is relatively large compared to that between the rod and the ambient air, that is, h f >> h or h f = ∞. Determine the steady-state
∼
temperature distributions in the rod with the associated BCs.
a. Use the analytical approach.
b. Sketch the isotherms and isoflux in the rod, if T f < T ∞ and
h = a constant value.
3.3. A long fin of rectangular cross section (2LXL) with a thermal conductivity k is subjected to the BCs is shown on the sketch (the
left side is kept at T o , the right side is perfectly insulated, the
upper side is exposed to a constant flux, and the lower side is
""
exposed to a convection air flow). q = constant; steam T o , h = ∞;
air h = constant, T ∞ .
a. Determine the temperature distribution in the fin.
b. Approximately plot the temperature and heat flow profiles in
the fin, if T o > T ∞ .
3.4. Refer to Figure 3.1, and determine the temperature distributions
for 2-D heat conduction with the following BCs:
(1) x = 0, T = T o
x = a, T = T o
y = 0, T = T o
y = b, T = T s
(2) x = 0, T = T o
x = a, T = T o
y = 0, T = T s
y = b, T = T o
(3) x = 0, T = T o
x = a, T = T s
y = 0, T = T o
y = b, T = T o
(4) x = 0, T = T s
x = a, T = T o
y = 0, T = T o
y = b, T = T o
3.5. Refer to Figure 3.2, and determine the temperature distributions
for 2-D heat conduction with the following BCs:
(1) x = 0, T = T 1
(2) x = 0, T = T 1
x = a, T = T 1
y = 0, T = T 1
y = b, q ""
s = −k(∂T/∂y)
x = a, T = T 1
y = 0, q ""
s = −k(∂T/∂y)
y = b, T = T 1
(3) x = 0, T = T 1
x = a, q ""
s = −k(∂T/∂x)
(4) x = 0, q ""
s = −k(∂T/∂x)
x = a, T = T 1
y = 0, T = T 1
y = 0, T = T 1
y = b, T = T 1
y = b, T = T 1
3.6. Refer to Figure 3.3, and determine the temperature distributions
for 2-D heat conduction with the following BCs:
(1) x = 0, T = T 1
(2) x = 0, T = T 1
x = a, T = T 1
x = a, T = T 1
y = 0, T = T 1
y = 0, −k(∂T/∂y)
= h(T − T ∞ )
y = b, −k(∂T/∂y) = h(T − T ∞ )
y = b, T = T 1
65
2-D Steady-State Heat Conduction