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.
Highlights
The convection driven by two different density gradients with differing rates of diffusion is widely known to as “double-diffusive convection” and is an important fluid dynamics phenomenon see Mojtabi and Charrier-Mojtabi 1
The Nusselt number NuGr−1/4 and Sherwood number ShGr−1/4 which highlight the heat and mass transfer are shown in Figures 7 and 8, as functions of Sr for different values of Df in the aiding and opposing buoyancy cases
We found that the Dufour parameter reduces the heat transfer coefficient while increasing the mass transfer rate
Summary
The convection driven by two different density gradients with differing rates of diffusion is widely known to as “double-diffusive convection” and is an important fluid dynamics phenomenon see Mojtabi and Charrier-Mojtabi 1. Alam et al investigated the Dufour and Soret effects on steady combined free-forced convective and mass transfer flow past a semi-infinite vertical flat plate of hydrogen-air mixtures. They used the fourth-order Runge-Kutta method to solve the governing equations of motion. Babaelahi et al studied the heat transfer characteristics in an incompressible electrically conducting viscoelastic boundary layer fluid flow over a linear stretching sheet They solved the flow equations using the optimal homotopy asymptotic method OHAM and validated their results by comparing the OHAM solutions with Runge-Kutta solutions. The linearization method iteratively linearizes the nonlinear equations to give a system of higher-order deformation equations that are solved using the Chebyshev spectral collocation method
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