In this thesis the first generation of the air foil bearings was investigated with a new equations solving method. Reynolds equation was the main equation to calculate the pressure of lubricant film. Energy equation was used to calculate the temperature profile of the bearing and the lubricant film. To enhance the accuracy of the solving, the reynolds equation and the energy equation was solved couple using MATLAB software (thermohydrodynamic). Thermohydrodynamic solving indicated that the temperature is important parameter in reynolds equation and should not be assumed negligible. Effect of parameters such as load and speed on the temperature of the bearing was investigated. Generalized differential quadrature method was used to solve the problem either integrals or partial equations. Best weighting coefficients and points distribution were determined. generalized differential quadrature reduces the number of points of solution up to 80 percent and it also reduces the solution time. One chapter was assigned for design and fabrication of generation two and one foil bearings for practical aspect of working. Keywords: gas bearing; foil bearing; thermohydrodynamic; generalized differential quadrature
