# Physics of the Optimum Gas for Heat Transfer Gases are rather conductors of heat relative to liquieds. However, they can be used to directly cool a product in many cases where a liquid heat transfer needs a shell. Some applications in semiconductor processing require direct cooling of devices by gases, and though limited by reactivity considerations, there are still some considerations for choosing among eligible inert gases. These applications are at standard pressure or less in vacuum systems and near standard temperature or greater, well within the ideal gas range. The advantage of gases is their transport properties are relatively simple to evaluate at low density where the kinetic theory of gases is valid. In this particular case, the flow is usually forced-convection, unconfined, and laminar, which is further ideal, since transport estimates for turbulent flow are much harder to make. As BSL notes in section 1.4 and asks the reader to work out in problem 1A.2 (though the nearest problem is actually 1A.4), the mixture properties for viscosity (and also thermal conductivity) can be highly non-linear. Moreover, it is not just that the behavior is non-linear interpolating, but that the mixture property can be more extreme than the property of any of the single components. For example, they give data showing the viscosity of 75% hydrogen and 25% dichlorodifluoromethane as 135.1 micropoise, compared to 124 micropoise for dichlorodifluoromethane and 88.4 micropoise for hydrogen. Hence the problem of optimizing the thermal conductivity is non-trivial. Moreover in applications with combined mass and heat transfer, optimizing the gas composition so the heat transfer coefficient is maximum is further non-trivial, since the molar mass in addition to the thermal conductivity is highly relevant for the momentum transfer. Since the effective heat transfer coefficient (Nusselt number) depends on geometries, the optimum heat transfer fluid cannot even be given just as a function of the intensive thermodynamic properties of the system (e.g., what temperatures and pressures), but must include in principle the geometry and flow velocity. However, the sensitivity of the solution to these parameters may not be high. These calculations should enable the optimum to be found, and can be combined with cost coefficients to determine the optimum gas mixture for heat transfer with process economics. Fundamentally, what should be decisive is the molecular parameters of interaction, notably the energetic parameter of the Lennard-Jones, relative to the molecular weight. The semi-empirical mixing rule doesn't require estimating interaction parameters between unlike species, and it is remarkable it works as well as it does--for gases with differing polarities, it isn't expected that the energies of interactions would follow such a general rule. # Uniformly Sampling Composition Space It is simple to uniformly sample composition space in the case of two variables, since there is by the condition of fractions summing to 1 only one degree of freedom, which can take on a linear space. However, for higher cases that is not the case. A distribution which has a support satisfying the constraint of composition, namely that all mole fractions sum to 1, is sampled to quickly obtain sample points. This is not uniform, but near uniform when sufficiently densely sampled. # Related Projects More than one chemical engineering libraries allow you to compute the transport properties of gases, though they may not implement multicomponent mixing rules and instead use simple linear weighting. One library in wide use and well-funded is Cantera. # Dependencies Other than standard computational science libraries (numpy, scipy, matplotlib), this uses the ternary package to make ternary composition plots. # Data sources - Collision cross-sections and lennard-jones parameters: BSL Transport Phenomena, 2nd Edition - Heat capacities: Koretsky, Chemical and Engineering Thermodynamics # Related Literature - Optimum composition of gas mixture in a novel chimney-based LED bulb