro-annular passage is a basic and important microgeometry of microfluidic-systems from simple heat exchanger to the most complicated nuclear reactors. Therefore, heat transfer characteristics of gaseous flows in concentric micro-annular tubes with constant heat flux whose value was positive or negative were numerically investigated. The slip velocity, temperature jump, and shear stress work were considered on the slip boundary conditions. The numerical methodology was based on the arbitrary-Lagrangian–Eulerian method. The computations were performed for two thermal cases. That is, the heat flux that was constant at the inner wall and outer wall was adiabatic (case 1) and the heat flux that was constant at the outer wall and the inner wall was adiabatic (case 2). Each constant heat flux of $104\u2002Wm\u22122$ for the positive value and $\u2212104\u2002Wm\u22122$ for the negative value was chosen. The outer tube radius ranged from $20\u2002\mu m$ to $150\u2002\mu m$ with the radius ratios of 0.02, 0.05, 0.1, 0.25, and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranges from 0.1 to 0.8. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro-annular tubes were obtained. The wall and bulk temperatures with positive heat flux are compared with those of negative heat flux cases and also compared with those of the simultaneously developing incompressible flow. The results show that the Nusselt number of compressible slip flow is different from that of incompressible flow. However, the temperatures normalized by heat flux have different trends whether heat flux value is positive or negative. A correlation for the prediction of the heat transfer characteristics of gas slip flow in concentric micro annular tubes is proposed.