Improvement of heat-transfer correlations for supercritical methane coolant in rectangular channel

In this article, the conjugate heat transfer of the methane coolant inside a rectangular channel is studied and the related Nusselt correlations are improved. The compressible methane flow enters the cooling channel at supercritical pressure and subcritical temperature. The coolant flow absorbs heat from the heated walls and exits the channel with a supercritical temperature. An in-house solver is developed employing Semi-Implicit Method for Pressure-Linked Equations-Consistent (SIMPLEC) algorithm accompanied by the appropriate thermodynamic and transport property relations for the supercritical conditions of the methane coolant. The solver is validated with the experimental data found in the open literature. The behavior of pseudo-critical temperature and density versus pressure are studied and new relations are proposed. The accuracy of different Nusselt relations for estimating heat transfer coefficient of methane at supercritical pressures is evaluated. The variation of thermofluidic parameter correction factors (i.e. non-dimensional density, temperature, isobaric specific heat, viscosity, and thermal conductivity) through the cooling channel is investigated. Further, the current Nusselt relations are developed, and improved correlations are proposed for methane at the supercritical pressure inside a rectangular channel. The accuracy of the modified correlations is studied at different outlet pressures, heat transfer, and mass flow rates.