Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN: 9781305387102
Author: Kreith, Frank; Manglik, Raj M.
Publisher: Cengage Learning
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Chapter 2, Problem 2.47P
To determine
Temperature distribution along the web and plot the results.
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Q1/The thermal conductivity 14.4w/m.k for the block of stainless
steel shown below is well insulated on the front and back surfaces,
and the temperature in the block varies linearly in both the x- and
y directions,
Find: The heat fluxes and heat flows in the x- and y-directions.
5 cm
15°C
10°C
-5 cm -
10 cm
5°C
0°C
Q2-Consider a two layer composite wall of copper and Teflon as
shown below. The copper has a thickness of 10cm but the
thickness of the Teflon is to be determined. The temperature on
the left boundary is equal to 200 C and on the right boundary 25C.
Determine the thickness of the Teflon layer so that the heat flux
is equal to 200W/m2.
L2
T = 200C
Te = 25 C
L1 = 01m
TA
T3
%3D
- 007 = 5
coper
télon
Tc
A steel pipe (outside diameter 100 mm) is covered with two
layers of insulation. The inside layer, 40 mm thick, has a
thermal conductivity of 0.07 W/(m K). The outside layer,
20 mm thick, has a thermal conductivity of 0.15 W/(m K).
The pipe is used to convey steam at a pressure of 600 kPa. The
outside temperature of insulation is 24°C. If the pipe is 10 m
long, determine the following, assuming the resistance to
conductive heat transfer in steel pipe and convective resistance
on the steam side are negligible:
a. The heat loss per hour.
b. The interface temperature of insulation.
Some sections of the Alaska pipeline above ground are supported by vertical steel supports (k = 25 W/mK), which have a length of 1 m and a cross-sectional area of 0.05 m². Under normal operating conditions, the temperature variation along the length of the steel support is given by the expression T = 100 – 150x + 10x², where T and x have units of °C and m, respectively. Temperature variations in the cross-sectional area of the support are negligible. Evaluate the temperature and the heat conduction rate at the pipeline-support junction (x = 0) and at the support-soil interface (x = 1 m). Explain the difference in heat rates.
Chapter 2 Solutions
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Ch. 2 - A plane wall, 7.5 cm thick, generates heat...Ch. 2 -
2.2 A small dam, which is idealized by a large...Ch. 2 - 2.3 The shield of a nuclear reactor is idealized...Ch. 2 - A plane wall 15 cm thick has a thermal...Ch. 2 - 2.5 Derive an expression for the temperature...Ch. 2 - A plane wall of thickness 2L has internal heat...Ch. 2 - 2.7 A very thin silicon chip is bonded to a 6-mm...Ch. 2 - 2.9 In a large chemical factory, hot gases at 2273...Ch. 2 - 2.14 Calculate the rate of heat loss per foot and...Ch. 2 - 2.15 Suppose that a pipe carrying a hot fluid with...
Ch. 2 - Prob. 2.16PCh. 2 - Estimate the rate of heat loss per unit length...Ch. 2 - The rate of heat flow per unit length q/L through...Ch. 2 - A 2.5-cm-OD, 2-cm-ID copper pipe carries liquid...Ch. 2 - A cylindrical liquid oxygen (LOX) tank has a...Ch. 2 - Show that the rate of heat conduction per unit...Ch. 2 - Derive an expression for the temperature...Ch. 2 - Heat is generated uniformly in the fuel rod of a...Ch. 2 - 2.29 In a cylindrical fuel rod of a nuclear...Ch. 2 - 2.30 An electrical heater capable of generating...Ch. 2 - A hollow sphere with inner and outer radii of R1...Ch. 2 - 2.34 Show that the temperature distribution in a...Ch. 2 -
2.38 The addition of aluminum fins has been...Ch. 2 - The tip of a soldering iron consists of a 0.6-cm-...Ch. 2 - One end of a 0.3-m-long steel rod is connected to...Ch. 2 - Both ends of a 0.6-cm copper U-shaped rod are...Ch. 2 - 2.42 A circumferential fin of rectangular cross...Ch. 2 - 2.43 A turbine blade 6.3 cm long, with...Ch. 2 - 2.44 To determine the thermal conductivity of a...Ch. 2 - 2.45 Heat is transferred from water to air through...Ch. 2 - 2.46 The wall of a liquid-to-gas heat exchanger...Ch. 2 - Prob. 2.47PCh. 2 - The handle of a ladle used for pouring molten lead...Ch. 2 - 2.50 Compare the rate of heat flow from the bottom...Ch. 2 - 2.51 Determine by means of a flux plot the...Ch. 2 - Prob. 2.52PCh. 2 - Determine the rate of heat transfer per meter...Ch. 2 - Prob. 2.54PCh. 2 - 2.55 A long, 1-cm-diameter electric copper cable...Ch. 2 - Prob. 2.56PCh. 2 - Prob. 2.57PCh. 2 - Prob. 2.58P
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- Steel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 600 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 8 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Heat loss per hour. = kJ / hour. b. Temperature between insulation layers. = ° Carrow_forwardSteel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 500 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 8 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Heat loss per hour. = Answer kJ / hour. b. Temperature between insulation layers. = Answer ° C.arrow_forwardIn a thermal power plant, a horizontal copper pipe of "D" diameter, "L" length and thickness 1.2 cm enters into the boiler that has the thermal conductivity as 0.37 W/mK. The boiler is maintained at 113C and temperature of the water that flows inside the pipe is at 29C. If the energy transfer (Q) is 118779 kJ in 7 hours. Calculate: 4-Length of the pipe, if D = 0.017 L. 5-Pipe Diameter (in mm)arrow_forward
- Steel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to deliver steam with a pressure of 800 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 10 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Heat loss per hour. = AnswerkJ / hr. b. Temperature between insulation layers. = Answer ° C.arrow_forwardA pipe of length L connects to thermal reservoirs that are kept constant at temperatures T₁ and T₂. The pipe contains a gas with a thermal conductivity K, a density p, and a heat capacity cp. What is the temperature T of the gas in the tube at a distance x = 0.2L away from the thermal reservoir with temperature T₁ ? Select one: a. b. T = 0.5(T₁+T₂) T = T₁ +0.2 (T₂-T₁) c. T = T₁ +0.2(T₂-T₁) d. T = T₁ +0.2(T₁ - T₂)arrow_forwardSteel is sequentially heated and cooled to relieve stresses and to make it less brittle. Consider a 100 mm thick plate that is initially at a uniform temperature of 300 °C and is heated on both sides in a gas fired furnace for which To 700 °C and h=500 W/m². K. How long will it take the coldest spot to reach 550 °C in the plate? Materials properties are given in this graph. == = Steel plate: 11 T₁ = 300°C T(0,t) = 550°C L = 50 mm Combustion gases p=7800 kg/m3 Cp = 500 J/kg-K k = 45 W/m-K T∞ = 700°C h = 500 W/m²-Karrow_forward
- A wood stove heats a small cabin with the following dimensions 8 m x 6 m x 3 m (length x width x height) to 25°C. Of the heat generated by burning wood, 60% is lost up the chimney. The cabin also loses heat through walls, ceiling and floor. Assume that all sides of the house except the floor are insulated with a 10 cm thick polyethylene foam layer having a thermal conductivity htc = 0.038 W/(m•°C). The heat loss through the floor is 1/5 of the heat loss through the ceiling. Outside air is at -5°C. a) How much heat is lost in total from the ceiling, walls, and floor? b) How many kg of wood per hour is needed as fuel for the cabin to maintain its temperature if heat value of wood is AH = 18,000 kJ/kg?arrow_forwardA carbon steel plate (thermal conductivity = 45 W/m°C) 600 mm x 900 mm x 25 mm is maintained at 310°C. Air at 15°C blows over the hot plate. If convection heat transfer coefficient is 22 W/m.°C and 250 W is lost from the plate surface by radiation, calculate the inside plate temperature.arrow_forward= 31. A circular fin of diameter D = 0.25 inches and length L 4 inches transfers heat at a rate Q = 5.66 Btu/hr to air. The convective heat transfer coefficient is 3.62 Btu/hr-ft²- °F and the temperature difference between the fin-wall interface and the air is 100 °F. What is the thermal conductivity of the fin? What is the temperature of the fin tip?arrow_forward
- Steel pipe (outer diameter 100 mm) is covered with two layers of insulation. The inner layer, 40 mm thick, has a thermal conductivity of 0.07 W / (m K). The outer layer, 20 mm thick, has a thermal conductivity of 0.15 W / (m K). Pipes are used to delivering steam with a pressure of 600 kPa. The temperature on the outer insulation surface is 24 ° C. If the pipe is 10 m long, determine the following: (assuming that the conduction heat transfer resistance of the steel pipe and the vapor convection resistance are negligible). a. Hourly heat loss ... (kj / hr)b. temperature between insulation layers ... (° C.)arrow_forwardPresents the diagram of the problem, necessary formulas, clearance and numerical solution: An iron plate 2 cm thick has a cross-sectional area of 5,000 cm2. One of the faces is at 150 ◦C and the other is at 140 ◦C. How much heat flows through the plate each second? For iron, kT = 80 W/m K.arrow_forwardMaterials expand when heated. Consider a metal rod of length L0 at temperature T0. If the temperature is changed by an amount ∆T, then the rod's length approximately changes by ∆L = ∝Lo∆T, where a is the thermal expansion coefficient and ∆ T is not an extreme temperature change. For steel, ∝ = 1.24 X 10- 5 0 c- 1. (a) A steel rod has length Lo = 40 cm at To = 40°C. Find its length at T = 90°C. (b) Find its length at T = 50°C if its length at To= 100°C is 65 cm. ( c) Express length L as a function of T if Lo = 65 cm at To = 100°C.arrow_forward
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