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.
Highlights
Scientific problems and phenomena in our world are essentially nonlinear and modeled by the nonlinear differential equations
The main goal of this paper is to present an analytical approximate solution of the steady three-dimensional problem of condensation film on the inclined rotating disk
The motion of the condensate film using centrifugal forces on a cooled rotating disk is considered by Sparrow and Gregg (1959)
Summary
Scientific problems and phenomena in our world are essentially nonlinear and modeled by the nonlinear differential equations. The main goal of this paper is to present an analytical approximate solution of the steady three-dimensional problem of condensation film on the inclined rotating disk. This problem was studied by Wang (2007) and Rashidi and Dinarvand (2009). The motion of the condensate film using centrifugal forces on a cooled rotating disk is considered by Sparrow and Gregg (1959) They transformed the Navier-Stokes equations into a system of nonlinear boundary value problems and Consider a disk rotating in its plane with angular velocity Following residual functions to minimize them for obtaining the unknown parameters: The accuracy chosen for computing a1 to a5 by Newton's m
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