Exploring the complex interplay of factors in convective heat transfer: a comprehensive parametric analysis in three-dimensional permeable cavities

ABSTRACT

This examination aimed to mathematically investigate the blended convective intensity movement inside a three-layered nook that consolidates a spinning roundabout chamber and an undulating permeable pit. Using the limited component technique (FEM), mathematical reproductions were executed across different boundaries, enveloping the Darcy number going from${10}^{-5}\mathit{to}{10}^{-2}$ Hartmann number (going from 0 to 100, the angular velocity between − 4000 and 4000, and the number of undulations in the permeable pit. The results, addressed through stream capability, isotherms, and isentropic forms, clarify the effect of these boundaries on movement, heat transport, and entropy age. The ends suggest that for an ideal upgrade of intensity move rates in a three-layered undulating permeable cavity with a pivoting chamber and exposed to an attractive field, explicit circumstances are suggested, a Darcy number more prominent than or equivalent to ${10}^{-2}$, a Hartmann number of 0, undulation of the permeable pit (N = 3), and angular velocity surpassing 2000 in the stream heading. The study investigates convective heat transfer in a rotating cylindrical chamber, analyzing parameters like Darcy number, Hartmann number, and rotation speed for optimizing heat transfer systems in complex porous cavities. The optimal heat transfer occurs when the aspect ratio is fixed at 0.3 and porous media occupies 90% of the channel. A 150% enhancement in the Nusselt number can be observed when the cylinder’s rotational speed increases. The study also found that increasing angular velocity and Darcy number positively affects the Nusselt number. The research aims to understand the interplay of factors affecting convective heat transfer and fluid dynamics and offer practical implications for optimizing heat transfer systems. The novelty of this study lies in its thorough examination of convective heat transfer in a rotating cylinder-shaped porous cavity, focusing on factors like Darcy number, Hartmann number, rotation speed, and pit geometry. It provides insights for optimizing heat transfer efficiency in complex cavities and explores the impact of external magnetic fields and fluid dynamics. The study investigates the influence of parameters like Hartmann number, angular speed, and Darcy number on thermal and flow characteristics in a porous cavity filled with Fe₃O₄/MWCNT-water nanofluid, highlighting their importance for optimizing heat transfer efficiency.

KEYWORDS:

• Undulation cavity
• FEM
• porous media
• MHD
• entropy
• natural convection
• heat transfer

Disclosure statement

No potential conflict of interest was reported by the author(s).

Nomenclature

Latin symbols	=
$\mathit{Da}$	=	Darcy number
$\mathit{Ha}$	=	Hartman number
$\mathit{K}$	=	Permeability ${\mathrm{m}}^2$
$\mathit{Nu}$	=	Nusselt number
$\mathit{Pr}$	=	Prandtl number
$\mathit{T}$	=	Temperature $\left(\mathit{K}\right)$
$\mathit{S}$	=	entropy
$\mathit{Pr}$	=	Prandlt number
$\mathit{Ra}$	=	Rayleigh number
N	=	Porous region undulation
$B_0$	=	Magnetic field intensity
$\mathit{Fc}$	=	Forcheimer coefficient
$\mathit{k}$	=	Thermal conductivity ($\mathit{W}.m^{-1}.K^{-1}$)
$\mathit{N}$	=	number of ripples
$\mathit{Gr}$	=	Grashof number
$\mathit{P}$	=	the dimensionless fluid pressure
$\mathit{u},\mathit{v},\mathit{w}$	=	Velocity components (m/s)
$\mathit{x},\mathit{y},\mathit{z}$	=	Coordinates
Fc	=	Forchheimer coefficient
Greek symbols	=
$\mathit{\alpha }$	=	effective thermal diffusivity of porous medium and fluid $m^2{s}^{-1}$
$\mathit{\beta }$	=	volumetric thermal expansion coefficient of the fluid $\mathit{K}{ }^{-1}$
$\mathit{\lambda }$	=	Thermal expansion coefficient $K^{-1}$
$\mathit{\epsilon }$	=	Porosity
$\mathit{\mu }$	=	Dynamic viscosity ($\mathit{W}.\mathit{\hspace{0.17em}}{m}^{-1}.K^{-1}$)
$\mathit{\sigma }$	=	Electrical conductivity $\mathrm{\Omega }.\mathrm{M}$
$\mathit{\theta }$	=	non-dimensional temperature
$\mathit{\rho }$	=	Kinematic diffusivity $\mathit{\hspace{0.17em}}{m}^2.\text{^}{s}^{-1}$
$\mathit{\varphi }$	=	Density $\mathit{kg}.m^{-3}$
Indices	=
$\mathit{avg}$	=	average
$\mathit{F}$	=	Fluid
$\mathit{loc}$	=	Local
$\mathit{c}$	=	Cold
$\mathit{h}$	=	Hot
$\mathit{nf}$	=	Nanofluid
$\mathit{p}$	=	Porous medium

Additional information

Funding

The financial support from DGRSDT projects [B00L02UN480120230001], ALGERIA.