課程名稱︰熱傳學
課程性質︰機械系大三必修
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）︰2009/12/11
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 :
(1) A fluid with negligible viscosity flows between parallel plates. The low
viscosity allows the assumption that the fluid velocity throughout the
flow is a constant value V. The energy equation becomes
dT d^2T
(V/α)── = ( ── ) (此處的d為偏微分,partial)
dx dy^2
. .
(a) Derive an expression for NuH for the case of qH>0 , qS=0.
(b) For a thermally fully developed flow, sketch the temperature profile across
the flow for the following three cases, where Th is the temperature of the
upper plate and heat flow is positive in the y-direction. (26%)
.─────Th .─────Th .─────Th
qH qH qH
y
↑
.─────Th .─────Th .─────Th └→x
qS qS qS
. . . . . . . .
Case1: qH>0,qS=0 Case2: qH>0,qS=qH Case3:qH<0,qS=-qH
(2) Water is heated at a rate of 10 kg/s from a temperature of 15℃ to 35℃ by
passing it through five identical tubes, each 5.0 cm in diameter, whose
surface temperature is 60.0℃. Please estimate (a) the steady rate of heat
transfer and (b) the length of tubes necessary to accomplish this task.
(20%)
↙60℃
ρ = 997 kg/m^3 ┌───────┐
k = 0.607 W/m℃ Water │ ↑ │
μ = 0.891*10^3 m^2/s 15℃ ─┼→ │D=5cm ├→ 35℃
Cp = 4180 J/kg℃ 10kg/s │ ↓ │
Pr = 6.14 └───────┘ 5 tubes
(此為管子的側面圖)
(3) A man plays a golf game and hits ball with Re=2.0*10^5, he tries to improve
his hit distance with a smaller ball. Is his decision correct? Please
explain the possible criterion. (Assume hit ball with the same force under
the same weather conditions) (10%)
(4) For a laminar flow, the local Nusselt number at location x over a flat
plate is
Nux = 0.332 * Re^(1/2) * Pr^(1/3) Pr > 0.6
Please derive the average Nusselt number under the same conditions. (10%)
(5) Consider steady, laminar, two dimensional, incompressible flow with
constant properties and a Prandtle number of unity. For a given geometry,
is it correct to say that both the average friction and heat transfer
coefficients depend on the Reynolds number only? Please explain it. (10%)
(6) A hot fluid is flowing through a long insulated pipe. Heat is lost to the
ambient by natural convection from the outside surface of the insulation.
(24%)
Group A
1. k (insulation)
2. k (pipe) ( k(pipe) > k(insulation) )
3. R1 (inside radius of pipe)
4. R2 (outside radius of pipe)
5. R3 (outside radius of insulation)
6. Tf (inlet temperature of fluid)
7. T∞ (ambient air temperature)
8. mf (mass flow rate of fluid)
Group B
9. h inside
10. h outside
11. Re inside (Reynolds number)
12. Nu inside (Nusselt number)
13. Gr (Grashof number)
14. q (heat loss to surroundings)
dt│
15. ─│ (Temperature gradient in insulation)
dr│r=R3
increase 9 10 12 13 14 15
k(insulation) ____ ____ ____ ____ ____ ____
R2 ____ ____ ____ ____ ____ ____
T∞ ____ ____ ____ ____ ____ ____
mf ____ ____ ____ ____ ____ ____
Please fill in with I, D, S
I:Increase
D:Decrease
S:Same
(本題是在增加左列的條件時，考慮Group B 當中 9,10,12~15的增減情形,填入I,D,S)
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