## Entropy Generation Due to Natural Convection within Porous Rhombic Enclosures with Various Inclination Angles

Monday, October 17, 2011
Exhibit Hall B (Minneapolis Convention Center)
Tanmay Basak, Chemical Engineering, Indian Institute of Technology Madras, Chennai, India and R. Anandalakshmi, Chemical Engineering, IIT Madras, Chennai, India

Porous media forms an extensive area for heat transfer due to its high
volumetric heat transfer coefficient.  This technology is used in solar
collectors to increase its efficiency in utilizing solar energy for drying
grain, home heating, etc., by natural convection. Based on the second law
of thermodynamics, energy efficiency in thermal processing can be
increased by reducing exergy losses due to irreversibilities, measured as
`entropy generation'. In this study, analysis of entropy generation during
natural convection in porous rhombic enclosures with various inclination
angles $\varphi$ have been carried for efficient thermal processing in
solar heating applications. Enclosure is bounded by adiabatic top wall,
cold side walls, isothermally (case 1) and non-isothermally (case 2)
heated bottom wall. Simulations are performed for the range of Darcy
number, $Da = 10^{-5}-10^{-3}$ and Rayleigh number, $Ra = 10^{3}-10^{6}$
for various $\varphi$s ($\varphi=30^\circ$, $45^\circ$ and $75^\circ$).
Entropy generation contours due to heat transfer ($S_{\theta}$) and fluid
friction irreversibility ($S_{\psi}$) are analyzed for both cases based on
their local distribution.  At low $Da$ ($Da=10^{-5}$), the entropy
generation in the cavity is dominated by $S_{\theta}$ for all $\varphi$s.
On increase of $Da$ to $10^{-3}$, the fluid flow intensifies and the fluid
flow irreversibility, $S_{\psi}$ also increases for all $\varphi$s. The
maximum values of $S_{\theta}$ are found to occur near the hot-cold
junctions in case 1 whereas that occurs in various locations on the left
wall due to high flow for case 2.  Significant $S_{\psi}$ is also observed
in the interior regions due to the friction between counter rotating
circulation cells for $\varphi=45^\circ$ and $75^\circ$ in case 1 and for
$\varphi=75^\circ$ in case 2. The total entropy generation rate
$S_{total}$ is found to increase with $Da$ for all $\varphi$s and the
average Bejan number $Be_{av}$ is found to be less than $0.5$, indicating
the dominance of $S_{\psi}$ at higher $Da$ for all $\varphi$s in both
cases.  The total entropy generation ($S_{total}$)  is found to be
significantly low for $\varphi=30^\circ$ and high for $\varphi=75^\circ$
at $Da=10^{-3}$ in both cases.  It is found that, high heat transfer rate
($\overline{Nu_b}$)  with minimum entropy generation ($S_{total}$)
occurs for $\varphi=30^\circ$ cavities at $Da=10^{-3}$ in case 1. The
non-isothermal heating strategy is energy efficient due to its less total
entropy generation ($S_{total}$)  besides with low heat transfer rate
(Nusselt number, $\overline{Nu_b}$) due to its less heating effect than
case 1 for all $\varphi$s. Overall, rhombic cavities with
$\varphi=30^\circ$ may be the optimal geometrical design in solar heating
applications irrespective of heating strategy.