Motion in a straigth line
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Heat Transfer – Assignment 1 Essentials of Conduction, Convection, and Radiation Given: March 13th, 2014 Due: Beginning of class, March 20th, 2014 Instructions: • ξ is a parameter related to your student ID, with ξ 1 corresponding to the last digit, ξ 2 to the last two digits, ξ 3 to the last three digits, etc. For instance, if your ID is 199225962, then ξ 1 = 2, ξ 2 = 62, ξ 3 = 962, ξ 4 = 5962, etc. • For each problem, list all assumptions made. • Keep a copy of the assignment – the assignment will not be handed back to you. • You must be able to remember your solutions. Problems: 1. A flat wall is exposed to an environmental temperature of 38 ◦ C. The wall is covered with a layer of insulation 2.5 cm thick whose thermal conductivity is 1.4 W/m· ◦ C, and the temperature of the wall on the inside of the insulation is 315 ◦ C. The wall loses heat to the environment by convection. Compute the value of the convec- tion heat-transfer coefficient which must be maintained on the outer surface of the insulation to ensure that the outer-surface temperature does not exceed 41 ◦ C. Answer: h ≥ 5115 W/m 2 ◦ C 2. A black 20-by-20 cm plate has air forced over it at a velocity of 2 m/s and a temperature of 0 ◦ C. The plate is placed in a large room whose walls are at 30 ◦ C. The back side of the plate is perfectly insulated. Calculate the temperature of the plate resulting from the convection-radiation balance. Take the convective heat transfer h as 12 W/m 2 · ◦ C. Are you surprised at the result? Answer: 9.6 ◦ C 3. Two large black plates are separated by a vacuum. On the outside of one plate is a convection environment of T = 80 ◦ C and h = 100 W/m 2 · ◦ C, while the outside of the other plate is exposed to 20 ◦ C and h = 15 W/m 2 · ◦ C. Make an energy balance on the system and determine the plate temperatures. Answer: 350 K and 312 K
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Transcript of Motion in a straigth line
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Heat Transfer Assignment 1Essentials of Conduction, Convection, and Radiation
Given: March 13th, 2014Due: Beginning of class, March 20th, 2014
Instructions:
is a parameter related to your student ID, with 1 corresponding to the lastdigit, 2 to the last two digits, 3 to the last three digits, etc. For instance, ifyour ID is 199225962, then 1 = 2, 2 = 62, 3 = 962, 4 = 5962, etc.
For each problem, list all assumptions made.
Keep a copy of the assignment the assignment will not be handed back toyou.
You must be able to remember your solutions.
Problems:
1. A flat wall is exposed to an environmental temperature of 38C. The wall is covered with a layer of insulation2.5 cm thick whose thermal conductivity is 1.4 W/mC, and the temperature of the wall on the inside of theinsulation is 315C. The wall loses heat to the environment by convection. Compute the value of the convec-tion heat-transfer coefficient which must be maintained on the outer surface of the insulation to ensure that theouter-surface temperature does not exceed 41C.Answer: h 5115 W/m2C
2. A black 20-by-20 cm plate has air forced over it at a velocity of 2 m/s and a temperature of 0C. The plate isplaced in a large room whose walls are at 30C. The back side of the plate is perfectly insulated. Calculate thetemperature of the plate resulting from the convection-radiation balance. Take the convective heat transfer h as12 W/m2C. Are you surprised at the result?Answer: 9.6C
3. Two large black plates are separated by a vacuum. On the outside of one plate is a convection environment ofT = 80C and h = 100 W/m2C, while the outside of the other plate is exposed to 20C and h = 15 W/m2C.Make an energy balance on the system and determine the plate temperatures.Answer: 350 K and 312 K
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4. Using kinetic theory, derive Fouriers law of heat conduction in a gas:
qx =kTx q
y =k
Ty q
z =k
T z
with
k = 5kB4
3RT
2.
with k the thermal conductivity, the collision cross-section, kB the Boltzmann constant and R the gas constant.
5. Starting from the first law of thermo d(me)+PdV = QW and Fouriers law qx =kT/x derive the heatequation: (cT )
t =x
(k Tx
)+
y
(k Ty
)+
z
(k T z
)
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