Analysis of the unsteady upper-convected Maxwell fluid having a Cattaneo–Christov heat flux model via two-parameters Lie transformations

Abstract

The study investigates the dynamics of an upper-convected Maxwell fluid flow within the framework of magnetohydrodynamics (MHD) over an stretching surface. The analysis incorporates the Cattaneo–Christov heat flux model to explore the system’s thermal behavior. The inclusion of thermal radiation, heat generation-absorption, and suction-injection effects significantly augments the thermal characteristics. Despite its linear nature, the system demonstrates a pronounced level of nonlinearity in its temporal behavior. Through the application of a two-parameter Lie method, nonlinear partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). This method amalgamates three independent variables into a single independent similarity variable, $\xi$. Graphical representations are employed for momentum and thermal analyses, and the ODEs are numerically solved using the bvp4c function in MATLAB. The model’s validity is confirmed through tables and graphs with a consistent assessment. An increase in Hartmann number $M_{s}$ boosts the system’s internal energy but slows down fluid velocity. The momentum Deborah number $\beta _{1}$ escalates velocity amplitude but decreases fluid temperature over time, whereas the heat Deborah number $\beta _{2}$ results in a decrease in fluid temperature.