Axial Conduction in a Partially Heated Microchannel Subjected to Isothermal Boundary Condition

A numerical study has been carried out to study the effects of axial conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel subjected to constant wall temperature at bottom of substrate while the other exposed surfaces are kept insulated. The study is carried out for different partial heating cases. They are: (i) The entire bottom surface of microchannel is subjected to constant wall temperature while all other outer surfaces are insulated (ii) 6 mm of bottom surface is insulated from both inlet and outlet end of micro channel and remaining length of bottom surface is subjected to constant wall temperature (iii) 6 mm of bottom surface is insulated from inlet end of micro channel and remaining length of bottom surface is subjected to constant wall temperature (iv) 6 mm of bottom surface is insulated from outlet end of micro channel and remaining length of bottom surface is subjected to constant wall temperature. Simulations are carried out for different conductivity ratio, Re and substrate thickness to channel depth ratio. It is found that value of Nuavg is increasing with decreasing value of ksf upto ksf approximately equal to 25 and beyond that on decreasing ksf value further, value of Nuavg starts decrease rapidly. This sudden decrease in Nuavg value is because under such situation the case becomes a one side heating problem rather than three sided heating problem. Now as ksf is increased beyond a range axial back conduction comes into play and this causes value of Nuavg to decrease. Thus, there exists an optimum ksf for which Nuavg is maximum for given flow Re and wall thickness ratio. Secondly, it is observed that higher axial conduction causes the boundary condition experienced at the solid fluid interface to drift more towards iso-flux condition although isothermal condition is applied on outer surface