Optimization of micro-heat sink based on theory of entropy generation in laminar forced convection

The entropy generation (<(S)over dot>(gen)) due to fluid friction and convective heat transfer is studied en-route the microscale. The <(S)over dot>(gen) for water-flow through a circular tube for the constant wall heat flux boundary condition is estimated. The number of tubes (N) en-route the microscale is increased by correspondingly decreasing each tube diameter, for fixed total mass flow rate and the total heat flow rate is also kept constant. There exists an optimum tube diameter (D-N,D-opt) and a corresponding optimum natural number N (N-opt) at which, the sum-total <(S)over dot>(gen) is minimum. Criterion for D-N,D-opt is obtained in terms of Reynolds number and a modified Brinkman number, which shows that D-N,D-opt depends only on the total heat flow rate. Unlike other reported studies, the fluid temperature in the denominator of the entropy generation terms is considered as local and variable. The difference in <(S)over dot>(gen) based on reported studies and this investigation increases significantly especially towards the microscale.