Citation
Liu, ChungYen (1962) Part I. Kinetic theory description of plane, compressible Couette flow. Part II. Kinetic theory description of conductive heat transfer from a fine wire. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Q16RJR92. https://resolver.caltech.edu/CaltechETD:etd12092005133941
Abstract
PART I:
By utilizing the twostream Maxwellian in Maxwell's integral equations of transfer we are able to find a closedform solution of the problem of compressible plane Couette flow over the whole range of gas density from free molecule flow to atmospheric. The ratio of shear stress to the product of ordinary viscosity and velocity gradient, which is unity for a Newtonian fluid, here depends also on the gas density, the plate temperatures and the plate spacing. For example, this ratio decreases rapidly with increasing plate Mach number when the plate temperatures are fixed. On the other hand, at a fixed Mach number based on the temperature of one plate, this ratio approaches unity as the temperature of the other plate increases. Similar remarks can be made for the ratio of heat flux to the product of ordinary heat conduction coefficient and temperature gradient.
The effect of gas density on the skin friction and heat transfer coefficients is described in terms of a single rarefaction parameter, which amounts to evaluating gas properties at a certain "kinetic temperature" defined in terms of plate Mach number and plate temperature ratio. One interesting result is the effect of plate temperature on velocity "slip". In the NavierStokes regime most of the gas follows the hot plate, because the gas viscosity is larger there. As the gas density decreases the situation is reversed, because the velocity slip is larger at the hot plate than at the cold plate. In the limiting case of a highly rarefied gas most of the gas follows the cold plate.
Limitations of the present sixmoment approximation at high plate Mach numbers are discussed and it is concluded that an eightmoment approximation would eliminate these difficulties. The results obtained in this simple geometry suggest certain conclusions about hypersonic flow over solid bodies when the surface temperature is much lower than the kinetic temperature.
PART II:
The Maxwell moment method utilizing the twosided Maxwellian distribution function is applied to the problem of conductive heat transfer between two concentric clylinders at rest. Analytical solutions are obtained for small temperature differences between the cylinders. The predicted heat transfer agrees very well with experiments performed by Bomelburg, SchaferRating and Eucken. Comparison with results given by the Grad's thirteen moment equations, and with those given by Fourier's "law" plus MaxwellSmoluchowski temperaturejump boundary condition shows that the twosided character in the distribution function is a crucial factor in problems involving surface curvature.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Aeronautics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Group:  GALCIT 
Thesis Committee: 

Defense Date:  1 January 1962 
Record Number:  CaltechETD:etd12092005133941 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd12092005133941 
DOI:  10.7907/Q16RJR92 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  4906 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  12 Dec 2005 
Last Modified:  21 Dec 2019 04:07 
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