A plane wall 15 cm thick has a thermal conductivity given by the relation k = 2.0 + 0.0005 T W/(m K) where T is in degrees Kelvin. If one surface of this wall is maintained at 150 °C and the other at 50 °C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.
GIVEN
A plane wall
Thickness (L) = 15 cm = 0.15 m
Thermal conductivity (k) = 2.0 + 0.0005 T W/(m K) (with T in Kelvin)
Surface temperatures: Th = 150 °C Tc = 50 °C
FIND
(a) The rate of heat transfer per square meter (q/A)
(b) The temperature distribution through the wall
ASSUMPTIONS
The wall has reached steady state
Conduction occurs in one dimension
SKETCH
Simplifying for steady state conduction with no internal heat generation but allowing for the
variation of thermal conductivity with temperature yields
Integrating
The constant can be evaluated using the first boundary condition
(a) The rate of heat transfer can be evaluated using the second boundary condition:
(b) Therefore, the temperature distribution is
0.00025 T 2 + 2.0 T = 890.7 – 1458 x
You might also like to view...
Which of the following statements describes the ecliptic?
A. the extension of Earth's equator on the celestial sphere B. the apparent path of the Sun across the celestial sphere C. the path of the Moon on the celestial sphere D. the extension of Earth's path on the celestial sphere E. The extension of Earth's equator on the celestial sphere and the apparent path of the Sun across the celestial sphere are correct.
Scientists cannot agree on whether viruses are living or not because
A) they are much smaller than other simple living organisms B) they can reproduce but do not require any utilization of energy to do so C) they can only reproduce within a host cell and not independently D) under certain conditions they can reproduce, but they do not contain any DNA
The spiral arms are blue from the presence of Population ________ stars in them
Fill in the blank(s) with correct word
A self-sustained chain reaction occurs when the reproduction constant, K, is equal to
a. 3.0 b. 2.0 c. 2.5 d. 1.0 e. 0.5