Explanation Given information: The inner radius of the sphere is 1 m , the thickness of the sphere is 5 mm , the uniform heat flux is 7 kW / m 2 , the outer surface temperature is 20 ° C , the value of the constant k 0 is 1.33 W / m ⋅ K , and the temperature coefficient of the thermal conductivity is 0.0023 K − 1 . Write the expression for the variable thermal conductivity. k ( T ) = k 0 ( 1 + β T ) ...... (I) Here, the constant is k 0 , the temperature is T and the temperature coefficient of the thermal conductivity is β . Write the expression for the average thermal conductivity. k avg = k 0 [ 1 + β ( T 2 + T 1 2 ) ] ...... (II) Here, the outer surface temperature of the sphere is T 2 and the inner surface temperature is T 1 . Write the outer radius of the spherical container. r 2 = r 1 + t ...... (III) Here, the inner radius of the sphere is r 1 and the outer radius of the sphere is r 2 . Write the expression for the rate of heat transfer through a spherical container. Q ˙ sphere = ( 4 π k avg r 1 r 2 ) ( T 1 − T 2 ) r 2 − r 1 ...... (IV) Write the expression for the inner surface area of the pipe. A s = 4 π r 1 2 Write the expression for the heat flux. q ˙ = Q ˙ sphere A s ...... (V) Substitute 4 π r 1 2 for A s and ( 4 π k avg r 1 r 2 ) ( T 1 − T 2 ) r 2 − r 1 for Q ˙ sphere in Equation (V). q ˙ = ( 4 π k avg r 1 r 2 ) ( T 1 − T 2 ) r 2 − r 1 4 π r 1 2 = ( k avg r 2 r 1 ) ( T 1 − T 2 ) r 2 − r 1 ...... (VI) Write the expression for the temperature drop across the container of the wall. T d = T 1 − T 2 ...... (VII) Calculation: Convert the temperature from degree Celsius to Kelvin. T K = ( 273 + T ° C ) K T 2 K = ( 273 + 20 ° C ) K T 2 = 293 K Substitute 1.33 W / m ⋅ K for k 0 , 0.0023 K − 1 for β , and 293 K for T 2 in Equation (II). k avg = ( 1

Heat and Mass Transfer: Fundamentals and Applications

6th Edition

ISBN: 9781260440058

Author: CENGEL, Yunus

Publisher: MCGRAW-HILL HIGHER EDUCATION

See similar textbooks

Question

Chapter 2, Problem 122P

To determine

The drop in temperature across the container wall thickness.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 2, Problem 121P

Chapter 2, Problem 123P

Students have asked these similar questions

Exposure to high concentrations of gaseous ammonia can cause lung damage. The acceptable short term ammonia exposure level set by the occupational safety and health administration is 35 ppm for 15 min. consider a vessel filled with gaseous ammonia at 30 mol/L and 10 cm diameter circular plastic plug with thickeness of 2 mm is used to contain the ammonia inside the vessel. the ventilation system is capable of keeping the room safe with fresh air, provded that the rate of ammonia being release is below .2 mg/s. if the diffusion coefficient of ammonia through the plug is 1.3*10^-10 m^2/s, determine whether or not the plug can safelt contain the ammonia inside the vessel.

The state of stress at a point is σ = -8.00 kpsi, σy = 12.00 kpsi, σ% = -18.00 kpsi, Try = 7.00 kpsi, Tyz = 4.000 kpsi, and Tzx = -18.00 kpsi. Determine the principal stresses. The principal normal stress σ1 is determined to be kpsi. The principal normal stress σ2 is determined to be The principal normal stress σ3 is determined to be kpsi. kpsi. The principal shear stress T₁ T1/2 is determined to be kpsi. The principal shear stress 72/ is determined to be [ kpsi. The principal shear stress T1/3 is determined to be kpsi.

The constant 180 N-m counterclockwise couple acts on the L-shaped rod ABC, which rotates freely in the vertical plane about the pin at A. At this moment, the angular velocity of the rod is 2 rad/s counterclockwise. Determine the angular acceleration of the rod and the reactions at A in the position shown. Answer: a=1.7 rad/s², Ax = 25.3 N, Ay = 603 N 180 N-m 1.2 m 24 kg 20 kg B 1.0 m

Chapter 2 Solutions

Heat and Mass Transfer: Fundamentals and Applications

Ch. 2 - How does transient heat transfer from steady heat...Ch. 2 - Is heat transfer a scalar or a vector quantity?...Ch. 2 - Does a hear flux vector at a point P on an...Ch. 2 - From a heat transfer point of view, what is the...Ch. 2 - What is heat generation in a solid? Give examples.Ch. 2 - Heat generation is also referred to as energy...Ch. 2 - In order to size the compressor of a new...Ch. 2 - In order to determine the size of the heating...Ch. 2 - Consider a round potato being baked in an oven....Ch. 2 - Consider an egg being cooked in boiling water in a...

Knowledge Booster