Numerical simulation of magnetohydrodynamics nanofluid flow in a semi-porous channel with a new approach in the least square method

Present study deals with the flow of a fluid with added nanoparticles in a semi-permeable channel with a transverse magnetic effect. We have used Maxwell-Garnett and Brinkman models for effective electrical conductivity and viscosity, respectively. Water-based nanofluids with silver and copper nanoparticles have been used in the present investigation. Firstly, governing differential equations have been nondimensionalized with appropriate similarity transformations. We have also proposed an efficient technique to handle coupled differential equations by the weighted residual method (WRM). Here the least square method has been modified to solve coupled linear/nonlinear differential equations. Residual errors are examined graphically to see the efficiency of the proposed scheme. By taking particular values of Hartmann number, Reynolds number, and volume fraction viz. 0.5, 0.5, and 0.05, respectively, it is seen that residual error almost equal to zero in 6th term approximation. Moreover, for validation, present results have been incorporated with previously published works in special cases. Finally, the nature of the solutions has been reviewed by varying the values of the involved parameters. In this regard, the values of volume fraction are taken in between 0.01 and 0.09. Further, the values of the Hartmann number are considered between 0 and 4, and finally, values of the Reynolds number are taken in between 1 and 5.

Automated summary

This study investigates the flow of a fluid with added nanoparticles in a semi-permeable channel under a transverse magnetic effect, utilizing Maxwell-Garnett and Brinkman models. An efficient weighted residual method is proposed for solving coupled differential equations, and residual errors are analyzed for efficiency evaluation. It is found that residual error is almost zero in 6th term approximation under specific parameter values, and validation with previous works confirms the effectiveness of the proposed scheme.