Effects of fractional derivative and heat source/sink on MHD free convection flow of nanofluids in a vertical cylinder: A generalized Fourier's law model

• DOI: 10.1016/j.csite.2021.101518
• Publication Date: 2021-10-04T15:52:18Z
• Authors: Nehad Ali Shah; Abderrahim Wakif; Rasool Shah; Se-Jin Yook; Bashir Salah; Yasir Mahsud; Kashif Hussain
• Keywords: Integral transform

This research looked at the unsteady free convection flows of an incompressible viscous fluid with heat/sink in a vertical cylinder containing mixture 47 nm alumina nanoparticles water. The flow direction is subjected to perpendicular magnetic field. generalization entails taking into account new version constitutive equation for thermal flux, known as generalized Atangana-Baleanu derivative, which based on time-fractional derivative Mittag-Leffler kernel. Using Laplace transform and finite Hankel transform, closed forms analytical solutions temperature velocity fields, represented Bessel G–function Lorenzo Hartley functions, are determined. appropriate particularizations yield corresponding fractional derivatives power-law kernel exponential function one-parametric function. It also possible acquire usual situation, corresponds classical Fourier's law. To compare models Atangana-Baleanu, Caputo, Caputo-Fabrizio time derivatives, numerical simulations produced program Mathcad carried out visually depicted.