Rakesh Yadav
RK4-Assisted Computational Modeling of MHD CuO–Water Nanofluid Flow and Thermal Transport over a Porous Stretching SurfaceThe present work explores the coupled hydrodynamic, thermal, and nanoparticle transport mechanisms arising in magnetohydrodynamic (MHD) CuO–H₂O nanofluid flow over a porous stretching surface. The formulation is established within Buongiorno’s two-component nanofluid framework, with particular emphasis on the combined contributions of Brownian diffusion and thermophoretic particle migration. By employing suitable similarity transformations, the governing conservation equations for momentum, energy, and nanoparticle concentration are reduced from their original nonlinear form to a coupled system of ordinary differential equations. The resulting nonlinear boundary-value problem is addressed through an efficient shooting strategy in conjunction with the classical fourth-order Runge–Kutta (RK4) integration scheme. The unknown wall gradients corresponding to the velocity, temperature, and nanoparticle concentration fields are estimated through an iterative procedure until the prescribed far-field boundary conditions are satisfied.The computational investigation examines the sensitivity of the flow and transport characteristics to key dimensionless parameters, particularly the magnetic interaction parameter, Brownian motion parameter, thermophoresis parameter, and Lewis number. The associated wall transport rates, quantified through the skin-friction coefficient, Nusselt number, and Sherwood number, are evaluated numerically and their variations are illustrated using MATLAB-based graphical analysis. To establish the reliability of the proposed computational framework, the numerical predictions are cross-checked against benchmark results reported in the literature and independently verified using the MATLAB BVP4C solver. The results reveal a notable improvement in thermal transport when CuO nanoparticles are suspended in the conventional water-based fluid, highlighting their potential for enhanced heat-transfer applications. Moreover, intensification of the magnetic field produces a damping effect on the fluid motion, leading to a reduction in the velocity boundary-layer thickness, while simultaneously increasing the thermal and nanoparticle concentration boundary-layer thicknesses. These findings provide useful insight into the regulation of coupled momentum, heat, and mass transport in MHD nanofluid systems involving porous stretching surfaces.