Heat transfer,development length,and friction factor correlations for the asymptotic region of a laminar arc constrictor

A rigorous equilibrium model is formulated for the laminar flow of plasma through the heating region of a constricted arc plasma generator. The resulting equations are solved for an argon gas using an implicit finite-difference scheme, and the wall shear stress and heat transfer are computed from momentum and energy balances for a wide range of flow rates and arc currents. Friction factors based on this method are in agreement with empirical values to within approximately 10 per cent, and heat transfer calculations agree with the orders of magnitude predicted by a simplified arc model. A dimensionless number peculiar to the constricted arc, the so-called Ohmic heating parameter, is used to correlate the mean Nusselt numbers in the asymptotic arc regime. When the fluid properties are based on the mean temperature, the product of friction factor and Reynolds number is found to be a constant for currents below 200 Amp and to vary with the Ohmic heating parameter for larger currents. Correlations are also presented for the thermal development length, and the agreement with experiment is good.