Influences of an effective Prandtl number model on nano boundary layer flow of γ Al2O3–H2O and γ Al2O3–C2H6O2 over a vertical stretching sheet

Abstract Nanoparticles provide potentials in augmenting the performance of convective heat transfer in the boundary layer flow region. Prandtl number plays a vital role in controlling the momentum and thermal boundary layers. In view of this, the influences of an effective Prandtl number model which is derived from experimental data (Pop et al., 2007) on the nano boundary layer, steady, two-dimensional and laminar flow of an incompressible γ Al2O3–H2O and γ Al2O3–C2H6O2 nanofluids over a vertical stretching sheet are investigated for the first time in the present article. The models which are used for viscosity and thermal conductivity also derived from experimental data (Maiga et al., 2004a; Maiga et al., 2005). The second law of thermodynamics also analysed for the present problem. The transformed governing nonlinear boundary layer equations are solved numerically using fourth order Runge–Kutta method with shooting technique and analytical solutions are presented for a special case. The numerical results obtained for the temperature profile, skin friction coefficient and reduced Nusselt number are presented through plots for two different cases such as with and without effective Prandtl number. It is found that the increasing values of nanoparticle volume fraction of γ Al2O3 nanoparticles decrease the temperature of the nanofluids in the presence of effective Prandtl number and increase in the absence of effective Prandtl number. The entropy generation number is higher for ethylene glycol based nanofluids compared to water based nanofluids.