Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 2, Problem 2.11P
Consider steady-state conditions for one-dimensional conduction in a plane wall having a thermal conductivity
Determine the heat flux and the unknown quantity for each case and sketch the temperature distribution, indicating the direction of the heat flux. 
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(A) Consider a plane wall of thickness L and thermal conductivity k. The two sides of the
wall are maintained at constant temperatures of T1 and T2 respectively. Show that the
temperature distribution through the wall is represented as
Т, - Т,
T =
- x +
x+T|
L
Assume one dimensional steady state heat conduction
Problems
within the wall is T(x) = a(L- ) +b where
a = 10°C/m2 and b 30°C, what is the thermal con-
ductivity of the wall? What is the value of the convec-
tion heat transfer coefficient, h?
2.11 Consider steady-state conditions for one-dimensional
conduction in a plane wall having a thermal conductiv-
ity k 50 W/m K and a thickness L = 0.25 m, with no
internal heat generation.
2.
T2
T1
L
Determine the heat flux and the unknown quantity for
each case and sketch the temperature distribution, indi-
cating the direction of the heat flux.
2
Case
TC)
dTldx (K/m)
T2(°C)
1
50
-20
2
-30
- 10
3
70
160
4
40
-80
5
30
200
Write down the Fourier heat conduction equation and explain the meaning of each term in the equation in units. Find the heat conduction coefficient of a cylindrical material with a diameter of 25mm, a length of 30mm, temperatures of its two surfaces T1 = 40.2oC, T2 = 38.9oC, respectively, and a given thermal power amount of 22.4W.
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
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- 1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.arrow_forward2.29 In a cylindrical fuel rod of a nuclear reactor, heat is generated internally according to the equation where = local rate of heat generation per unit volume at r = outside radius = rate of heat generation per unit volume at the centerline Calculate the temperature drop from the centerline to the surface for a 2.5-cm-diameter rod having a thermal conductivity of if the rate of heat removal from its surface is 1.6 .arrow_forward1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.arrow_forward
- A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6arrow_forward1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4arrow_forward2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.arrow_forward
- 2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)arrow_forwardOne end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?arrow_forwardEstimate the rate of heat loss per unit length from a 5-cm ID, 6-cm OD steel pipe covered with high-temperature insulation having a thermal conductivity of 0.11 W/(m K) and a thickness of 1.2 cm. Steam flows in the pipe. It has a quality of 99% and is at 150C. The unit thermal resistance at the inner wall is 0.0026(m2K)/W the heat transfer coefficient at the outer surface is 17W/(m2K) and the ambient temperature is 16C.arrow_forward
- Q1: Consider one-dimensional conduction in a plane composite wall (Im x Im) as shown in the figure below. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m K. The middle wall B experiences uniform heat generation dg, while there is no generation in walls A and C. The temperatures at the interfaces are T=261°C and T; -211°C. Assuming negligible contact resistance at the interfaces: A) Determine the outside surface temperature of walls A and C? B) Compute the value of dg? (20 M) A B. ーム k= 25 Wim-K A = 50 W/m-K L = 30 mm Le= 30 mm L = 20 mm %3Darrow_forward1250 W/m and a = 90 W/m2 and the ég An infinite wall that has a thickness of L = 0.22 m has a uniform heat generation of thermal conductivity of k = 20 W/m-°C. At x = 0 the heat flux going into the wall is temperature of the surface at x = L is T = 42 °C. Find an equation for the steady state temperature distribution in this wall as a function of the position x. Also find the value of the temperature at x = 0. ég k do x= 0 x = Larrow_forwardPlease try to solve fast thank uarrow_forward
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