Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk

Abstract

In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential equations but can also be used to solve nonlinear differential equations. This method has not previously been used to solve a nonlinear condensation problem. The dimensionless velocity and temperature profiles are shown, and the influence of Prandtl number and rotation ratio on the flow field and the Nusselt number are discussed in detail. In order to assess the accuracy of the solutions obtained by this method, the problem is also solved numerically using the Matlab bvp4c solver. The validity of our solutions is verified by the numerical results.

Application of variation of the parameters method for micropolar flow in a porous channel

“…The method of variation of parameters is a general method that has been used to solve nonhomogeneous linear differential equations [18]. More recently, it has been known from the literature that it can also be used to solve nonlinear differential equations [19][20][21][22][23][24][25][26]. In nonlinear equations, whereas the term that disrupting homogeneity is the function of both independent and dependent variable, in linear equations this term is only the function of the independent variable.…”

“…Arslantürk [23][24][25] applied this method for the thermal analysis of solid fins with different profiles and the analysis of the optimal dimensions of a space radiator. Güngör and Arslantürk [26] studied the three-dimensional problem of condensation film on an obliqued rotating disk under the steady-state condition using the variation of parameters method. Moreover, this method enables the determination of unknown variable parameters that arise from nonlinear equations where no closed form solutions are available.Therefore, it is expected that this method can be used in the solution of boundary layer equations [27] that must be solved iteratively by fulfilling a suitable boundary condition that can transform an interval problem into a finite interval problem.…”

Thermal analysis of longitudinal a porous fin with temperature-dependent internal heat generation using the variation of parameters method

“…Arslantürk [23][24][25] investigated the validity of this method to estimate temperature distribution in the solid fins with various geometries and to establish optimal dimensions of a space radiator. Güngör and Arslantürk [26] solved the three--dimensional problem of condensation film on an obliqued rotating disk under the steady-state condition using this method. Figure 1 shows a porous fin with rectangular geometry.…”

Investigation of Three-Dimensional Condensation Film Problem over an Inclined Rotating Disk Using a Nonlinear Autoregressive Exogenous Model

“…[ 7 ] using the similarity transformation and solving the problem using the perturbation method. Several other techniques are used to solve the condensation film problem, such as homotopy analysis method (HAM) [ 8 ], homotopy perturbation method (HAM) [ 9 , 10 ], classical Runge–Kutta and shooting method [ 11 ], extended optimal homotopy asymptotic method (EOHAM) [ 12 ], variational iteration method (VIM) [ 13 ], control volume finite element method (CVFEM) [ 14 ], differential transformation method (DTM) [ 15 ], spectral quasi linearization method (SQLM) [ 16 ], optimal homotopy analysis method (OHAM) [ 17 ], variation of parameter method (VPM) [ 18 ], and Akbari-Ganji method (AGM) [ 19 ].…”