Exploring the effects of nanoparticle radius and inter-particle spacing on mixed convective dusty nanofluid flow over an extending heated surface: A numerical analysis

This work has investigated a water-based dusty nanofluid flow past an extending surface that contains copper nanoparticles. The influences of the magnetic field, gravitational field, nanoparticle radius, interparticle spacing, thermal radiation, and heat source are also taken into account in this research. PDEs are used for presenting a mathematical model, which similarity variables are then used to convert into ODEs. Using the shooting approach, a numerical solution is determined. To assure the correctness of the numerical solution while keeping computational performance, we have employed both absolute tolerance (AbsTol = 10 −5 ) and relative tolerance (RelTol = 10 −5 ) for the derived results. Based on the acquired data, it is concluded that a larger magnetic factor increases drag force whereas a higher mixed convection factor decreases it. The heat transfer rate is increased by the larger thermal radiation factor and thermal Biot number. The axial velocity profiles are enhanced by the larger mixed convection component. Conversely, transverse velocity profiles are reduced close to the sheet’s surface by a larger mixed convection factor, while an opposite tendency is seen far from the sheet’s surface. The axial and transverse velocity distributions of both phases are decreased by the larger inter-particle spacing. The axial and transfer velocity profiles of both phases are boosted by the larger nanoparticle radius. The temperature profiles of both phases are heightened by the greater thermal Biot number and heat source factor. Overall, the analysis highlights that the embedded parameters significantly influence the velocity and thermal distributions of the nanofluid flow with a more pronounced impact on the nanofluid flow phase compared to the dusty nanofluid flow phase. These insights provide valuable guidance for the optimization of flow and thermal properties in engineering systems involving dusty nanofluids.