Keller-Box shooting method and its application to nanofluid flow over convectively heated sheet with stability and convergence

• Published in: Numerical heat transfer. Part B, Fundamentals Vol. 76; no. 3; pp. 152 - 180
• Main Authors: Nawaz, Yasir, Shoaib Arif, Muhammad
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.09.2019; Taylor & Francis Ltd
• Subjects: Accuracy; Boundary conditions; Chemical reactions; Coefficient of friction; Computational fluid dynamics; Convergence; Dirichlet problem; Endothermic reactions; Exothermic reactions; Flow control; Flow stability; Fluid flow; Iterative methods; Methods; Nanofluids; Nonlinear differential equations; Nonlinear equations; Ordinary differential equations; Organic chemistry; Partial differential equations; Rotating disks; Runge-Kutta method; Skin friction; Stability criteria; Temperature gradients; Wall temperature
• ISSN: 1040-7790; 1521-0626
• DOI: 10.1080/10407790.2019.1644924

The main aim of the present contribution is to present a coupling of Keller-Box method using Jacobi and Gauss-Seidel iterative methods with shooting approach and also this method is implemented on nanofluid flow problem. Present method of Keller-Box shooting method can be considered as an explicit approach whereas the standard Keller-Box method is an implicit method. Previously constructed nanofluid flow models are extended with exothermic/endothermic chemical reactions and the flow is considered over stretching, rotating, porous disk which is convectively heated from its bottom with the hot liquid. Similarity transformations are utilized to reduce the set of nonlinear partial differential equations into nonlinear ordinary differential equations with an assumption. Presently modified Keller-Box shooting method using Jacobi and Gauss-Seidel iterative methods is applied to investigate MHD nanofluid flow problem subject to Dirichlet, Neumann, and Robin's boundary conditions. Von Neumann stability criterion is adopted to check the stability of the present method using Gauss-Seidel iterative method. The bounds for maximum errors are found for Jacobi and Gauss-Seidel iterative methods and convergence conditions are given for the case of Gauss-Seidel iterative method. The obtained results from presently developed modified Keller-Box shooting method are in good agreement with those obtained by Matlab built in solver "bvp4c" in case of wall temperature gradient and obtained results are in good agreement with those obtained by Runge-Kutta (4, 5) shooting method in case of skin friction coefficient.