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LenKa [72]
3 years ago
13

2 Consider airflow over a plate surface maintained at a temperature of 220°C. The temperature profile of the airflow is given as

The airflow at 1 atm has a free stream velocity and temperature of 0.08 m/s and 20°C, respectively. Determine the heat flux on the plate surface and the convection heat transfer coefficient of the airflow
Engineering
1 answer:
lutik1710 [3]3 years ago
6 0

Answer:

Heat flux on the plate surface is 1.45 x 10⁴ W/m², Heat transfer coefficient is 72.6 W/m². K

Explanation:

<u>The temperature profile of the airflow is given as</u>

<u>T(y) = T∞ – (T∞ - Ts)exp[(-V/</u>α<u> fluid)y]</u>

<u>Calculate the mean film temperature of air</u>

T(f) = T(s) + T∞/2, where T(s) is the surface temperature of the plate and T∞ is the temperature of free stream

Substitute Ts = 220 C and T∞ = 20 C

T(f) = 220 +20/2 = 120 C

Obtain the properties of air from Table A- 15 (Properties of air at 1 atm pressure) in the text book of from the internet at T(f) = 120 C, which would give us the quantities of thermal diffusivity (α fluid) and the thermal conductivity (k) of air

α fluid = 3.565 x 10⁻⁵ m²/s

k = 0.03235 W/m.k

<u>Calculate the temperature gradient for the given profile</u>

T(y) = T∞ – (T∞ - Ts)exp({-V/α fluid}y)

Where, T∞ is the ambient temperate, V is the free stream velocity of air and y is the temperature displacement thickness

<u>Differentiate the expression with respect to y</u>

dT/dY = - (T∞ - Ts){-V/α fluid}e[(-V/α fluid) x 0]

dT/dy = -(T∞ - Ts){-V/α fluid}

<u>Substitute T∞ = 20 C, Ts = 220 C, V = 0.08 m/s and </u>α<u> = 3.565 x 10⁻⁵ m²/s</u>

dT/dy = - (20 - 220)(-0.08/3.565 x 10⁻⁵)

dT/dy = -448807.8541

<u>Calculate the heat flux on the plate surface</u>

Q = -kdT/dy

K = 0.03235 W/m.k, dT/dy = -448807.8541

Q = -(0.03235)(-448807.8541)

Q = 1.45 x 10⁴ W/m²

Therefore, the heat flux on the plate surface is 1.45 x 10⁴ W/m²

<u>Calculate the heat transfer coefficient</u>

Q = h(Ts - T∞), where h is the transfer coefficient

1.45 x 10⁴ = h(220 - 20)

H = 72.6 W/m2.k

Therefore, the heat transfer coefficient is 72.6 W/m². K

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A large prime number isP = 232582657 - 1
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32582657

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If any number is in the form of 2^{n}-1 is known as Mersenne prime. Here, n is a prime number.

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The cross-section of a rough, rectangular, concrete() channel measures . The channel slope is 0.02ft/ft. Using the Darcy-Weisbac
bazaltina [42]

Answer:

The following are the answer to this question:

Explanation:

In point a, Calculating the are of flow:

\bold{Area =B \times D_f}

         =6\times 5\\\\=30 \ ft^2

In point b, Calculating the wetter perimeter.

\bold{P_w =B+2\times D_f}

      = 6 +2\times (5)\\\\= 6 +10 \\\\=16 \ ft

In point c, Calculating the hydraulic radius:

\bold{R=\frac{A}{P_w}}

   =\frac{30}{16}\\\\= 1.875 \ ft

In point d, Calculating the value of Reynolds's number.

\bold{Re =\frac{4VR}{v}}

     =\frac{4V \times 1.875}{1 \times 10^{-5} \frac{ft^2}{s}}\\\\

     =750,000 V

Calculating the velocity:

V= \sqrt{\frac{8gRS}{f}}

   = \sqrt{\frac{8\times 32.2 \times 1.875 \times 0.02}{f}}\\\\=\frac{3.108}{\sqrt{f}}\\\\

\sqrt{f}=\frac{3.108}{V}\\\\

calculating the Cole-brook-White value:

\frac{1}{\sqrt{f}}= -2 \log (\frac{K}{12 R} +\frac{2.51}{R_e \sqrt{f}})\\\\ \frac{1}{\frac{3.108}{V}}= -2 \log (\frac{2 \times 10^{-2}}{12 \times 1.875} +\frac{2.51}{750,000V\sqrt{f}})\\

\frac{V}{3.108} =-2\log(8.88 \times 10^{-5} + \frac{3.346 \times 10^{-6}}{750,000(3.108)})

After calculating the value of V it will give:

V= 25.18 \ \frac{ft}{s^2}\\

In point a, Calculating the value of Froude:

F= \frac{V}{\sqrt{gD}}

= \frac{V}{\sqrt{g\frac{A}{\text{Width flow}}}}\\

= \frac{25.18}{\sqrt{32.2\frac{30}{6}}}\\\\= \frac{25.18}{\sqrt{32.2 \times 5}}\\\\= \frac{25.18}{\sqrt{161}}\\\\=  \frac{25.18}{12.68}\\\\= 1.98

The flow is supercritical because the amount of Froude is greater than 1.  

Calculating the channel flow rate.

Q= AV

   =30x 25.18\\\\= 755.4 \ \frac{ft^3}{s}\\

4 0
3 years ago
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