Journal of Applied Mathematics

On the Solution of Double-Diffusive Convective Flow due to a Cone by a Linearization Method

Mahesha Narayana and Precious Sibanda

Full-text: Open access

Abstract

The paper details the use of a nonperturbation successive linearization method to solve the coupled nonlinear boundary value problem due to double-diffusive convection from an inverted cone. Diffusion-thermo and thermal-diffusion effects have been taken into account. The governing partial differential equations are transformed into ordinary differential equations using a suitable similarity transformation. The SLM is based on successively linearizing the governing nonlinear boundary layer equations and solving the resulting higher-order deformation equations using spectral methods. The results are compared with the limited cases from previous studies and results obtained using the Matlab inbuilt bvp4c numerical algorithm and a shooting technique that uses Runge-Kutta-Fehlberg (RKF45) and Newton-Raphson schemes. These comparisons reveal the robustness and validate the usage of the linearisation method technique. The results show that the nonperturbation technique in combination with the Chebyshev spectral collocation method is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 587357, 19 pages.

Dates
First available in Project Euclid: 14 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1355495026

Digital Object Identifier
doi:10.1155/2012/587357

Mathematical Reviews number (MathSciNet)
MR2880821

Zentralblatt MATH identifier
1235.76089

Citation

Narayana, Mahesha; Sibanda, Precious. On the Solution of Double-Diffusive Convective Flow due to a Cone by a Linearization Method. J. Appl. Math. 2012 (2012), Article ID 587357, 19 pages. doi:10.1155/2012/587357. https://projecteuclid.org/euclid.jam/1355495026


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