Mathematical and disorder analysis of diffusivity and conductivity dependent magnetized Cross liquid wavy motion

Reduction in the system's existing energy due to material dynamics, surface resistance, and heat transfer is a major cause of irreversible processes. Since, for a better understanding of the system energy loss, a proper design of different closed and open systems is a modern‐day challenge. To address the influence of irreversibility, the additional formulation for entropy generation is formulated in the newly modeled flow problem. Thermal radiation is modeled using the Rosseland approximation, and entropy generation analysis is conducted to assess the thermodynamic irreversibility arising from heat transfer, fluid friction, and mass diffusion. The behavior of tensor‐dependent mass diffusivity and conductivity differentiates the role of the substance diffusivity and its conductivity significantly. However, this particular study in investigates the steady two‐dimensional wavy flow of the Cross liquid over a vertical wavy surface, encountering the maximum impact of gravity and electrical conductivity. The thermal behavior is elaborated in the presence of thermal stratification, heat generation, and radiation. The mass flow is examined in the presence of a chemical reaction. The newly formulated non‐dimensional equations are based on the Lie group analysis. The boundary layer contribution is determined by adopting a low Reynolds theory. The influence of key dimensionless factors, including the magnetic, radiation, stratification, chemical reaction rate, temperature and concentration ratio, and Brinkman number on the flow speed, concentration, entropy generation, and temperature is thoroughly examined. The results indicate that the larger values of magnetic factor and thermal radiation enhance entropy generation, while higher thermal and solutal stratification suppress heat and mass transfer rates. The amplitude of the wave is found to significantly reduce the flow velocity, indicating pronounced shear‐thinning behavior. Comparisons with existing work and previous work show excellent agreement in limiting cases, validating the current model and numerical approach.