Applications of fractional calculus to thermodynamics analysis of hydromagnetic convection in a channel

Abstract

The present analysis signifies the impacts of fraction calculus on the MHD analysis of an incompressible fluid flow with entropy generation, viscous dissipation, and joule heating carried out between two endless vertical plates. The left vicinity of the MHD fluid flow channel has a convectively hot MHD fluid with a specific temperature that produces the heat transfer coefficient inside the flow channel. The MHD fluid flow model has been formulated with the fractional order derivative, which is an exciting area of research. The transient form of the system of dimensionless PDEs with imposed boundary conditions is transformed to a fractional order derivative model, which was formerly solved via the Finite Difference Scheme (FDS). The graphical illustrations signify the significance of the transverse magnetic field, viscous dissipation, and Ohamic heating alongside Biot and Bejan numbers. The velocity and temperature illustrations have been shown graphically to observe the influences within the flow channel. With predetermined values of the corresponding dimensionless parameters, the coefficient of skin friction and Nusselt number accompanied by a range of convection constraints are displayed graphically within the flow channel.