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Paul [167]
2 years ago
11

Consider a very long, cylindrical fin. The temperature of the fin at the tip and base are 25 °C and 50 °C, respectively. The dia

meter of the fin is 3 cm. The thermal conductivity of the fin is 150 W/m·K. The heat transfer coefficient is 123 W/m2·K. Estimate the fin temperature in °C at a distance of 10 cm from the base
Engineering
1 answer:
nekit [7.7K]2 years ago
7 0

Answer:

98°C

Explanation:

Total surface area of cylindrical fin = πr² + 2πrl , r = 0.015m; l= 0.1m; π =22/7

22/7*(0.015)² + 22/7*0.015*0.1 = 7.07 X 10∧-4 + 47.1 X 10∧-4 = (54.17 X 10∧-4)m²

Temperature change, t = (50 - 25)°C = 25°C = 298K

Hence, Temperature =  150 X (54.17 X 10∧-4) X 298/123 = 242.14/124 = 2.00K =

∴ Temperature change = 2.00K

But temperature, T= (373 - 2)K = 371 K

In °C = (371 - 273)K = 98°C         

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A thin-walled tube with a diameter of 12 mm and length of 25 m is used to carry exhaust gas from a smoke stack to the laboratory
nlexa [21]

Answer:

(a)  h₁   = 204.45 W/m²k

(b) h₀ = 46.80 W/m².k

(c) T = T = 15.50°C

Explanation:

Given Data;

Diameter = 12mm

Length = 25 m

Entry temperature = 200°C

Flow rate = 0.006 kg/s

velocity = 2.5 m/s.

Step 1: Calculating the mean temperature;

(200 + 15)/2

Mean temperature = 107.5°C = 380.5 K

The properties of air at mean temperature 380.5 K are given as:

v = 24.2689*10⁻⁶m²/s

a = 35.024*10⁻⁶m²/s

μ    = 221.6 *10⁻⁷Ns/m²

k = 0.0323 W/m.k

Cp = 1012 J/kg.k

Step 2: Calculating the prantl number using the formula;

Pr = v/a

   = 24.2689*10⁻⁶/ 35.024*10⁻⁶

   = 0.693

Step3: Calculating the reynolds number using the formula;

Re = 4m/πDμ

    = 4 *0.006/π*12*10⁻³ * 221.6 *10⁻⁷

    = 0.024/8.355*10⁻⁷

    = 28725

Since Re is greater than 2000, the flow is turbulent. Nu becomes;

Nu = 0.023Re^0.8 *Pr^0.3

Nu = 0.023 * 28725^0.8 * 0.693^0.3

     = 75.955

(a) calculating the heat transfer coefficient:

Nu = hD/k

h = Nu *k/D

  = (75.955 * 0.0323)/12*10^-3

h   = 204.45 W/m²k

(b)

Properties of air at 15°C

v = 14.82 *10⁻⁶m²/s

k = 0.0253 W/m.k

a = 20.873 *10⁻⁶m²/s

Pr(outside) = v/a

                  = 14.82 *10⁻⁶/20.873 *10⁻⁶

                 = 0.71

Re(outside) = VD/v

                   = 2.5 * 12*10⁻³/14.82*10⁻⁶

                    =2024.29

Using Zakauskus correlation,

Nu = 0.26Re^0.6 * Pr^0.37 * (Pr(outside)/Pr)^1/4

    = 0.26 * 2024.29^0.6 *  0.71^0.37 * (0.71/0.693)^1/4

    = 22.199

Nu = h₀D/k

h₀ = Nu*k/D

     = 22.199* 0.0253/12*10⁻³

h₀ = 46.80 W/m².k

 (c)

Calculating the overall heat transfer coefficient using the formula;

1/U =1/h₁ +1/h₀

1/U = 1/204.45 + 1/46.80

1/U = 0.026259

U = 1/0.026259

U = 38.08

Calculating the temperature of the exhaust using the formula;

T -T₀/T₁-T₀ = e^-[uπDL/Cpm]

T - 15/200-15 = e^-[38.08*π*12*10⁻³*25/1012*0.006]

T - 15/185 = e^-5.911

T -15 = 185 * 0.002709

T = 15+0.50

T = 15.50°C

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2 years ago
Two kilograms of oxygen fills the cylinder of a piston-cylinder assembly. The initial volume and pressure are 2 m3 and 1 bar, re
valentinak56 [21]

Answer: Heat transfer (Q) is 521 kJ.

Explanation: In the piston-cilinder assembly, we can suppose that the oxygen act as an ideal gas, so, it can be used the General Gas Equation:

PV=\frac{m}{M}RT, where:

P is pressure;

V is volume;

m is mass;

M is molar mass;

R is a constant: R = 8.314.10^{-5} m³bar.K⁻¹.mol⁻¹;

T is temperature;

Using this equation, find the intial temperature:

PV = \frac{m}{M}RT

1.2 = \frac{2}{16}.8.314.10^{-5}.T

T = 1.924.10^{5} K

To determine the final temperature, use Combined Gas Law:

\frac{P_{i} . V_{i} }{T_{i} } = \frac{P.V }{T}, in which, the left side of the equality is related to the initial values and the right side, to the final values.

As pressure is constant:

\frac{V_{i} }{T_{i} } =\frac{V}{T}

T = \frac{V.T_{i} }{V_{i} }

T = \frac{4.1.924.10^{-5} }{2}

T = 3.85.10^{5} K

With the temperatures, calculate the heat transfer of the process:

Q = m.k.ΔT, where:

k is heat constant

ΔT = T - T_{i}

Q = m.k.ΔT

Q = 2.1.35.(3.85 - 1.92).10^{5}

Q = 521 kJ

The heat transfer in the process is 521 kJ.

6 0
2 years ago
Read 2 more answers
Tech A says that proper footwear may include both leather and steel-toed shoes. Tech B says that when working in the shop, you o
olga55 [171]

Answer:

Tech A is correct.

Explanation:

If a person is doing something dangerous in a shop, he should wear safety glasses to protect his eyes from danger and also wear leather shoes to protect himself from any electric shock. Leather boots will disconnect a person with direct earth and therefore he can save himself if he gets a electric shock.

6 0
2 years ago
A cylindrical drum (2 ft. dia ,3 ft height) is filled with a fluid whose density is 40 lb/ft^3. Determine (a. the total volume o
Ksivusya [100]

Answer:

a)V=9.42\ ft^3

b)Mass in lb = 376.8 lb

Mass in slug = 11.71 slug

c)v=0.025\ ft^3/lb

d)w=1276 \ lb/ft.s^2

Explanation:

Given that

d= 2 ft

r= 1 ft

h= 3 ft

Density

\rho = 40\ lb/ft^3

a)

We know that volume V given as

V=\pi r^2 h

V=\pi \times 1^2\times 3

V=9.42\ ft^3

b)

Mass = Density x volume

mass =40\times 9.42\ lb

mass= 376.8 lb

We know that

1 lb = 0.031 slug

So 376.8 lb= 11.71 slug

Mass in lb = 376.8 lb

Mass in slug = 11.71 slug

c)

we know that specific volume(v) is the inverse of density.

v=\dfrac{1}{\rho}\ ft^3/lb

v=\dfrac{1}{40}\ ft^3/lb

v=0.025\ ft^3/lb

d)

Specific weight(w) is the product of density and the gravity(g).

w= ρ X g

w = 40 x 31.9

w=1276 \ lb/ft.s^2

8 0
2 years ago
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