Non-similarity solution for Soret effect on natural convection over the vertical frustum of a cone in a nanofluid using new bivariate pseudo-spectral local linearisation method

In this paper, we present a numerical investigation of a highly coupled and nonlinear system of partial differential equations (PDEs) that model natural convection over the vertical frustum of a cone in a nanofluid in the presence of Soret effect. The system of PDEs are solved using a new numerical approach named as bivariate pseudo-spectral local linearisation method (BPSLLM). The solution method uses the so-called quasilinearisation method to linearise the equations in a sequential manner and applies spectral collocation to discretise all independent variables. To test the accuracy of the proposed method, error analysis and convergence tests are conducted. Further, the accuracy validation is conducted through comparison with asymptotic series solutions for limiting cases of small and large parameters. In order to unravel the interesting features of the problem, the effects of the physical parameters on skin-friction, heat, regular mass and nanoparticle mass transfer characteristics along the vertical frustum of a cone are given and the salient features are discussed.