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juin [17]
2 years ago
6

Air at 27°C and a velocity of 5 m/s passes over the small region As (20 mm × 20 mm) on a large surface, which is maintained at T

s = 127°C. For these conditions, 0.5 W is removed from the surface As. To increase the heat removal rate, a stainless steel (AISI 304) pin fin of diameter 5 mm is affixed to As, which is assumed to remain at Ts = 127°C. (a) Determine the maximum possible heat removal rate through the fin. (Hint: look back to Chapter 3 to see which fin case produces the maximum heat transfer.) (b) What fin length would provide a close approximation to the heat rate found in part (a)? (Hint: refer to Example 3.9.) (c) Determine the fin effectiveness, εf. (d) What is the percentage increase in the heat rate from As due to installation of the fin? In other words, what is the percentage increase in q obtained by adding the fin as compared to not having the fin?

Engineering
1 answer:
JulsSmile [24]2 years ago
5 0

Answer:

a) The maximum possible heat removal rate = 2.20w

b) Fin length = 37.4 mm

c) Fin effectiveness = 89.6

d) Percentage increase = 435%

Explanation:

See the attached file for the explanation.

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Show that for a linearly separable dataset, the maximum likelihood solution for the logisitic regression model is obtained by fi
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Answer:

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is explained in the attachment.

Explanation:

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3 years ago
What is the instantaneous center of zero velocity? List two approaches for determining the is the instantaneous center of zero v
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Explanation:

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Where these two lines will cut then it will the I-Center.Point A and B is moving perpendicular to the point I.

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3 years ago
What type of engineering do you think would help solve this SDG???
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4 0
2 years ago
A 50 Hz, four pole turbo-generator rated 100 MVA, 11 kV has an inertia constant of 8.0 MJ/MVA. (a) Find the stored energy in the
raketka [301]

Given Information:

Frequency = f = 60 Hz

Complex rated power = G = 100 MVA

Intertia constant = H = 8 MJ/MVA

Mechanical power = Pmech = 80 MW

Electrical power = Pelec = 50 MW

Number of poles = P = 4

No. of cycles = 10

Required Information:

(a) stored energy = ?

(b) rotor acceleration = ?

(c) change in torque angle = ?

(c) rotor speed = ?

Answer:

(a) stored energy = 800 Mj

(b) rotor acceleration = 337.46 elec deg/s²

(c) change in torque angle (in elec deg) = 6.75 elec deg

(c) change in torque angle (in rmp/s) = 28.12 rpm/s

(c) rotor speed = 1505.62 rpm

Explanation:

(a) Find the stored energy in the rotor at synchronous speed.

The stored energy is given by

E = G \times H

Where G represents complex rated power and H is the inertia constant of turbo-generator.

E = 100 \times 8 \\\\E = 800 \: MJ

(b) If the mechanical input is suddenly raised to 80 MW for an electrical load of 50 MW, find rotor acceleration, neglecting mechanical and electrical losses.

The rotor acceleration is given by

$ P_a = P_{mech} - P_{elec} = M \frac{d^2 \delta}{dt^2}  $

Where M is given by

$ M = \frac{E}{180 \times f} $

$ M = \frac{800}{180 \times 50} $

M = 0.0889 \: MJ \cdot s/ elec \: \: deg

So, the rotor acceleration is

$ P_a = 80 - 50 = 0.0889 \frac{d^2 \delta}{dt^2}  $

$  30 = 0.0889 \frac{d^2 \delta}{dt^2}  $

$   \frac{d^2 \delta}{dt^2} = \frac{30}{0.0889}  $

$   \frac{d^2 \delta}{dt^2} = 337.46 \:\: elec \: deg/s^2 $

(c) If the acceleration calculated in part(b) is maintained for 10 cycles, find the change in torque angle and rotor speed in revolutions per minute at the end of this period.

The change in torque angle is given by

$ \Delta  \delta = \frac{1}{2} \cdot \frac{d^2 \delta}{dt^2}\cdot (t)^2 $

Where t is given by

1 \: cycle = 1/f = 1/50 \\\\10 \: cycles = 10/50 = 0.2  \\\\t = 0.2 \: sec

So,

$ \Delta  \delta = \frac{1}{2} \cdot 337.46 \cdot (0.2)^2 $

$ \Delta  \delta = 6.75 \: elec \: deg

The change in torque in rpm/s is given by

$ \Delta  \delta = \frac{337.46 \cdot 60}{2 \cdot 360\circ  }   $

$ \Delta  \delta =28.12 \: \: rpm/s $

The rotor speed in revolutions per minute at the end of this period (10 cycles) is given by

$ Rotor \: speed = \frac{120 \cdot f}{P}  + (\Delta  \delta)\cdot t  $

Where P is the number of poles of the turbo-generator.

$ Rotor \: speed = \frac{120 \cdot 50}{4}  + (28.12)\cdot 0.2  $

$ Rotor \: speed = 1500  + 5.62  $

$ Rotor \: speed = 1505.62 \:\: rpm

4 0
3 years ago
Steam enters a turbine operating at steady state at 2 MPa, 323 °C with a velocity of 65 m/s. Saturated vapor exits at 0.1 MPa an
Lera25 [3.4K]

Answer:

\dot Q_{out} = 13369.104\,kW

Explanation:

The turbine is modelled after the First Law of Thermodynamics:

-\dot Q_{out} - \dot W_{out} + \dot H_{in} - \dot H_{out} + \dot K_{in} - \dot K_{out} + \dot U_{in} - \dot U_{out} = 0

The rate of heat transfer between the turbine and its surroundings is:

\dot Q_{out} = \dot H_{in}-\dot H_{out} + \dot K_{in} - \dot K_{out} - \dot W_{out} + \dot U_{in} - \dot U_{out}

The specific enthalpies at inlet and outlet are, respectively:

h_{in} = 3076.41\,\frac{kJ}{kg}

h_{out} = 2675.0\,\frac{kJ}{kg}

The required output is:

\dot Q_{out} = \left(8\,\frac{kg}{s} \right)\cdot \left\{3076.41\,\frac{kJ}{kg}-2675.0\,\frac{kJ}{kg}+\frac{1}{2}\cdot \left[\left(65\,\frac{m}{s} \right)^{2}-\left(42\,\frac{m}{s} \right)^{2}\right] + \left(9.807\,\frac{m}{s^{2}} \right)\cdot (4\,m) \right\} - 8000\,kW\dot Q_{out} = 13369.104\,kW

4 0
3 years ago
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