Implementing the multistep adams-bashforth numerical approach on magnetohydrodynamic radiated casson fluid with darcy forchheimer, dissipation and activation energy

The main goal behind the conduction of this work is to use the Adams-Bashforth method in the field of fluid dynamics to solve the Navier–Stokes equations based on the boundary layer flow of magnetohydrodynamic Casson fluid passing on the upper horizontal parabolic surface with variable fluid characteristics and Darcy-Forchheimer effect. The temperature flow rate and mass rate are also investigated with the help of thermal radiation, viscous dissipation, heat generation and activation energy. The Adams-Bashforth technique is widely used in numerical analysis, scientific computing, fluid dynamics, chemical kinetics, astrophysics and is particularly useful in solving the stiff ODEs, where other methods may fail to converge. It is particularly useful for simulating the flow of fluids around complex geometries, such as aircraft wings or turbine blade. The equations of basic governing laws (Momentum, temperature and concentration) are achieved in the form of PDE’s. These PDEs are then transmuted into ODEs via similarity variables and the numerical behaviors of these ODEs are obtained with Adam-Bashforth (Predictor-Corrector) along with RK-4 technique on the Matlab software. The initial guesses are modified by using secant method. Graphical analyses are used to explain how different parameters affect the temperature, velocity and mass transport rate. The finding of results revealed that the inertia coefficient, Hartmann number and fluid parameter make the decrement in the velocity field. The amplification in temperature of fluid is noted for varying the radiation coefficient, dissipation and thermal generation coefficient. The solutal field drops due to activation energy and reaction coefficient. The findings are useful to observe the flow attributes, behaviors and helpful in the designing of thermal equipment in the thermal industries.