Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium.

*(English)*Zbl 1268.76061
Comput. Math. Appl. 64, No. 9, 2816-2832 (2012); corrigendum ibid. 69, No. 12, 1518 (2015).

Summary: The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle \(\alpha \) in a porous medium is studied. The resulting nonlinear governing equations with associated boundary conditions are solved using an optimized, robust, extensively validated, variational finite-element method (FEM) and a finite-difference method (FDM) with a local non-similar transformation. The Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (Nt), whereas it increases with increasing angle \(\alpha \). In addition, the local Sherwood number is found to increase with a rise in Nt, whereas it is reduced with an increase in Nb and angle \(\alpha \). The effects of Lewis number, buoyancy ratio, and mixed convection parameter on temperature and concentration distributions are also examined in detail. The present study is of immediate interest in next-generation solar film collectors, heat-exchanger technology, material processing exploiting vertical and inclined surfaces, geothermal energy storage, and all those processes which are greatly affected by a heat-enhancement concept.

##### MSC:

76S05 | Flows in porous media; filtration; seepage |

76R10 | Free convection |

65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |

76M10 | Finite element methods applied to problems in fluid mechanics |

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\textit{P. Rana} et al., Comput. Math. Appl. 64, No. 9, 2816--2832 (2012; Zbl 1268.76061)

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