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Title: Calculation of the transport coefficients for dilute gases using an iterative solution of Boltzmann's equation
Author: Martin, Ronald
ISNI:       0000 0001 3620 1830
Awarding Body: University of Surrey
Current Institution: University of Surrey
Date of Award: 1972
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The second approximation to Boltzmann's equation for dilute gases, in the Chapman-Enskog form, is solved for several different potential models by using an iterative procedure. This method is presented as an alternative to the standard one of Chapman and Cowling. The first order perturbation function, &phis;, to the local Maxwellian distribution, f[(o)], obtained as an infinite series [mathematical equation] where the &phis;[(i)]'s are obtained by repeated iterations of the Boltzmann equation. The transport coefficients, such as thermal conductivity, lambda, and viscosity, eta[s], are obtained from &phis; as infinite series [mathematical equation] In the case of the Maxwellian and Pseudo-MaxweIlian potential models, for a single component gas, both the &phis;[(i)]'s and lambda[(i)]'s and eta[s][(i)]'s are found to follow exact geometrical progression which can s be summed. The transport coefficient obtained by performing these sums are found to correspond to the analytical values obtained by the Chapman-Cowling method. For the rigid sphere model the lambda[(i)]'s still seem to approximate closely to a geometrical progression. On assuming an exact geometrical progression for the lambda[(i)]'s, one obtains a value for the thermal conductivity which is in close agreement with that obtained by Chapman-Cowling. The iterative method is extended to deal with binary mixtures for the case of Maxwellian and Pseudo-Maxwellian potential models where exact geometrical progressions are again exhibited, and values for the transport coefficients are found to correspond to those for the Chapman-Cowling method. The significance of the form of the results obtained by the iterative procedure is discussed particularly with regard to the possibility of extending the method to deal with more general repulsive potentials and higher order mixtures.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available