Dual Solutions and Stability Analysis of Prandtl–Eyring Fluid in a Uniform Shear Flow Under Thermal Radiation and Transpiration

Abstract This study examines the complex phenomena of non-Newtonian Prandtl-Eyring fluid in a uniform shear flow along a deformable surface under the influence of surface transpiration and thermal radiation. Through Lie group analysis, the nonlinear governing partial differential equations are reduced to a system of similarity equations. Double solutions exist within specific rates of deformation of the surface. These two solution branches bifurcate from a particular value of the point of the surface deformation rate, known as the critical point. The stability analysis based on the sign of the smallest eigenvalue is employed to examine the physically stable solution, establishing that the upper solution branch is the stable one. The range of double solutions decreases, and the heat transfer rate increases with an increase in the suction parameter. The fluid velocity increases with the rise in material parameters, whereas temperature exhibits the opposite behaviour. These results are beneficial for applications that involve friction and heat regulation, such as the development of advanced coatings or industrial extrusion processes.