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The principal aim of this paper is to compare two analytical methods of decomposition employed for solving nonlinear problem of flow in converging-diverging channels, namely the Adomian Decomposition Method (ADM) and Generalized Decomposition Method (GDM). The comparison between ADM and GDM is conducted by using the numerical results of the studied problem as a guide. The results show that GDM method is more accurate and very efficient than ADM method. Indeed, ADM is a good method in solving the nonlinear problems, but we notice in solving the nonlinear problem of the Jeffery-Hamel flow that GDM is powerful, superior than ADM and clearly constitute an excellent choice for solving nonlinear problems.

This paper deals with the failure of an elastohydrodynamic lubrication rolling contact, operating in highly contaminated media. To achieve this goal, an original experimental device was built and then successfully used to investigate the effects of three operating parameters, called contaminant concentration ( C), rotational speed ( V), and load ( Q) on the evolution of wear, W, and arithmetic mean surface roughness, Ra. The influence of the above mentioned parameters is statistically explored using the analysis of variance (ANOVA). Mathematical models for wear and surface roughness were also established using the response surface methodology by employing multiple regression method. From this experimental research, it is clearly shown that the contaminant concentration is the major factor leading to the fast failure of machine elements. Finally, the obtained results justify and confirm the lifetime reduction of mechanisms in highly contaminated media.