Effects of axial heat conduction and viscous dissipation on heat transfer in circular micro-channels

The solution of the energy equation of circular micro-channels, which considers axial heat conduction, velocity slip, temperature jump, viscous dissipation and thermal entrance effect, is obtained by separation of variables. The expressions of temperature field, local and average Nusselt number are derived. The effects of Brinkman number, Peclet number, temperature jump and velocity slip on local Nusselt number are analyzed by numerical simulation using MatLab. The design criterion of whether the axial heat conduction and viscous dissipation should be considered in engineering is given by studying their contributions to average Nusselt number.

► We solve the energy equation of circular micro-channels considering scale effects.
► The heat transfer to the wall increases when axial heat conduction is considered.
► We find rule of the contribution of axial conduction to Nu varying with Pe and z/R0.
► We find rule of the contribution of viscous dissipation to Nu varying with Pe and z/R0.