Numerical analysis of nanofluid transport over a stretching surface with variable thermal conductivity, brownian motion and thermophoretic effects

Abstract

This paper presents a numerical investigation of nanofluid boundary layer flow over a linearly stretching sheet in the presence of variable thermal conductivity, thermophoretic diffusion and Brownian motion. Unlike earlier treatments, which examine these mechanisms individually or in pairs and usually alongside magnetic, radiative or chemically reactive effects, the three are treated here simultaneously and in isolation, so that their interaction can be identified without confounding. The governing partial differential equations for continuity, momentum, energy and nanoparticle concentration are reduced to a system of coupled nonlinear ordinary differential equations by similarity transformation, and the resulting boundary value problem is solved using a fourth order collocation scheme with damped Newton iteration and adaptive mesh refinement. The solver was validated against the exact Crane stretching sheet solution, for which f″(0) = −1, and against published benchmark values for the wall temperature gradient, with maximum absolute deviations of 1.13 × 10−6 and 1.515 × 10−4 respectively. Because the momentum equation decouples from the thermal and concentration fields in this formulation, the skin friction coefficient is invariant across every parameter examined, and the entire parametric response resides in the thermal and solutal fields. Increasing the thermal conductivity parameter thickens the thermal boundary layer and reduces the wall temperature gradient, while increasing the Prandtl number has the opposite effect. Thermophoresis and Brownian motion act on the concentration field in opposing directions: raising the thermophoresis parameter drives nanoparticles away from the heated wall and can reverse the sign of the wall concentration gradient, whereas raising the Brownian motion parameter restores a conventional concentration profile. At low values of the thermal conductivity and thermophoresis parameters the concentration profile develops an overshoot above its wall value before decaying, which is a direct consequence of the thermophoretic coupling term in the concentration equation. The findings clarify how variable conductivity modifies the classical Buongiorno response and provide reference solutions for the design of nanofluid based thermal systems.