課程名稱︰熱傳學
課程性質︰系定必修
課程教師︰馬小康
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰ 2010/01/15
考試時限（分鐘）：110min
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Problem(1) (10%)
Using a cylinder, a sphere, and a cubic as examples. Show that the rate of
heat transfer is inversely proportional to the nominal size of the object.
That is, heat transfer per unit area increases as the size of the object
decreases.
(圖為一圓柱、一球體跟一正方體)
圓柱的 A/V = 2/r , 球體的 A/V = 3/r , 正方體的 A/V = 6/r
Problem(2) (20%)
A plate fin exchanger surface can be considered as a series of flat plates as
shown below. Various alternatives have been proposed for increasing the
present value of the average heat transfer coefficient h0, and the overall
conductance, (h0A). Determine whether the ratios (h/h0) and (hA)/(h0A0)
increase, decrease, remain the same or are indeterminate when the indicated
changes are made. Assume all dimensions are large compared to the boundary
layer thickness.
├→ Ｗ ←┤ Side view:
▁▁▁▁▁▁▁ ┬
／ ／▏ ↓
／ ／ ▏ ┌─────────┐
／ ／ ▏ │ ─── │
／ ／ ▏ Ｈ │─── ───│↓
／▁▁▁▁▁▁／ ▏ │ L ─── │Ａ
▏ ▁▁▁▁▁▏ ▏ ↑ │─── ───│↑
▏／ ▏ ▏ ┴ │ ─── │
▏▇▇▇▇▇▇▏ ／ │─── ───│
▏／▇▇▇▇▇▏ ／ └─────────┘
▏▇▇▇▇▇▇▏ ／ (L為fin的長度)
▏／▇▇▇▇▇▏／ (A為fin之間的間隔)
▏▇▇▇▇▇▇▏ Number of fins : N
▇▇▇▇▇▇▇ Ub = Ubulk = 空氣流入的速度
change (h/h0) (hA)/(h0A0)
L to 2L ─── ───
L to 2L and N to 2N ─── ───
a to a/2 and N to 2N ─── ───
W to W/2 and H to H/2 ─── ───
Ub to 2Ub, L to 2L and N to N/2 ─── ───
*use S: Same or I: Increase or D: Decrease
Problem(3) (20%)
A fluid flows at a rate m between parallel plates spaced a distance w apart.
There is a uniform heat flux q0 from the top plate into the fluid, and the
bottom plate is adiabatic. There are two flow conditions that differ only
by flow regime.
A: Laminar flow
B: Turbulent flow
(a) Sketch the mean temperature (Tm) and upper wall temperature (T0) as a
function of distance and label clearly Tm and T0 for laminar flow (A) and
turbulent flow (B). (Te) is the entrance fluid flow temperature.
│ │
│ │
│ │
Te│ │
│ │
│ │
└─────────┘
0 x L
(b) Sketch carefully the temperature profiles at X = L and label clearly which
is A and B.
.
q0
───┼── ┬─────────────────
↑ │
m │
→ ｗ │
Flow │ Te
↓ │↙
────── ┴─────────────────
/////// x=0 → T
Problem(4) (10%)
A thermal couple is used to measure the fluid flow temperature with or without
the radiation shield. (a) Which one has a higher thermal couple reading?
(b) Please explain the reasons.
Problem(5) (15%)
A shell-and tube heat exchanger with 2-shell passes and 12-tube passes is used
to hear water (Cp = 4180 J/kgC) with ethylene glycol (Cp = 2680 J/kgC). Water
enters the tube at 22℃ at a rate of 0.8 kg/s and leaves at 70℃. Ethylene
glycol enters the shell at 110℃ and leaves at 60℃. If the overall heat
transfer coefficient based on the tube side is 280 W/m^2℃, determine the rate
of heat transfer and the heat transfer surface area on the tube side.
↓ Ethlyne 110℃
┌┐
││
│└─────────┐
70℃ ← ══╪═════════╗│
│╔════════╝│
└╫───────┐ │
┌╫───────┘ │
Water │╚════════╗│
22℃ → ══╪═════════╝│
0.8 kg/s │┌─────────┘
││
└┘
↓ 60℃
Problem(6) (15%) [Textbook problem 10-91]
You have probably noticed that water vapor that condenses on a canned drink
slides down, clearing the surface for further condensation. Therefore,
condensation in this case can be considered to be dropwise. Determine the
condensation heat transfer coefficient on a cold canned drink at 2℃ that is
placed in a large container filled with saturated steam at 95℃ (Table A-9).
Assumptions: The heat transfer coefficient relation for dropwise condensation
that was developed for copper surfaces is also applicable for aluminum
surfaces.
Problem(7) (20%) [Textbook problem 9-56]
A 15-cm-wide and 18-cm-high vertical hot surface in 25℃ air is to be cooled
by a heat sink with equally spaced fins of rectangular profiles. Determine
the optimum fin height and the rate of heat transfer by natural convection from
the heat sink if the base temperature is 85℃.
The criteria for optimum fin height H in the literature is given by
H = (h*Ac / p*k)^0.5
Take the thermal conductivity of fin materials to be 177 w/mC.
Assumptions:
1. Steady operating conditions exist.
2. Air is an ideal gas with constant proterties.
3. The atmospheric pressure at that location is 1 atm.
＼├→ W=15cm ←┤
↙ ▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁ ┬
▉ ／▏ ／▏ ／▏ ／▏ ▏↓
Ｈ ▉ ／ ▏ ／ ▏ ／ ▏ ／ ▏ ▏
▉ ／ ▏／ ▏／ ▏／ ▏ ▏
↗ ▉／ ／ ／ ／ ▏ ▏ L = 18cm
＼ ／ ／ ／ ／ ▏ ▏
▏ ▏ ▏ ▏ ▏ ▏
▏ ▏ ▏ ▏ ▏ ▏
▏ ▏ ▏ ▏ ▏ ▏↑
▏ ▏ ▏ ▏ ／▇▇▇ ┴
▏ ／▏ ／▏ ／▏ ／
▏ ／ ▏ ／ ▏ ／ ▏ ／↖
▏／ ▏／ ▏／ ▏／ 85℃
▉／ ▉／ ▉／ ▉／
├→Ｓ←┤ T∞ = 25℃
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