Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method

S. Mosayebidorcheh
  • S. Mosayebidorcheh
  • Young Researchers and Elite Club, Islamic Azad University, Najafabad Branch, Isfahan, Iran.
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T. Mosayebidorcheh
  • T. Mosayebidorcheh
  • Young Researchers and Elite Club, Islamic Azad University, Najafabad Branch, Isfahan, Iran.
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M. M. Rashidi
  • M. M. Rashidi
  • University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai Jiao Tong University, Shanghai, Peoples Republic of China.
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  •  Received: 13 September 2013
  •  Accepted: 29 April 2014
  •  Published: 30 June 2014

Abstract

In this paper, a similarity transformation is used to reduce the three-dimensional steady state condensation film on an inclined rotating disk by a set of nonlinear boundary value problems. This problem is solved using a new hybrid technique based on differential transform method (DTM) and Iterative Newton's Method (INM). The differential equations and its boundary conditions are transformed to a set of algebraic equations, and the Taylor series of solution is calculated. After finding Jacobian matrix, the unknown parameters computed using Multi-Variable Iterative Newton's Method. These techniques are used to obtain an approximate solution of the problem. In this solution, there is no need to restrictive assumptions or linearization. The results compared with the numerical solution of the problem, and a good accuracy of the proposed hybrid method observed. Finally, the velocity and temperature profiles demonstrated for different values of problem parameters.

 

Key words: Condensation film, rotating disk, nonlinear boundary value problem, differential transform method, iterative Newton's method, Jacobian matrix.