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The mathematical formulation is presented for a Non-Newtonian Casson fluid model
with unsteadiness and variable fluid film thickness factors in terms of partial differential
equations (PDEs). With the help of available similarity transformations, the governing PDEs
are converted into ordinary differential equations (ODEs). For the mass and heat transfer in
the mixed convection stagnation point flow of Casson fluid over an unsteady stretching sheet,
a detailed comparative analysis is carried out in this paper of the analytical and numerical
approximation techniques. The Homotopy Analysis Method (HAM) is applied for the
analytical solution while the RK4 with the Shooting Method (RKF45) and Finite Difference
Method (FDM) are used for the numerical solutions. The velocity and temperature profiles
are analyzed under the effects of embedded parameters such as the Casson fluid parameter,
unsteadiness parameter, mixed convection parameter, Prandtl number, Eckert number, and
stretching ratio. The results are presented in both graphical and tabulated forms and they
illustrate the dependence upon the embedded parameters for the mass and heat transfer
characteristics of Casson fluid. The MAPLES codes for these analytical and numerical
approximation schemes are created and successfully tested for validation. The limitations of
analytical and numerical methods, accuracy, and computational times are presented as well in
the end sections.
The final results obtained through these analytical and numerical methods provide
very valuable insights into the behavior of fluid flow and assist in the design and optimization
of various fluid engineering and mechanical industrial systems. Moreover, this study will
contribute by providing more solvable classes of the mixed convection stagnation point flow
of Non-Newtonian Casson fluid problems.