The existence of a minimum in the cylindrical Poiseuille flow of a rarefied gas has been known since the experiments of Knudsen [Ann. Phys. 4, 75 (1909)]. Previously, the phenomenon has been studied with models of the Boltzmann equation, but results for the Boltzmann equation itself have not been reported. In the present paper, proceeding from recent studies, first the SN numerical algorithm for solving the linearized Boltzmann equation for the cylindircal geometry is outlined. Then, explicit numerical results for a rigid sphere gas and the boundary condition of diffuse specular reflection are obtained. The results show a minimum of the flow rate, and generally, provide a good description of the experimental data.

The problem of thermal transpiration between parallel plates and in a cylindrical capillary is considered by using the Maxwellian diffuse-specular reflection at the surface. The relevant integral equations are solved by a simple numerical scheme and results for both the Poiseuille flow and the thermal creep flow rate are obtained. Some recently reported variational results for the Poiseuille flow appear to be inaccurate (off by about 10%–15%), and there is a need for further refinement in the variational calculations. The effect of partial accommodation is found more significant in the free molecule region than in the near continuum region. Thus to minimize the surface effects, the experiments on the thermal conductivity measurements via thermal transpiration would best be conducted in the near continuum region.

We report here an innovative feature of green nanotechnology-focused work showing that mangiferin-a glucose functionalized xanthonoid, found in abundance in mango peels-serves dual roles of chemical reduction and in situ encapsulation, to produce gold nanoparticles with optimum in vivo stability and tumor specific characteristics. The interaction of mangiferin with a Au-198 gold precursor affords MGF-AuNPs as the beta emissions of Au-198 provide unique advantages for tumor therapy while gamma rays are used for the quantitative estimation of gold within the tumors and various organs. The laminin receptor specificity of mangiferin affords specific accumulation of therapeutic payloads of this new therapeutic agent within prostate tumors (PC-3) of human prostate tumor origin induced in mice which overexpress this receptor subtype. Detailed in vivo therapeutic efficacy studies, through the intratumoral delivery of MGF-AuNPs, show the retention of over 80% of the injected dose (ID) in prostate tumors up to 24 h. By three weeks post treatment, tumor volumes of the treated group of animals showed an over 5 fold reduction as compared to the control saline group. New opportunities for green nanotechnology and a new paradigm of using mangiferin as a tumor targeting agent in oncology for the application of MGF-AuNPs in the treatment of cancer are discussed.

Numerically ’’exact’’ results for the thermal creep and viscous slip problems for the BGK model and Maxwellian diffuse specular reflection at the wall are obtained by using equations derived earlier by Cercignani, Loyalka, and Cipolla. Results obtained by the use of both the half range and the ’’full-range’’ expansions are found to be in complete agreement and provide standards of comparison for various approximate methods.