Pressurized steam at K flows through a long, thin-walled pipe of m diameter. The pipe is enclosed in a concrete casing that is of square cross section and m on a side. The axis of the pipe is centered in the casing, and the outer surfaces of the casing are maintained at K. What is the rate of heat loss per unit length of pipe?

rate of heat loss = 114.34(T - t)w/m

Explanation: Please find the attached file for the solution

Some figures are missing in the question. The complete question is;

"Pressurized steam at 450 K flows through a long, thin-walled pipe of 0.5-m diameter. The pipe is enclosed in a concrete casing that is of square cross section and 1.5 m on a side. The axis of the pipe is centered in the casing, and the outer surfaces of the casing are maintained at 300 K. What is the heat loss per unit length of pipe?"

Rate of heat loss per unit length of pipe = 1122 W/m

Explanation:

Heat analysis is given by the expression;

q = SkΔT(1-2)

Now for this problem, we will work under the following assumptions;

- steady state conditions

- negligible steam side convection resistance

- pipe wall resistance, contact resistance, and constant properties.

For concrete at 300K, the constant k = 1.4 W/m.K

From the heat analysis equation earlier, S is alternatively given an expression;

S = 2πL/(In(1.08w/D)) where w is width and D is Diameter

And thus,

q = [2πkL(T1-T2)] /(In(1.08w/D))

Now, rate of heat transfer per unit length is given by the expression;

q' = q/L

So,

q' = [2πk(T1-T2)] /(In(1.08w/D)

q' = [2π(1.4)(450-300)] /(In(1.08 x 1.5)/0.5)) = 1319.47/In(3.24) = 1122 W/m

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explanation:

scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.