Natural convection due to lateral uniform heat flux in a slender porous cavity saturated with nanofluid: Departure from LTE state

Abstract

The present article deals with the influence of the local thermal nonequilibrium (LTNE) state on natural convection in an enclosure filled with nanofluid-saturated porous medium. The flow is induced due to the maintenance of constant heat flux on the vertical walls and insulation of horizontal walls. The Darcy model has been adopted to describe the flow governing equations. These equations are solved numerically by using the alternate direction implicit method and analytically by applying parallel flow assumptions valid for large aspect ratios. Boundary layer analysis is performed to report the boundary layer thickness $(\delta x\sim 2^{1/2}{(k_{\mathit{\text{nf}}}/k_f)}^{1/10}{(R{a}_T)}^{-1/5})$ as well as the heat transfer rate of nanofluid ($N{u}_{\mathit{\text{nf}}}\sim {(k_{\mathit{\text{nf}}}/k_f)}^{-1/5}R{a}_T^{2/5}).$ The combined effect of LTNE state parameters (interface heat transfer coefficient (H), porosity scaled thermal conductivity ratio (γ)) and volume fraction of nanoparticle ($\varphi$) is addressed on the flow dynamics and heat transfer mechanism. Rigorous analysis, indicates that the average heat transfer rate of nanofluid and solid porous matrix are increasing function of H and γ, however, the role of γ is accelerated for a relatively high value of H. For increasing the value of γ from 1 to 10, the enhancement in the heat transfer rate of nanofluid is reported to be up to 27% at 10% volume fraction of nanoparticles. The average Nusselt number of nanofluid, as well as solid phase, are reduced when the value of $\varphi$ is increased under the LTNE circumstances. Furthermore, the flow structure is controlled by unicellular structure with rotating anticlockwise direction in the entire study. For the very small value of H the temperature distribution in the solid porous matrix is mainly by conduction mode and distribution is linear, however, for a relatively high value of H the distribution in the same is controlled by both conduction as well as convection, and it will be more pronounced for the higher value of γ.

Keywords:

• Darcy model
• finite difference method
• LTNE state
• nanoparticle
• natural convection
• porous medium

Authors’ contribution

Harish Chandra: Software, Investigation, Visualization, Validation, Data curation, Writing - original draft; Prof. P. Bera: Supervision, Writing - review & editing, Visualization, Methodology, Conceptualization.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

We are certified that, this manuscript has not been submitted in any other archive journal as well as conference.

Additional information

Funding

One of the authors, Harish Chandra, is grateful to SERB India for providing financial support (project grant no. EEQ/2020/000101 and MTR/2020/000187) during the preparation of this article.