MHD Flow and Heat Transfer in Sodium Alginate Fluid with Thermal Radiation and Porosity Effects: Fractional Model of Atangana–Baleanu Derivative of Non-Local and Non-Singular Kernel

Abstract

Heat transfer analysis in an unsteady magnetohydrodynamic (MHD) flow of generalized Casson fluid over a vertical plate is analyzed. The medium is porous, accepting Darcy’s resistance. The plate is oscillating in its plane with a cosine type of oscillation. Sodium alginate (SA–NaAlg) is taken as a specific example of Casson fluid. The fractional model of SA–NaAlg fluid using the Atangana–Baleanu fractional derivative (ABFD) of the non-local and non-singular kernel has been examined. The ABFD definition was based on the Mittag–Leffler function, and promises an improved description of the dynamics of the system with the memory effects. Exact solutions in the case of ABFD are obtained via the Laplace transform and compared graphically. The influence of embedded parameters on the velocity field is sketched and discussed. A comparison of the Atangana–Baleanu fractional model with an ordinary model is made. It is observed that the velocity and temperature profile for the Atangana–Baleanu fractional model are less than that of the ordinary model. The Atangana–Baleanu fractional model reduced the velocity profile up to 45.76% and temperature profile up to 13.74% compared to an ordinary model.

A novel multi fractional comparative analysis of second law analysis of MHD flow of Casson nanofluid in a porous medium with slipping and ramped wall heating

“…The impact of MHD and heat transmission for nanofluids was investigated by Khan et al. [12] using the same fractional model. While Sooppy Nisar et al.…”

“…Abro et al [10] and Arif et al [11] have published the comparative analysis of the Caputo-Fabrizio and Atangana-Baleanu fractional models for nanofluids. The impact of MHD and heat transmission for nanofluids was investigated by Khan et al [12] using the same fractional model. While Sooppy Nisar et al [13] examined the heat transport in nanofluids using clay nanoparticles.…”

Development of generalized Fourier and Fick’s law of electro-osmotic MHD flow of sodium alginate based Casson nanofluid through inclined microchannel: exact solution and entropy generation

“…Shah et al 25 reported the MHD free convection flow along with thermal memory. After that, the fractional analysis of the MHD flow of sodium alginate base fluid is reported by Khan et al 26 , by implementing the definition of Atangana–Baleanu derivative of the non-local and non-singular kernel.…”

Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

“…The important property of non-Newtonian fluid is viscosity. In many industrial problems, the comportment of non-Newtonian fluids is more important as compared to Newtonian fluids 1 , 2 . Some applications of non-Newtonian fluids can be seen in polymer engineering, manufacturing of foods, petroleum drilling, certain separation processes, and papers 3 , 4 .…”