Entropy Analysis and Melting Heat Transfer in the Carreau Thin Hybrid Nanofluid Film Flow

Abstract

Melting heat transfer has a vital role in forming energy storage devices such as flexible thin film supercapacitors. This idea should be welcomed in the thin film theoretical models to sustain technological advancement, which could later benefit humankind. Hence, the present work endeavors to incorporate the melting heat transfer effect on the Carreau thin hybrid nanofluid film flow over an unsteady accelerating sheet. The mathematical model that obeyed the boundary layer theory has been transformed into a solvable form via an apt similarity transformation. Furthermore, the collocation method, communicated through the MATLAB built-in bvp4c function, solved the model numerically. Non-uniqueness solutions have been identified, and solutions with negative film thickness are unreliable. The melting heat transfer effect lowers the heat transfer rate without affecting the liquid film thickness, while the Carreau hybrid nanofluid contributes more entropy than the Carreau nanofluid in the flow regime.

Thermocapillarity in Cross Hybrid Nanofilm Flow Past an Unsteady Stretching Sheet

“…The velocity profiles as We x varies are not included in the manuscript due to the insignificant variation among the profiles. However, a similar flow behavior has been reported by Naganthran et al [27] and Hayat et al [40]. Meanwhile, in terms of the heat energy progression of the present model, data in Table 4 show that the heat transfer rate or |θ (0)| increases for both cases of the hybrid nanofluid and mono nanofluid when We x increases.…”

“…Although some works under the scope of the thin hybrid nanofluid have been reported, it is still in the early stages and needs a more theoretical model, which has been examined under various possibilities and settings. For example, the work of Naganthran et al [27], which investigated the melting heat transfer effect in the thin film flow in the Carreau hybrid nanofluid over a stretching sheet presented transport phenomena behavior, which is associated with negative film thickness. Though it is an unreliable solution, it serves good reference for the experimentalist to be aware of those unfavorable trends in transport phenomena.…”

Irreversibility scrutinization on EMHD Darcy–Forchheimer slip flow of Carreau hybrid nanofluid through a stretchable surface in porous medium with temperature‐variant properties

“…Entropy generation 45–47 for Carreau hybrid NF over a stretching surface with heat transmission characterized by radiative heat flux, Darcy–Forchheimer porous medium, thermal conductivity fluctuation, viscous dissipation, and electric and magnetic fields is mathematically disclosed as $$${S}_{{\rm{G}}}=\frac{{k}_{{\rm{f}}}}{{T}_{\infty }^{2}}\left[\frac{{k}_{\mathrm{hnf}}(T)}{{k}_{{\rm{f}}}}+\frac{16{\sigma }^{* }{T}_{\infty }^{3}}{3{k}^{* }{k}_{{\rm{f}}}}\right]{\left(\frac{\partial T}{\partial y}\right)}^{2}+\frac{{\mu }_{\mathrm{hnf}}}{{T}_{\infty }}{\left[1+{{\rm{\Gamma }}}^{2}{\left(\frac{\partial u}{\partial y}\right)}^{2}\right]}^{\frac{n-1}{2}}{\left(\frac{\partial u}{\partial y}\right)}^{2}+\frac{{\mu }_{\mathrm{hnf}}}{{T}_{\infty }{k}_{{\rm{p}}}}{u}^{2}+\frac{{\sigma }_{\mathrm{hnf}}}{{T}_{\infty }}{(u{B}_{0}+{E}_{0})}^{2}.$$$ Making use of the similarity variables, the dimensionless form of the entropy generation becomes …”

“…Entropy generation [45][46][47] for Carreau hybrid NF over a stretching surface with heat transmission characterized by radiative heat flux, Darcy-Forchheimer porous medium, thermal conductivity fluctuation, viscous dissipation, and electric and magnetic fields is mathematically disclosed as…”

“…Their findings disclosed that hybrid NFs are the best thermal conductors and can be utilized for blood circulation in different human body parts. Naganthran et al 47 investigated entropy generation and heat transfer analysis in non‐Newtonian Carreau thin hybrid NF film flow past a stretching sheet. The rate of heat transference was found to dwindle when the Carreau fluid displays shear‐thickening characteristics.…”