Optimum Nusselt Number for Simultaneously Developing Internal Flow Under Conjugate Conditions in a Square Microchannel

A numerical study has been carried out to understand and highlight the effects of axial wall conduction in a conjugate heat transfer situation involving simultaneously developing laminar flow and heat transfer in a square microchannel with constant flux boundary condition imposed on bottom of the substrate wall. All the remaining walls of the substrate exposed to the surroundings are kept adiabatic. Simulations have been carried out for a wide range of substrate wall to fluid conductivity ratio (k_sf ∼ 0.17–703), substrate thickness to channel depth (δ_sf ∼ 1–24), and flow rate (Re ∼ 100–1000). These parametric variations cover the typical range of applications encountered in microfluids/microscale heat transfer domains. The results show that the conductivity ratio, k_sf is the key factor in affecting the extent of axial conduction on the heat transport characteristics at the fluid–solid interface. Higher k_sf leads to severe axial back conduction, thus decreasing the average Nusselt number (⁠$Nu¯$⁠). Very low k_sf leads to a situation which is qualitatively similar to the case of zero-thickness substrate with constant heat flux applied to only one side, all the three remaining sides being kept adiabatic; this again leads to lower the average Nusselt number (⁠$Nu¯$⁠). Between these two asymptotic limits of k_sf, it is shown that, all other parameters remaining the same (δ_sf and Re), there exists an optimum value of k_sf which maximizes the average Nusselt number (⁠$Nu¯$⁠). Such a phenomenon also exists for the case of circular microtubes.