A 1-cm-diameter, 30-cm-long fin made of aluminum (k=237 W / m ·K) is attached to a surface at 8

step 1 Okay, so the rate of heat transfer by fan as given by the equation Q equal to k times ACS times

A 1-cm-diameter, 30-cm-long fin made of aluminum (k=237 W /...

A 1-cm-diameter, 30-cm-long fin made of aluminum $(k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ is attached to a surface at $80^{\circ} \mathrm{C}$. The surface is exposed to ambient air at $22^{\circ} \mathrm{C}$ with a heat transfer coefficient of $18 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. If the fin can be assumed to be very long, the rate of heat transfer from the fin is (a) $2.0 \mathrm{~W}$ (b) $3.2 \mathrm{~W}$ (c) $4.4 \mathrm{~W}$ (d) $5.5 \mathrm{~W}$ (e) $6.0 \mathrm{~W}$

A 1-cm-diameter, 30-cm-long fin made of aluminum $(k=237 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})$ is attached to a surface at $80^{\circ} \mathrm{C}$. The surface is exposed to ambient air at $22^{\circ} \mathrm{C}$ with a heat transfer coefficient of $18 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. If the fin can be assumed to be very long, the rate of heat transfer from the fin is
(a) $2.0 \mathrm{~W}$
(b) $3.2 \mathrm{~W}$
(c) $4.4 \mathrm{~W}$
(d) $5.5 \mathrm{~W}$
(e) $6.0 \mathrm{~W}$

Key Concepts

Fin Geometry

The geometry of a fin, including parameters such as length, cross-sectional area, and perimeter, directly influences its heat transfer performance. The cross-sectional area affects the ability to conduct heat along the fin and the perimeter affects the convective losses, both of which are essential in determining the effectiveness of the fin in dissipating heat.

Thermal Conductivity

Thermal conductivity is an intrinsic material property that measures the ability of a material to conduct heat. In fin analysis, a higher thermal conductivity allows heat to be more effectively distributed along the fin, which in turn affects the temperature distribution and the overall rate of heat transfer.

Convection Heat Transfer

Convection is the mechanism of heat transfer where heat is carried away by fluid motion, in this case, ambient air. The heat transfer coefficient quantifies the convective heat transfer between the fin surface and the surrounding fluid, and is critical in determining overall heat removal from the fin.

Extended Surface (Fin) Analysis

This concept involves using fins to enhance heat transfer from a surface by increasing the area available for convection. In this analysis, fins are modeled to extend the surface area and allow for more efficient heat removal or delivery. The analysis typically involves solving the steady?state conduction equation within the fin while accounting for heat loss by convection along the fin’s surface.

Transcript

Please give Ace some feedback