Unsteady Fractional Casson Fluid Flow with Thermal Radiation and Heat Sink in a Convectively Heated Coutte Channel

The Casson fluid is regarded as one of the most well-known fluid kinds in the non-Newtonian substance group. Some characteristics are incomprehensible when seen only via the Newtonian flow problem lens. Therefore, it is more productive to use the non-Newtonian fluid motion. Synthetic lubricants, some oil paints, biological fluids, and other polymer solutions are only a few of the noteworthy scientific and industrial applications for Casson fluids. The Atangana–Baleanus in Caputo sense model (ABC) and the Caputo–Fabrizio model (CF) have been used to study the Casson fluid flow issue with heat sink effected by symmetric wall temperature. The Riemann sum approximation was used to invert all solutions from the Laplace domain to the time domain for both the CF and ABC models in the transient state, yielding approximation solutions for dimensionless temperature, velocity, skin friction, and Nusselt numbers. The steady-state instances were obtained through perturbation techniques. The effects of many dimensionless parameters on momentum, energy, frictional force, and heat transfer are examined and represented using illustrative graphs. It has been observed that raising the Casson fluid and heat sink parameters dramatically decreases the fluid's temperature and velocity. The flow are significantly impacted by the presence of symmetric wall temperature. It's also crucial to take note of the results, which show that while temperature and velocity in the CF and ABC models decrease as the fractional parameter increases, they both increase when the time and relaxation interval parameter increases. However, it was also demonstrated that an increase in thermal radiation led to a spike in the temperature profile. Additionally, it was observed that although a condition of instability developed at the top plate as a result of an enhancement in the fractional parameter, skin friction rose at the lower plate as a result of an increase in both heat radiation and the fractional parameter.