A unified slip-transpiration framework for NePCM flow over deforming boundaries

Purpose – The purpose of this study is to develop an exact analytical framework for boundary layer flow of Nano-Encapsulated Phase Change Material (NePCM)-enhanced fluids over stretching and shrinking surfaces, accounting for key physical effects such as velocity slip, wall transpiration and thermal radiation. Design/methodology/approach – The governing Navier–Stokes equations are formulated for NePCM suspensions and solved analytically to obtain closed-form exponential and algebraic solutions for the velocity, temperature and concentration fields. Numerical computations are further used to validate the analytical solutions and to ensure the reliability of the computational framework for benchmarking purposes. Findings – The analysis reveals the existence of dual and triple solution branches for the skin friction coefficient, thermal gradient and species gradient, highlighting the strong nonlinearity of the system. A critical turning point in the transpiration parameter $(s_c)$ is identified, beyond which no physically admissible solutions exist for the shrinking sheet. The results demonstrate that NePCMs significantly suppress temperature gradients, while thermal radiation and the Stefan number play a decisive role in regulating the thermal boundary layer thickness. Originality/value – To the best of the authors’ knowledge, this work presents the first exact analytical treatment of NePCM-enhanced boundary layer flow over stretching and shrinking surfaces with slip, transpiration and radiation effects. It provides fundamental physical insight into complex flow transitions and establishes a rigorous theoretical foundation for the design of advanced thermal management systems in microelectronics and aerospace applications.

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