Complete theory of the elastic wall jet: A new flow geometry with revisited two-phase nanofluids

In the present research, it is solved in an innovative manner the essentially Non-Similar nanofluids jet discharged over a generalized non-linearly stretching wall. The Non-Similar set-up is interpreted as a combination of wall jet flow at the leading edge and non-linearly stretching sheet flow far away from it. Nanofluids are simulated employing Buongiorno's two-phase model together with a modified boundary condition for nanoparticles transport equation. The compositely-transformed partial differential equations (PDE) of Non-Similar forms were solved numerically after employing a new mapping function to abridge the horizontal coordinate of an infinite length into a finite one. The numerical algorithm contains quasi-linearization technique together with an implicit algorithm of tridiagonal form. It should be pointed out that such a new Non-Similar setup is brought into account for the first time in the literature. In this respect, we summarize the outstanding novel findings of the present work as: I. Accounting a modified boundary condition for nanoparticles concentration at the wall, the socalled and widely-used Brownian motion parameter, namely Nb, will have absolutely NO impact on Nusselt number or more precisely, on Energy Equation. In this respect, it is presented a new way of defining dimensionless variables. II. As the stretching ratio increases, it is observed a discrepancy in boundary layer thickness; it expands close to the jet area, shrinks in the transition region and adapts the far-field condition, either by expanding or shrinking, depending on the stretching ratio. III. As the stretching ratio increases, Nusselt number decreases slightly shortly after the jet origin and then increases dramatically to match the stretching region. IV. As the stretching ratio increases, nanoparticles at the wall become more concentrated at the downstream and hence, close to the jet region as well as the transition region, the concentration is sparse. V. As thermophoresis parameter, namely N-t, increases, convective heat transfer coefficient drops non-uniformly, from the leading edge to downstream, as well as nanoparticles concentration at the wall. VI. As Schmidt number increases, convective heat transfer drops; however, nanoparticles concentration at the wall increases over the entire spatial domain. ARTICLE INFO Article history: Received 6 May 2020 Received in revised form 16 October 2020 Accepted 19 November 2020 Available online 21 November 2020 Keywords: The non-linearly stretching wall jet Two-phase nanofluids Heat transfer and nanoparticles concentration analysis Numerical solution Non-similar flow (C) 2020 Elsevier Masson SAS. All rights reserved.

Automated summary

This study innovatively tackles the non-similar nanofluids jet discharged over a generalized non-linearly stretching wall, introducing a new non-similar setup for the first time and revealing novel findings such as the discrepancy in boundary layer thickness with increasing stretching ratio, and the impact of thermophoresis parameter and Schmidt number on heat transfer and nanoparticles concentration.