Impact of generalized fourier law in thermal flux convective flow over a vertical plate: Analysis of fractional derivative

Abstract

In this paper, a convective fluid flow mixed with different nanoparticles (NPs) flowing on a vertical plate is studied. The impacts of slip boundary wall, Newtonian heating, and magnetic field are also pondered. Using Fourier’s rule of heat conductivity and Caputo-time (CT) fractional derivative (FD), the nondimensional governing equations for this mathematical model are obtained. The Laplace transformation (LT) technique is used to get a generalized solution to the equations of momentum and energy. The physical interpretation of velocity distribution in some particular cases is well recognized in the past research works and is also highlighted to scrutinize some further physical perception into the subject and to fortify the novelty of this research communication. Furthermore, graphical depictions are created using the mathematica program to assess the physical importance of the considered topic. As a result, we concluded that the blood-based aluminium oxide ([Formula: see text] NPs show more decaying behavior as compared to titanium dioxide ([Formula: see text] NPs for temperature and velocity profile. Moreover, changing the fractional parameter’s value for a long period of time improves thermal and velocity profiles.

Solution of Water and Sodium Alginate-Based Casson Type Hybrid Nanofluid with Slip and Sinusoidal Heat Conditions: A Prabhakar Fractional Derivative Approach

“…In 1971, the Prabhakar work was proposed by an Indian mathematician, Professor Tilak Raj Prabhakar, who anticipated a generality of the Mittag-Leffler function involving three parameters. Using the Prabhakar derivative along with precise fractional coefficients might be a valuable path for choosing suitable numerical models that are recognized as a good arrangement between trial and hypothetical outcomes [37,38]. Due to massive uses in fluid mechanics, researchers studied fractional models based on Caputo, CF, AB, and Prabhakar's time-fractional derivatives to study the memory effects of different Newtonian and non-Newtonian models in [39][40][41][42][43][44].…”