Monday, October 17, 2011

Exhibit Hall B (Minneapolis Convention Center)

Natural convection in a square cavity surrounded by vertical conducting

walls of definite wall thickness ($t_i$) has been studied numerically

using heatline approach. The phenomenon of conjugate natural convection

is used in many physical situations where heat is transported through

walls, such as building insulations, flat-plate solar collectors, heat

exchangers, etc. The cavity is heated from right wall, cooled from left

wall and the horizontal walls are maintained adiabatic. Three different

cases are considered based on the location of wall thickness: Finite wall

thickness on (a) cold side of the cavity ($t_{1}$) [case 1] (b) hot side

of the cavity ($t_{2}$) [case 2] and (c) both hot and cold sides of the

cavity ($t_{1}=t_{2}$) [case 3]. Finite element simulations are carried

out over a range of Rayleigh numbers ($Ra=10^{3}-10^{5}$) for various wall

thicknesses ($t=0.2$ and $t=0.8$ where $t = t_1 + t_2$) and conductivity

ratios ($K=0.1$ and $10$). Numerical results are presented in terms of

streamlines ($\psi$), isotherms ($\theta$) and heatlines ($\Pi$). At lower

$Ra$ ($Ra=10^{3}$), the strength of fluid and heat flow is weak and heat

transport is mainly due to conduction in both solid and fluid phases for

low $K$ ($K=0.1$) and $t$ ($t=0.2$) in all three cases. On the other hand,

the strength of fluid and heat flow increase with $K$ ($K=10$) for all

three cases even at $Ra=10^{3}$ and those are independent of $t$ at high

$K$ ($K=10$). At higher $Ra$ ($Ra=10^{5}$), the strength of fluid and

heat flow increases due to convection. Case 1 shows maximum magnitude of

heatfunction at $K=0.1$, although streamfunction magnitudes are almost

same for all three cases at $Ra=10^{5}$ irrespective of $t$. Increase in

$K$ ($K=10$) shows almost identical streamfunction and heatfunction

magnitude at $t=0.2$ and $Ra=10^{5}$. Increase in wall thickness shows

almost pure conduction dominant heat transport in the fluid phase

irrespective of $Ra$ for all three cases at low $K$. Various qualitative

and quantitative features on variations of local and average Nusselt

numbers for all three cases are adequately explained based on heatlines.

Results show that average Nusselt number is maximum for low $t_i$ and high

$K$ and that is independent of location of wall thickness at $Ra=10^{5}$.

Also, low $Ra$ and high conducting walls show maximum average Nusselt

number than high $Ra$ and low conducting walls. Overall, it is shown that

heatlines give suitable guidelines on location of wall thickness in

conjugate natural convection based on conductivity ratio ($K$).

**Extended Abstract:**File Not Uploaded

See more of this Session: Poster Session: Fluid Mechanics

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

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