Abstract
In this article, the application of Caputo fractional operators of order α, α∈ (0,1) has been studied. Heat transmission near the surface of a vertical plate in the flow of optically thick radiating Casson nanofluid along with mass diffusion in the presence of heat source/sink and constant magnetic flux is investigated. In the fluid problem, an H2O-based Casson nanofluid with carbon nanotube (CNTs) suspensions is investigated. The non-dimensionalized governing PDEs have been solved analytically via the combination of Fourier-sine and Laplace transform techniques and closed form of solutions are attained for the velocity, temperature, and concentration fields in terms of the Mittag-Leffler function. The physical behavior of the significant parameters has been scrutinized graphically. As a result, it is identified that the concentration, temperature, and velocity curves escalate drastically with the raising values of the fractional quantity α due to the alteration in mass, thermal, and momentum boundary layers with higher values of time t. When t>1, the species level in the fluid along with the fluid temperature and velocity rises with the fractional quantity α and decelerates when 0<t<1. Further analysis reveals that as the magnetic field is strengthened, the flow curves decelerate rapidly. Also, tables have been presented to show the influence of the controlling physical quantities on the friction drag and heat transmission rate.
•The application of Caputo fractional operators of order α, α∈(0,1) is studied.•Heat transfer of vertical plate for flow of optically thick radiant Casson nanofluid.•Analysis reveals that as the magnetic field is strengthened.