The main purpose of this numerical investigation is to estimate energetically the thermo-magnetohydrodynamic (MHD) irreversibility arising in Stokes’ second problem by successfully applying the first and second thermodynamic laws to the unsteady MHD free convection flow of an electrically conducting dissipative fluid. This fluid flow is assumed to originate periodically in time over a vertical oscillatory plate which is heated with uniformly distributed temperature and flowing in the presence of viscous dissipation and Ohmic heating effects. Moreover, the mathematical model governing the studied flow is formulated in the form of dimensional partial differential equations (PDEs), which are transformed into non-dimensional ones with the help of appropriate mathematical transformations. The expressions of entropy generation and the Bejan number are also derived formally from the velocity and temperature fields. Mathematically, the resulting momentum and energy conservation equations are solved accurately by utilizing a novel hybrid numerical procedure called the Gear-Generalized Differential Quadrature Method (GGDQM). Furthermore, the velocity and temperature fields obtained numerically by the GGDQM are exploited thereafter for computing the entropy generation and Bejan number. Finally, the impacts of the various emerging flow parameters are emphasized and discussed in detail with the help of tabular and graphical illustrations. Our principal result is that the entropy generation is maximum near the oscillating boundary. In addition, this thermodynamic quantity can rise with increasing values of the Eckert number and the Prandtl number, whereas it can be reduced by increasing the magnetic parameter and the temperature difference parameter.

Evolutionary approaches have a critical role in different disciplines such as real-world problems, computer programming, machine learning, biological sciences, and many more. The design of the stochastic model is based on transition probabilities and non-parametric techniques. Positivity, boundedness, and equilibria are investigated in deterministic and stochastic senses. An essential tool, Euler–Maruyama, is studied for the solution of said model. Standard and nonstandard evolutionary approaches are presented for the stochastic model in terms of efficiency and low-cost approximations. The standard evolutionary procedures like stochastic Euler–Maruyama and stochastic Runge–Kutta fail to restore the essential features of biological problems. On the other hand, the proposed method is efficient, of meager cost, and adopts all the desired feasible properties. At the end of this paper the comparison section is presented to support efficient analysis.

In this work, we obtain non-Gaussian (NG) stochastic solutions to $\chi$-Wick-type stochastic ($\chi$-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems (HCSs), the $\chi$-Wick product ($\chi$-Wk-product) and an $\chi$-Hermite transform ($\chi$-Hr-transform) are proposed. We provide a new set of non-Gaussian solitary wave solutions (NG-SWSs) to Burgers’ equations with variable coefficients. NG white noise functional solutions (NG-WNFSs) to $\chi$-Wk-TS Burgers’ equations with variable coefficients are shown. The symmetry coefficients of partial differential equations and the symmetrical properties of SPDEs are critical in determining the best solution.