Thermogravitational convection of power‐law nanofluid in a cavity with a heat‐generated section on the bottom wall

Abstract

Optimization of cooling systems for electronic devices is one of the crucial challenges in the modern engineering world. Inclusion of nanosized particles to working heat transfer liquids can enhance the heat removal from the heated elements in electronics. Taking into account these data, the present research is devoted to numerical analysis of natural convection in a cavity filled with a non‐Newtonian nanosuspension under an influence of a heat‐generating wall section. The paper contains the simulation outcomes for two different cases, namely, a heat‐generating wall section with constant heat flux and a heat‐generating wall section with constant temperature. The considered phenomenon has been described using the single‐phase nanofluid model where the base liquid is a pseudoplastic fluid. The rheological parameters of the host liquid including the coefficient of flow density and an indicator of fluid behavior are the empirical data of MWCNT nanofluids. The non‐Newtonian nature of the nanoliquid has been described by the Ostwald‐de‐Waele power law. Detailed analysis has been carried out for different governing parameters including the Rayleigh number, the volume fraction of nanoparticles, and the size of the heater using the non‐primitive dimensionless variables and the finite difference method. Obtained results illustrate different temperature patterns for various boundary conditions. Moreover, in the case of heat‐generating element, the average Nusselt number is greater than for the isothermal heater. It should be noted that the considered nanofluid model reflects the energy transference degradation with a growth of the nanoparticles concentration.

Thermogravitational convection of a pseudoplastic nanofluid with varying parameters in an enclosure having a thermally generating wall section

“…The flow structure and energy transport of the liquid in the chamber are defined employing a single-phase approach having effective properties and primitive variables [24][25][26]:…”

“…As a result of the use of new characteristics, the differential relations can take the view [24][25][26]:…”

“…The set of unsteady Equations ( 7)-( 9) with additional conditions (11) was solved by the finite difference method [1,[24][25][26]. The unsteady terms are discretized employing the first-order scheme, and the coordinate derivatives are approximated using the second-order schemes.…”

“…The flow structure and energy transport of the liquid in the chamber are defined employing a single‐phase approach having effective properties and primitive variables [24–26]: $$$$\begin{equation}\frac{{\partial u}}{{\partial x}} + \frac{{\partial v}}{{\partial y}} = 0\end{equation}$$$$ $$$$\begin{equation}{\rho _{nf}}\left( {\frac{{\partial u}}{{\partial t}} + u\frac{{\partial u}}{{\partial x}} + v\frac{{\partial u}}{{\partial y}}} \right) = - \frac{{\partial p}}{{\partial x}} + \frac{{\partial {\tau _{xx}}}}{{\partial x}} + \frac{{\partial {\tau _{xy}}}}{{\partial x}}\end{equation}$$$$ $$$$\begin{equation}{\rho _{nf}}\left( {\frac{{\partial v}}{{\partial t}} + u\frac{{\partial v}}{{\partial x}} + v\frac{{\partial v}}{{\partial y}}} \right) = - \frac{{\partial p}}{{\partial y}} + \frac{{\partial {\tau _{xy}}}}{{\partial x}} + \frac{{\partial {\tau _{yy}}}}{{\partial y}} + g{\left( {\rho \beta } \right)_{nf}}\left( {T - {T_0}} \right)\end{equation}$$$$ …”

“…As a result of the use of new characteristics, the differential relations can take the view [24–26]: $$$$\begin{equation}\frac{{{\partial ^2}\Psi }}{{\partial {X^2}}} + \frac{{{\partial ^2}\Psi }}{{\partial {Y^2}}} = - \Omega \end{equation}$$$$ $$$$\begin{equation}\frac{{\partial \Omega }}{{\partial \tau }} + \frac{{\partial \Psi }}{{\partial Y}}\frac{{\partial \Omega }}{{\partial X}} - \frac{{\partial \Psi }}{{\partial X}}\frac{{\partial \Omega }}{{\partial Y}} = {H_1}\left( \phi \right){\left( {\frac{{Ra}}{{\Pr }}} \right)^{\frac{{n - 2}}{2}}}\left[ {{\nabla ^2}\left( {\bar M\Omega } \right) + {S_\Omega }} \right] + {H_2}\left( \phi \right)\frac{{\partial \Theta }}{{\partial X}}\end{equation}$$$$ …”