Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated

#### Videos

Textbook Question
Chapter 1, Problem 1.1P

The thermal conductivity of a sheet of rigid, extruded insulation is reported to be k = 0.029 W/m K . The measured temperature difference across a 20-mm-thick sheet of the material is T 1 = T 2 = 10 ° C .

1. What is the heat flux through a 2 m × 2 m sheet of the insulation?
2. What is the rate of heat transfer through the sheet of insulation?

(a)

Expert Solution
To determine

Heat Flux through a Sheet of insulation of dimension 2 m×2 m .

Heat Flux through a Sheet of insulation of dimension 2 m×2 m is 14.5 W/m2 .

### Explanation of Solution

Given:

Thermal conductivity of insulation is 0.029W/mK , thickness of Sheet is 20 mm , temperature difference through sheet is 10°C and dimension of sheet is 2m×2m .

Concept used:

Write the expression for heat flux passing through the sheet of insulation.

QA=kΔTΔx   ...... (1)

Here, Q is the rate of heat transfer, A is the cross-sectional area of sheet, k is thermal conductivity of specimen, ΔT is the temperature difference through the sheet and Δx is the thickness of sheet.

Calculation:

Substitute 10°C for ΔT , 0.029W/mK for k and 20mm for Δx in equation (1).

QA=(0.029)10( 20 mm( 1 m 1000mm ))=14.5 W/m2

Conclusion:

Thus, heat Flux through a Sheet of insulation of dimension 2 m×2 m is 14.5 W/m2 .

(b)

Expert Solution
To determine

Rate of heat transfer through sheet of insulation.

Rate of heat transfer through sheet of insulation is 58W .

### Explanation of Solution

Concept used:

Calculate the area of rectangular sheet as follows:

A=2 m×2 m=4 m2

Write the expression for rate of heat transfer.

Q=kAΔTΔx   ...... (2)

Calculation:

Substitute 10°C for ΔT , 0.029W/mK for k , 4m2 for A and 20mm for Δx in equation (1).

Q=(4)(0.029)10( 20 mm( 1 m 1000mm ))=58W

Conclusion:

Thus, rate of heat transfer through sheet of insulation is 58W .

### Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
02:31
Students have asked these similar questions
Stainless steel pipes with a thermal conductivity of 17 W/ (m° C) are used to transport hot oil. The temperature inside the tube is 130 ° C. The inner diameter of the pipe is 8 cm and the thickness of the pipe wall is 2 cm. The pipe is then insulated with 4 cm thick insulation with a thermal conductivity of 0.035 W / (m° C). The ambient temperature of the pipe is 25 ° C. Calculate the temperature between the steel and the insulation if we assume a steady state. A picture of the pipe can be seen below.
a flat wall is covered with a layer of insulation 1.0 in. thick whose thermal conductivity is 0.8 Btu/hr-ft- F. the temperature of the wall on the inside of the insulation is 600F. the wall loses heat to the environment by convection on the surface of the insulation. the average value of the convection heat transfer coefficient on the inslation surface is 950 Btu/hr-ft^2-F. compute the bulk temperature of the environment if the outer surface of the insulation does not exceed 105 F.
A 3 inch schedule 40 pipe is covered with two layers of                                                 insulations. The inner layer (k1 = 0.050) is 2 inches thick and                                                 the outer layer (k2 = 0.037) is 1(1/4) inches thick. Calculate                                                 the heat loss, in Btu/hr per unit length, if the outer surface                                                 temperature of the pipe is 670°F and the outer surface                                                 temperature of the outer layer of insulation is 100°F.
• Copyright, Community Guidelines, DSA & other Legal Resources: Learneo Legal Center
• bartleby, a Learneo, Inc. business