الفهرس 
INTRODUCATIONOnly 14 pages are availabe for public view
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Abstract
Reynolds equation is a partial differential equation,derived from the Navier-Stokes equations and is one of the fundamental Reynolds equations of the hydrodynamic lubrication theory. Solution of equation describes the pressure distribution of the lubricant in a journal bearing with finite length. The parameters involved in the Reynolds equation are viscosity, density and film thickness of lubricant. However, an accurate analysis of the fluid film hydrodynamics obtained using many numerical solution of the Reynolds equation. Differential Transform Method (DTM) is one of the powerful numerical methods applied to solve linear and nonlinear partial differential equations. This study aims to apply DTM to solve Reynolds equation in partial differential form to get pressure distribution of journal bearing. Results obtained from the DTM compared with available solutions obtained using other numerical methods and show good agreement. This work consists of four chapters, the first is an introduction, in this chapter we introduced a literature work and the scope of our work. In chapter two, we present a mathematical study for differential transform method (DTM). The concept of differential transform solves linear and nonlinear initial value problems which is an iterative procedure for getting solutions of differential equations in the form of Taylor series. There are differences between transformation method which is called differential transform method and the high-order Taylor series method, which depends on computing the coefficients of the Taylor series of the solution using the initial and boundary conditions and the partial differential equation method. But, the high-order Taylor series method requires more computation for large orders. ABSTRACT In chapter three, we present a mathematical study for solving Reynolds equation which is an application to lubricating problems. The method of differential transform method is applied to obtain the approximate solution. In Sec.3.1, we present a mathematical modeling for the problem by deduce the Reynolds equation from Navier Stocks equation and then we apply some assumptions to get the final form of the equation which we will solve. In Sec.3.2, we present a mathematical study for solving Reynolds equation using differential transform method.In chapter four, we will discuss the results of previous chapter and compare between the numerical results of differential transform method and exact analytic solutions of Reynolds equation. In chapter five we give conclusions of this thesis and we suggest many ideas of the future works to researchers.