Abstract: A method for resolving the energy equation of the circular microchannel, which considers axial heat conduction, temperature jump, velocity slip and thermal entrance is presented. The energy equation can be transformed into the eigenvalue problem by separation of variables. The temperature jump condition provides a procedure for determining the eigenvalues. The undermined coefficients of the complete solution to the energy equation are derived by the orthogonality eigenfunction and then the expressions of temperature field and Nusselt number are obtained. The expressions for temperature and the Nusselt number are achieved. Simulation of heat transfer in the circular microchannel is conducted and it is revealed that heat transfer to the wall increases with the effect of axial conduction. The effect of thermal entrance is to increase the local Nusselt number. The smaller the velocity slip coefficient, the larger the asymptotic value of the Nusselt number.

Key words: axial heat conduction, velocity slip, temperature jump, thermal entrance, nusselt number eigenvalue problem