Purpose Most existing studies on oblique stagnation-point flow over a vertical plate consider only steady-state conditions, whereas unsteady flow is more relevant to practical applications such as spraying and cooling, creating a research gap. This study aims to address this gap by analyzing the unsteady oblique stagnation-point flow of Maxwell fluid over a vertical plate. Design/methodology/approach A detailed analysis is conducted on the unsteady oblique stagnation-point flow of a Maxwell fluid over a vertical plate, incorporating time-dependent oscillatory and stretching motions. A mathematical model is developed by combining the constitutive framework of Maxwell fluids with the Cattaneo–Christov heat flux model, which explicitly includes thermal relaxation time. The formulation systematically accounts for buoyancy forces. The model is solved using physics-informed neural networks (PINN) and the homotopy analysis method (HAM), yielding two-dimensional and three-dimensional velocity and temperature distributions. Findings A comparative analysis indicates that HAM requires approximately twice as much computation time as PINN. Through iterative refinement, PINN effectively reduces residuals in the governing equations and boundary conditions, with predictions agreeing well with analytical solutions. Fluid velocity increases with the velocity ratio, whereas a higher Grashof number strengthens buoyancy and reduces bulk velocity. A larger Deborah number extends the relaxation time, and the fluid’s elastic behavior impedes flow and lowers velocity. Originality/value This study investigates the unsteady oblique stagnation-point flow of Maxwell fluid over a vertical plate with buoyancy effects, a topic insufficiently explored in existing literature. The results are validated and agree well with published data.
Bai et al. (Tue,) studied this question.