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The similarity solution for the steady stagnation flow toward an off-centered rotating disc gives a system of nonlinear partial differential equations. These nonlinear differential equations are analytically solved by applying a newly developed method called DTM-Padé technique (the combination of the differential transform method (DTM) and the Padé approximation). This technique is extended to give solutions for nonlinear differential equations with boundary conditions at infinity. Graphical results are presented to investigate influence of the rotation ratio α on the radial velocity, azimuthal velocity, and the induced velocity. In order to show the effectiveness of the DTM-Padé technique, the results obtained from the DTM-Padé technique are compared with available solutions obtained using shooting method to generate the numerical solution. The obtained results demonstrate the reliability of the algorithm and the DTM-Padé technique is an attractive method in solving the systems of nonlinear partial differential equations.

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This article presents a parametric study for and optimization of a transcritical power cycle. First, thermal efficiency, exergy efficiency, and specific network are selected as objective functions for parametric optimization. In order to optimize these functions, a procedure based on artificial neural networks (ANNs) and genetic algorithms (GAs) is proposed. This procedure comprises three steps.Step 1 is to find thermal efficiency, exergy efficiency, and specific network for different values of inlet turbine pressure, inlet turbine temperature, and fraction of the maximum power using the robust numerical code, engineering equation solver. In step 2, three distinct multi-layer perceptron ANNs based on the data obtained from step 1 are trained. In step 3, three distinct GAs are used to optimize the thermal efficiency, exergy efficiency, and specific network. The variables and fitness functions in these algorithms constitute, respectively, the inputs and outputs of the corresponding trained neural networks. For the purpose of validation of this study, for a special case, the results were compared with a previously reported case and were found to be in good agreement. Also in this article, this optimization process is applied to four different working fluids. Several interesting features among optimal objective functions and decision variables involved in the transcritical power cycle are identified.