Question

Consider an aluminum pin fin (k = 240 W/m·K) with a 2 mm by 2 mm square cross-section and a length of 4 cm that is attached to a surface at 100o C. The fin is exposed to air at 25o C with a convection heat transfer coefficient of 20 W/m2 · o C. Determine the rate of heat transfer and the tip temperature of the fin for the following cases:

(a) Convection from the fin tip.

(b) Adiabatic tip with uncorrected length.

(c) Adiabatic tip with corrected length (you should end up with the same answers as part a).

(d) Infinitely long fin.

Answer #1

The extent to which the tip condition affects the thermal
performance of a fin depends on the fin geometry and thermal
conductivity, as well as the convection coefficient. Consider an
alloyed aluminum (k = 180 W/m*K) rectangular fin of length L = 10
mm, thickness t = 1 mm, and width w >> t. The base
temperature of the fin is Tb = 100°C, and the fin is exposed to a
fluid of temperature T∞ = 25°C. Assuming a uniform...

A fin of rectangular profile has a thermal conductivity of 14
W/m C, thickness of 2.0 mm, and length of 23 mm. The base of the
fin is maintained at a temperature of 220 o C while the fin is
exposed to a convection environment at 23 o C with h=25 W/m2 o C.
Calculate heat lost per meter of fin depth for the three tip
conditions. (a) Convection, (b) Adiabatic, and (c) T (x=L) = 23 o
C.

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for which T∞ = 20°C and h = 50 W/m2 K.
Provide a sketch and state your assumptions (1 point)
Use Table 3.5 in the book (grading is based on the use of
that particular table) to...

A pin fin of uniform, cross-sectional area is fabricated of an
aluminum alloy with a thermal conductivity of 160 W/m K. The fin
diameter is 4mm, and the fin is exposed to convective conditions
characterized by a convection coefficient of 220 W/m^2K. It is
reported that the fin efficiency is 65 %. Determine the fin length
and the fin effectiveness. Assume the fin length is very long
compared to its diameter.

A stainless-steel fin (k = 16 W/m. °C) has a length of
15 cm and a square cross section 12.5 by 12.5 mm attached to a wall
maintained at 250 °C. The heat-transfer coefficient is 40 W/m. °C,
and the environment temperature is 90 °C. Calculate the percentage
increase in heat transfer after attaching the fin.

An aluminum fin 1.6 mm thick surrounds a tube 2.5 cm
in diameter. The length
of the fin is 12.5 mm. The tube-wall temperature is 200◦C, and the
environment
temperature is 20◦C. The heat-transfer coefficient is 60 W/m2 · ◦C.
Consider the heat dissipated in a pipe 1.20 m long if the fins are
4.2 mm apart from center to center
Explain your procedure with formulas

It's a heat transfer question.
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300K. Plot the temperature distribution along the center
axis line (T vs x). Include a contour plot across the
cross section of the fin. Assume zero contact resistance between
the sections.
K=19.8W/m-k Cp=557J/Kg-K Rho= 7900Kg/m^3...

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71 mm thick horizontal plate made of an opaque material of
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