HW3Heat is generated uniformly inside a plane wall at a rate of =2.4 x103 W/m3. The wall is 40 mm thick and its thermal conductivity k=0.8W/m.k . The left hand side of the wall is exposed to a convection environment with T=50 \deg C and h=80 W/m2.k. The temperature on the right-hand side of the wall is maintained at T2=20 \deg C.a. Use x=0 at the left wall x and find the temperature distribution T(x) in the wall. b. Use T(x) to find the maximum temperature in the wall
The upper surface of a Plywood roof is maintained at
T_(s)=5\deg C by blowing warm air over the lower surface of the roof. The emittance of the surface of the roof is
\epsi =0.08 and it is losing heat to night sky that acts like a black body at
T_(sky )=200K. The upper surface is also exposed to ambient air at
T_(out )=10\deg C with convection coefficient
h_(out )=8(W)/(m^(2)). The Plywood roof is 12 mm thick and
k=0.12(W)/(m).K for Plywood. The convection coefficient for warm air blowing over the lower surface of the roof is
h_(in )=25(W)/(m^(2)).K.
The temperature at the upper surface of the roof is known, Find the net rate of heat loss from the upper surface of the roof to the surroundings. (answer:
158.4(W)/(m^()) 2)
Find the temperature of the warm air blowing over the lower surface of the roof that is needed to transfer enough heat through the Plywood to make up for the net heat loss in the upper surface. (answer:
27.2\deg C )
Q#3:
40\deg C water with
hw=800(W)/(m^(2)).K is flowing in a polycarbonate (PC) tube. The inner and outer diameters of the tube are 25 mm and 35 mm respectably. A thin metallic heater element bonded to the outer surface of the tube is being used to heat the water. The tube and heater are covered with a
10-mm thick layer of expanded polystyrene (EPS). The outer surface of EPS layer is exposed to air at TA
=10\deg C and
hA=12(W)/(m^(2)).K. Assume
KPC=0.29(W)/(m).K and KEPS
=0.035(W)/(m).K. The rate of heat transfer to the water in the tube is 300
(W)/(m), but some of the thermal energy produced by the heater is lost to the air.
a. Find the temperature of the heater element needed to transfer
300(W)/(m) of heat to the water in the tube (answer:
100.17\deg C )
b. Find the total rate at which the heater element must generates thermal energy. (answer:
335.5(W)/(m) )
Q#5: HW3
Heat is generated uniformly inside a plane wall at a rate of
q^(?)=2.4\times 103(W)/(m)3. The wall is 40 mm thick and its thermal conductivity
k=0.8(W)/(m).k. The left hand side of the wall is exposed to a convection environment with
T\infty =50\deg C and
h=80(W)/(m)2.k. The temperature on the right-hand side of the wall is maintained at
T=20\deg C.
a. Use
x=0 at the left wall
x -> and find the temperature distribution
T(x) in the wall.
b. Use
T(x) to find the maximum temperature in the wall
Q#5: HW3
Heat is generated uniformly inside a plane wall at a rate of
q^(?)=2.4\times 103(W)/(m)3. The wall is 40 mm thick and its thermal conductivity
k=0.8(W)/(m).k. The left hand side of the wall is exposed to a convection environment with
T\infty =50\deg C and
h=80(W)/(m)2.k. The temperature on the right-hand side of the wall is maintained at
T=20\deg C.
a. Use
x=0 at the left wall
x -> and find the temperature distribution
T(x) in the wall.
b. Use
T(x) to find the maximum temperature in the wall
