A metaheuristic approach for the comparative study of MHD flow of nano liquids in a semi-porous channel

Abstract In this paper, magneto-hydrodynamic flow of four different nanoliquids is presented. Two types of nanoparticles, viz. alumina and CuO are considered in water and ethylene glycol as base fluids. Appropriate models for nanoliquid physical properties are considered to incorporate the nanoparticle aggregation effects, nanoparticle shape, and size of the nanoparticles. Similarity transformations are used to convert the partial differential equations of the flow to nonlinear ordinary differential equations. The resultant system of equations is solved by Runge–Kutta finite difference method and an error function is designed which is optimized by using a metaheuristic algorithm, namely particle swarm optimization. The effect of flow parameters, viz. mass transfer parameter and Hartmann number and the nanoliquid parameters like nature of the base liquid, nanoparticle material, nanoparticle size, concentration of nanoparticle in base liquid on velocity distributions have been analyzed and discussed. The nanoparticle concentration and the particle size are found to have a significant role in the nanoliquid flow in the channel. The numerical results obtained from the proposed numerical method are validated with the previously published work under some special cases. The proposed numerical method holds excellent potential in mathematical modeling problems where the resultant equations are nonlinear coupled ordinary differential equations with unknown initial or boundary conditions.