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      Sequential Implicit Numerical Scheme for Pollutant and Heat Transport in a Plane-Poiseuille Flow

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          A sequential implicit numerical scheme is proposed for a system of partial differential equations defining the transport of heat and mass in the channel flow of a variable-viscosity fluid. By adopting the backward difference scheme for time derivative and the central difference scheme for the spatial derivatives, an implicit finite difference scheme is formulated. The variable-coefficient diffusive term in each equation is first expanded by differentiation. The next step of the sequential approach consists of providing a solution of the temperature and concentration, before providing a solution for the velocity. To verify the numerical scheme, the results are compared with those of a Matlab solver and a good agreement are found. We further conduct a numerical convergence analysis and found that the method is convergent. The numerical results are investigated against the model equations by studying the time evolution of the flow fields and found that the data, such as the boundary conditions, are perfectly verified. We then study the effects of the flow parameters on the flow fields. The results show that the Solutal and thermal Grashof numbers, as well as the pressure gradient parameter, increase the flow, while the Prandtl number and the pollutant injection parameter both decrease the flow. The conclusion of the study is that the sequential scheme has high numerical accuracy and convergent, while a change in the pollutant concentration leads to a small change in the flow velocity due to the opposing effects of viscosity and momentum source.

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          Author and article information

          Journal of Applied and Computational Mechanics
          Shahid Chamran University of Ahvaz
          01 January 2020
          : 6
          : 1
          : 13-25
          [1 ] Department of Mathematics, Rivers State University, Port Harcourt, Nigeria

          This work is licensed under a Creative Commons Attribution Non Commercial 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/legalcode

          Mechanics of engineering. Applied mechanics

          Chaos, fractals & dynamical systems,Engineering,Nanotechnology,Sensor materials,Mechanical engineering,Renewable energy
          Finite difference methods,Fluid flows,Experimental order of convergence,Sequential implicit method,Pollutant dispersion


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