Thermal activity of conventional Casson nanoparticles with ramped temperature due to an infinite vertical plate via fractional derivative approach

With inspired thermal characteristics and dynamic applications of nanoparticles, the researchers are motivated to suggest multidisciplinary significances of nano-materials in various thermal engineering and industrial processes. In this analysis, a mixed free convection nanofluid flowing on a vertical plate is discussed with heat transfer in the drilling of nanofluid. The Casson liquid is assumed as a base fluid with uniform suspension of clay nanoparticles. The leading partial differential governing equations with physical properties of nanoparticles are demonstrated with corporal flow phenomenon and imposed thermal conditions. In the governing partial differential equations, the partial derivative with respect to time is replaced by the most recent definition of fractional derivatives i.e. Atangana-Baleanu time-fractional derivative, and then the solution of temperature and velocity field is found by utilizing the Laplace transformation. The effects of different parameters with different values are deliberated and plotted graphically and numerically for temperature and momentum equations. The main results and conclusions are accomplished at the end of this exertion and compared with existing literature. It is concluded that the velocity profile boost up with Grashof number. The results of temperature and momentum equations show a more decaying tendency as compared to Caputo-Fabrizio fractional derivative.

Automated summary

The study discusses the mixed free convection of nanofluid on a vertical plate and heat transfer in the drilling of nanofluid. By using the Atangana-Baleanu time-fractional derivative and Laplace transformation, the impact of physical properties of nanoparticles on the temperature and velocity field is investigated. The results show that the velocity profile increases with the Grashof number, and the decaying trend of temperature and momentum equations is more significant compared to the Caputo-Fabrizio fractional derivative.