Ab initio simulation of heat transfer through a mixture of rarefied gases José L. Strapasson ⇑ , Felix Sharipov Departamento de Física, Universidade Federal do Paraná, Caixa Postal 19044, Curitiba 81531-990, Brazil article info Article history: Received 21 September 2013 Received in revised form 28 November 2013 Accepted 2 December 2013 Keywords: Gaseous mixture Ab initio potential Heat transfer abstract The heat flux problem for a binary gaseous mixture confined between two parallel plates with different temperatures is studied on the basis of the direct simulation Monte Carlo method with an implementa- tion of ab initio potential. The calculations were carried for a wide range of the gas rarefaction, for several values of the mole fraction and for two values of the temperature difference. The smaller value of the dif- ference corresponds to the limit when the nonlinear terms are negligible, while the larger value describes a nonlinear heat transfer. The heat flux, temperature, and mole fraction distributions are presented. To study the influence of the intermolecular potential, the same simulations are carried out for the hard sphere molecular model. A relative deviation of the results based on this model from those based on the ab initio potential is analyzed. It is pointed out that the difference between the heat flux of the two potentials is about 8% and 5% for the small and large temperature differences, respectively. The tem- perature distribution between plates is weakly affected by the molecular potential, while the chemical composition variation is the most sensitive quantity for the considered problem. The reported results can be used as benchmark data to test model kinetic equations for gaseous mixtures. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction In our previous paper [1], we showed that any intermolecular potential can be implemented into the direct simulation Monte Carlo (DSMC) method [2] with the same computational effort as that for the hard sphere (HS) molecular model. Since reliable infor- mation about intermolecular potentials of many gases can be found in literature, see e.g. Refs. [3,4], it is not necessary to use the potentials like variable hard spheres [2], variable soft spheres [5] and generalized hard spheres [6] elaborated specifically for the DSMC method. Recently, the ab initio (AI) potentials were cal- culated for practically all noble gases and their mixtures, see e.g. Refs. [7–14]. An implementation of this potential into the DSMC [15] made this method completely free from tuned parameters usually extracted from experiments. Such an approach allows us to obtain benchmark data which can be used to test kinetic models and approximate methods in order to solve many practical prob- lems of heat and mass transfer with modest computational effort, but without losing reliability. Our recent paper [16] reports benchmark data for the Couette flow of helium–argon mixture over the whole range of the gas rar- efaction based on the AI intermolecular potential. A comparison of the results obtained for the AI potential with those for the HS potential showed that the Couette flow is weakly sensitive to the potential. In the present paper, we continue to study the influence of the intermolecular potential on various types of mixture flows. More specifically, a heat transfer through a mixture confined be- tween two plates is calculated applying the DSMC technique. The calculations are carried out over a wide range of the gas rarefaction for both AI and HS potentials. The flow to be considered here is a classical problem of fluid mechanics. Many researchers studied this problem in case of a sin- gle rarefied gas, see e.g. Refs. [17–26]. On our knowledge, there are very few papers [27–31] on heat transfer through a mixture of rar- efied gases. The works [27,30,31] provide results based on the Boltzmann equation with the HS potential. The paper [28] reports results on the heat flux based on the linearized McCormack (MC) model [32] of the Boltzmann equation. The paper [29] is also based on the MC model, but two potentials were used, viz., HS and the so- called realistic potential (RP). A comparison of results based on these two potentials showed that the heat transfer is strongly sen- sitive to the potential. As was shown in Refs. [33–38], many other phenomena in gaseous mixtures are very sensitive to the potential of the intermolecular interaction. Thus, it is important to obtain benchmark results based on the ab initio calculations for a large number of phenomena. The aim of the present paper is to calculate the heat flux through a binary mixture of rarefied gases confined between two parallel plates based on the AI potential implemented into the DSMC method. To study the influence of the potential on heat flux, temperature and chemical composition distributions, the same problem will be solved for the HS molecular model too. 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.12.011 ⇑ Corresponding author. Tel.: +55 4136722356. E-mail addresses: jstrapasson@fisica.ufpr.br (J.L. Strapasson), sharipov@fisi- ca.ufpr.br (F. Sharipov). International Journal of Heat and Mass Transfer 71 (2014) 91–97 Contents lists available at ScienceDirect International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt