Mathematical Modeling for Experimental Data to Investigate the Convective Heat Transfer in Non‐newtonian Nanofluid's Flow over a Thin Needle

The flow of homogeneous non-Newtonian nanofluid over a horizontal moving thin needle is studied through experimental data-based mathematical approach. Experimental data is collected for nanofluids which are prepared by spreading the SiO2, MgO, and TiO2 nanoparticles with correspondingly diameters (20-30 nm, 60-70 nm), (20, 40 nm), and (30, 50 nm) at volume fractions (5%-20%) in ethylene glycol (EG). The rheological power-law model of viscosity is employed on the current experimental data to govern the co-relation expression and is further used in heat and mass flow equations. The problem is reduced to ordinary differential equations by employing similarity conversion and then numerically solved. The influence of various volume fractions and diameter of nanoparticles on the distribution of velocity and temperature are discussed through the graphical results. Moreover, velocity and thermal boundary layer thicknesses, momentum and displacement thickness, skin friction coefficient, and Nusselt number are also studied in detail and displayed graphically. The results indicate that enhancing nanoparticle volume fraction causes the decline in velocity profile and rise in temperature profiles. On the contrary, the velocity is amplified and temperature is reduced with enhancing the diameter of the nanoparticle. Newtonian model for nanofluid is not valid in all cases. So, a non-Newtonian model is applied for nanofluid flow that follows the experimental behavior in the current study. This experimental based model has not investigated before.