Exploration of irreversibility and thermal motion of a nanoliquid with the Newton boundary condition by using the Darcy–Forchheimer rule

Abstract

This study has been conducted to focus on magnetohydrodynamic flow of a nanoliquid through a microchannel in the presence of a magnetic field. In this article, carbon nanotubes suspended in an aqueous medium were our considered fluid, and we focused on both singlewall and multiwall carbon nanotubes. The numerical calculations have been made via the fourth‐ and fifth‐order Runge–Kutta–Fehlberg method. The flow of the nanoliquid in a microchannel with porosity has been scrutinized with the existence of mutual effects, like, the nanoparticle volume fraction, suction or injection, thermal‐dependent heat source, convective boundary conditions, Darcy friction factor, and thermal motion of the nanoparticles. The influence of every major parameter on the profile of momentum, temperature, and entropy generation has been displayed graphically, and we discuss their physical aspects. The numerical outcomes demonstrated that the momentum profile augmented with the buoyancy force, angle of inclination, and Darcy number. Thermal energy was enriched with the heat source parameter, Darcy number, and Hartmann number. The irreversibility rate declined with the volume fraction of nanoparticle and radiation parameter, while it increases with the buoyancy force, Eckert parameter, and Darcy friction factor.

Irreversibility analysis of micropolar nanofluid flow using Darcy–Forchheimer rule in an inclined microchannel with multiple slip effects

“…Under the above presumption, the governing equations of the momentum, microrotation, energy, entropy generation, and Bejan number are as follows 4,37 : $$${\rho }_{\mathrm{nf}}{\nu }_{0}\frac{du{^{\prime} }}{dy{^{\prime} }}=-\frac{{dp}}{{dx}{^{\prime} }}+({\mu }_{\mathrm{nf}}+q)\frac{{d}^{2}u^{\prime} }{dy{{\prime} }^{2}}+q\frac{dN^{\prime} }{dy^{\prime} }-{\sigma }_{\mathrm{nf}}{B}_{0}^{2}u^{\prime} +({\rho \beta )}_{\mathrm{nf}}g* (T^{\prime} -{T}_{a}^{^{\prime} })\mathrm{sin\lambda }-\frac{{\mu }_{\mathrm{nf}}}{L}u^{\prime} -{\rho }_{\mathrm{nf}}\frac{F{u^{\prime} }^{2}}{\surd L},$$$ $$${\rho }_{\mathrm{nf}}{j\nu }_{0}\frac{dN{^{\prime} }}{dy{^{\prime} }}={\eta }_{\mathrm{nf}}\frac{{d}^{2}N^{\prime} }{d{y^{\prime} }^{2}}-q\left(2N^{\prime} +\frac{du^{\prime} }{dy^{\prime} }\right),$$$ …”

“…The fluid injection takes place at the bottom plate y a ′ = − and suction takes place at the upper plate y a ′ = . Under the above presumption, the governing equations of the momentum, microrotation, energy, entropy generation, and Bejan number are as follows 4,37 :…”

“…The dimensional local entropy generation is, 4,37 $$${E}_{g}=\frac{1}{{T}_{a}^{2}}{\left(\frac{dT^{\prime} }{dy^{\prime} }\right)}^{2}\left({k}_{\mathrm{nf}}+\frac{16\sigma * {T}_{a}^{{\prime} 3}}{3k^{\prime} }\right)+\frac{{\mu }_{\mathrm{nf}}+k}{{T}_{a}^{^{\prime} }}{\left(\frac{du^{\prime} }{dy^{\prime} }\right)}^{2}+\frac{2q}{{T}_{a}^{^{\prime} }}\left(N{{\prime} }^{2}+N^{\prime} \frac{du^{\prime} }{dy^{\prime} }\right)\,+\frac{{\sigma }_{\mathrm{nf}}}{{T}_{0}}{B}_{0}^{2}u{{\prime} }^{2}+{\eta }_{\mathrm{nf}}{\left(\frac{dN^{\prime} }{dy^{\prime} }\right)}^{2}+\frac{{\mu }_{\mathrm{nf}}}{L}u{{\prime} }^{2}+{\rho }_{\mathrm{nf}}\frac{Fu{{\prime} }^{3}}{\sqrt{L}}.$$$…”

“…The influence of magnetic field in incompressible Williamson fluid flowing over a radiative stretched surface and significance and insignificant relation of parameters with Nusselt number was studied by Shafiq and Sindhu 35 . Analysis of irreversibility of a nanomaterial in a space between parallel pipes in the existence of magnetic field was done by Barnoon et al 36 Gireesha et al 37 deliberated the impression of magnetic field on a magnetohydrodynamic flowing of a nanomaterial with Newton boundary constraints and Darcy–Forchheimer rule were employed. The consequence of ion‐slip effects irreversibility in an MHD micropolar liquid flowing with rotating effect and the outcome shows that entropy production decreases as in the enhancement of magnetic parameter were explored by Opanuga et al 38 The combined effect of magnetic field and ohmic dissipation on heat and mass transfer flow of nanofluid over a cone discussed by Upreti et al 39 Singh et al 40 numerically investigated the combined effect of magnetic field and slip on micropolar fluid flowing through a porous wedge with Hall and ion‐slip.…”

Flow and thermal analysis of Oldroyd 8 constant fluid in a porous channel

“…Liu et al 29 studied the irreversibility rate of electro‐MHD flow over a rectangular curved channel. Gireesha et al 30 explored the molecular randomness in a channel system with a Forchheimer drag using carbon nanotube nanoparticles. Ignacio et al 31 analyzed the entropy generation in a permeable inclined channel with the effect of nonlinear thermal radiation.…”