Three-dimensional boundary layer flow and heat transfer of an unsteady viscous non-axisymmetric stagnation point with stability analysis and asymptotic solutions

Abstract

This study aims to investigate the behaviour of unsteady three-dimensional (3D) boundary layer flow and heat transfer generated by a non-axisymmetric stagnation point over a shrinking surface. The influence of thermal radiation is also included to represent realistic thermal environments. In particular, the work here focuses on how the shear-to-strain rate parameter and shrinking effects influence the flow structure, heat transfer rate, and stability of the solution. The governing partial differential equations describing the mass, momentum, and energy transport are reduced into a system of ordinary differential equations using an appropriate similarity transformation for the non-axisymmetric stagnation point flow. The resulting boundary value problem is solved numerically using the bvp4c solver. In addition, stability analysis is carried out to distinguish physically meaningful solutions between dual solution branches. An asymptotic analysis is also developed for large values of the shear-to-strain rate parameter to provide analytical inputs into the limiting behaviour of the system. The results show that the shear-to-strain rate parameter has a significant impact on the flow and thermal fields. An increase in this parameter leads to a reduction in both the reduced skin friction coefficients and the heat transfer rate at the surface. The presence of a shrinking surface generates dual solutions due to bifurcation behaviour, resulting in upper and lower solution branches. Stability analysis confirms that upper solution corresponds to a physically stable flow configuration. Furthermore, the asymptotic results indicate that both skin friction and heat transfer increase in proportion to the square root of the shear-to-strain rate parameter for large parameter values, which corresponds to thinner momentum and thermal boundary layers. The findings provide information into controlling flow and heat transfer in systems involving stagnation point flow over shrinking or stretching surfaces. Understanding the stability characteristics helps in identifying physically realizable operating conditions, which is important in industrial processes such as aerodynamic surface design, cooling technologies, and material processing where non-uniform strain fields may occur. This work extends the existing stagnation point flow studies by incorporating a non-axisymmetric 3D configuration with unsteady effects, thermal radiation, and shrinking surface conditions. The main originality of this work lies in the combined use of numerical simulation, stability analysis, and asymptotic analysis within a single non-axisymmetric stagnation point flow framework, which has not been simultaneously addressed in previous studies. The integration of these three approaches provides more understanding of the flow behaviour across different parameter regimes.