Tuesday, October 18, 2011: 10:15 AM

102 C (Minneapolis Convention Center)

Heatline method is used to analyze natural convection via differentially

heated enclosure convection [Case 1: hot and cold side walls with

horizontal adiabatic walls] and Rayleigh-Benard convection [Case 2: hot

and cold horizontal walls with vertical adiabatic walls] for rhombic

enclosures with various inclination angles, $\varphi$. An accurate

prediction of the flow structure and heat distribution in such

configurations are of great important due to its significant engineering

applications such as ventilation of rooms, cooling of electronics devices

or air flow in buildings. Simulations are performed for the range of

Rayleigh number, $Ra = 10^{3}-10^{5}$ for various inclination angles

($\varphi=30^\circ$, $45^\circ$, $60^\circ$, $75^\circ$ and $90^\circ$)

using Galerkin finite element method. Interesting features of heat flow

patterns are visualized by heatlines for various $\varphi$s in both cases.

At $Ra = 10^3$, heatlines and isotherms are less distorted and flow

circulation is very weak at $\varphi=30^\circ$ in both cases. Increase in

$\varphi$ ($\varphi=90^\circ$) shows more distorted heatlines with closed

loop heatline cells due to increase in flow strength compared to

$\varphi=30^\circ$ at $Ra = 10^3$ in case 1 whereas heatlines and

isotherms are found to be parallel and orthogonal to adiabatic walls,

respectively indicating pure conduction dominant heat transfer with

stagnant fluid condition for $\varphi=90^\circ$ in case 2 at $Ra = 10^3$.

At $Ra = 10^5$, strength of fluid and heat flow increases for all

$\varphi$s due to enhanced convection effect and $\varphi=90^\circ$ shows

maximum magnitude of streamfunction ($\psi_{max}$) and heatfunction

($\Pi_{max}$) values in both cases. It is found that, both $\psi_{max}$

and $\Pi_{max}$ values are comparatively higher in case 2. Both cases are

compared based on local ($Nu$) and average Nusselt numbers

($\overline{Nu}$) and those are adequately explained based on heatlines.

It is found that $\overline{Nu}$ is independent of $\varphi$ at $Ra =

10^3$ in both cases. Also, $\overline{Nu}$ increases with $Ra$ and shows

its maximum at $Ra = 10^5$ for all $\varphi$s in both cases. It is also

shown that, $\varphi=30^\circ$ shows low heat transfer rate in case 1

compared to case 2 whereas $\varphi=90^\circ$ shows high heat transfer

rate in case 1 compared to case 2. Heat transfer rate is almost similar

for $\varphi=45^\circ$ in both cases. Overall, average heat transfer rate

is maximum for case 1 at $\varphi \ge 45^\circ$, eventhough $\psi_{max}$

and $\Pi_{max}$ values are high in case 2.

**Extended Abstract:**File Not Uploaded

See more of this Session: Fundamental Research In Transport Processes I

See more of this Group/Topical: Engineering Sciences and Fundamentals

See more of this Group/Topical: Engineering Sciences and Fundamentals