In this paper, the effect of convective boundary conditions, heat generation, Brownian motion, and thermophoresis on heat transfer characteristics of a moving cylinder embedded into cooling medium consists of water with nanoparticles are studied. The governing boundary-layer equations transformed to ODE using similarity transformation method and then solved analytically using optimal homotopy asymptotic method for the general case. The velocity, temperature, and concentration profiles within the boundary-layer plotted and discussed in details for various values of the different parameters. Moreover, the effect of boundary-layer behavior on the surface shear stress, rate of heat and mass transfer investigated.

This research investigates the impact of second-order slip conditions, Stefan flow, and convective boundary constraints on the stagnation-point flow of couple stress nanofluids over a solid sphere. The nanofluid density is expressed as a nonlinear function of temperature, while the diffusion-thermo effect, chemical reaction, and thermal radiation are incorporated through linear models. The governing equations are transformed using appropriate non-similar transformations and solved numerically via the finite difference method (FDM). Key physical parameters, including the heat transfer rate, are analyzed in relation to the Dufour number, velocity, and slip parameters using an artificial neural network (ANN) framework. Furthermore, response surface methodology (RSM) is employed to optimize skin friction, heat transfer, and mass transfer by considering the influence of radiation, thermal slip, and chemical reaction rate. Results indicate that velocity slip enhances flow behavior while reducing temperature and concentration distributions. Additionally, an increase in the Dufour number leads to higher temperature profiles, ultimately lowering the overall heat transfer rate. The ANN-based predictive model exhibits high accuracy with minimal errors, offering a robust tool for analyzing and optimizing the thermal and transport characteristics of couple stress nanofluids.