Stability Analysis for Joule Heating on the Fluid Flows over an Exponentially Shrinking Sheet - Saran, Har Lal; Reddy, Ch. Ram (Discontinuity, Nonlinearity, and Complexity, 2026)
The goal of this research is to understand the influences of Joule heating and aligned magnetic field with fluid flows on an exponential shrinking sheet. Relevant similarity transformations are used to extract ordinary differential equations (ODE's) from the associated flow governing partial differential equations (PDE's). The set of resulting ODEs is solved by a shooting algorithm, which utilizes the Runge-Kutta and Newton-Raphson techniques. The impact of magnetic and Joule heating parameters on the fluid velocity and fluid temperature profiles, as well as the skin friction coefficient and heat transfer rate, are investigated. As a result, the multiple solutions are appearing for each combination and hence, the stability solutions are extracted using temporal stability analysis. In addition, the streamline patterns are provided graphically along with the eigenvalue behavior for each of these solutions. Moreover, the flow separation is identified in the shrinking region. This type of research is extremely beneficial in the fields of aerodynamics (i.e. production of engine components, aircraft turbines and high-performance automatic parts) and medicine.