Computational modeling and analysis for the effect of magnetic field on rotating stretched disk flow with heat transfer

Salman Ahmad ^a,*, T. Hayat ^a,b, A. Alsaedi ^b, Habib Ullah ^a, Faisal Shah ^a

a. Department of Mathematics, Quaid-I-Azam University 45320, Islamabad, 44000, Pakistan
         b. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.Box 80257, Jeddah, 21589, Saudi Arabia

Abstract: Time-dependent viscous fluid flow due to a stretchable rotating disk is investigated. Magnetic field is applied in vertical direction to the disk. Temperature equation is assisted with Joule heating effect. Governing system of PDE’s is transformed to dimensionless form by suitable variables. One of the numerical techniques known as finite difference scheme is adopted to tackle the given dimensionless partial differential system. This method results in a system of simple algebraic equations. The unknown function is analyzed inside domain of interest. In this technique of solution, a system is subdivided into many smaller parts called finite elements. The obtained simpler algebraic equations are then assembled to form a system of equations which governs the original problem. Variational method is used to get approximate solution by reducing the error function. Behaviors of pertinent variables on surface drag force, temperature, velocity and heat transfer rate are shown graphically. The obtained outcomes guarantee that velocity decreases for Hartmann number while it enhances with Reynolds number. Temperature increases for higher Prandtl, Eckert and Hartmann numbers. Skin friction boosts for larger values of Hartmann number. Nusselt number enhances with Hartmann number.

Keywords: Finite difference scheme; Magnetic field; System of partial differential equations; Joule heating; Rotating stretchable disk