Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Textbook Question
Chapter 4, Problem 4S.1P
A long furnace. constructed from refractory brick with a thermal conductivity of
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Given:
Plate thickness: 30 mm
k = 45 W/m°C
Uniform volumetric heat generation: q = 25 MW/m³
Temperature on the right surface: 450K
Temperature on the left surface: 390K
Determine the following:
(i) The equation for t(x).
(ii) The maximum temperature and its location.
(iii) The heat flow from each surface of the plate.
B6
A pipe wall with inner and outer radii ri and ro, whose temperatures are
kept in Tj and To, is discussed. The heat transfer coefficient of the
cylinder depends on the temperature, and k = ko (1 + aT) relationship
can be written, where k, and a are constant. Subtract an equation for
the heat passing through the unit length of the pipe. What is the
thermal resistance of the pipe wall.
Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 4 - In the method of separation of variables (Section...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Consider the two-dimensional rectangular plate of...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - A two-dimensional rectangular plate is subjected...Ch. 4 - Using the thermal resistance relations developed...Ch. 4 - Free convection heat transfer is sometimes...Ch. 4 - Consider Problem 4.5 for the case where the plate...Ch. 4 - Prob. 4.9PCh. 4 - Based on the dimensionless conduction heat rates...
Ch. 4 - Determine the heat transfer rate between two...Ch. 4 - A two-dimensional object is subjected to...Ch. 4 - An electrical heater 100 mm long and 5 mm in...Ch. 4 - Two parallel pipelines spaced 0.5 m apart are...Ch. 4 - A small water droplet of diameter D=100m and...Ch. 4 - A tube of diameter 50 mm having a surface...Ch. 4 - Pressurized steam at 450K flows through a long,...Ch. 4 - The temperature distribution in laser-irradiated...Ch. 4 - Hot water at 85°C flows through a thin-walled...Ch. 4 - A furnace of cubical shape, with external...Ch. 4 - Laser beams are used to thermally process...Ch. 4 - A double-glazed window consists of two sheets of...Ch. 4 - A pipeline, used for the transport of crude oil,...Ch. 4 - A long power transmission cable is buried at a...Ch. 4 - A small device is used to measure the surface...Ch. 4 - A cubical glass melting furnace has exterior...Ch. 4 - An aluminum heat sink (k=240W/mK), used to cool an...Ch. 4 - Hot water is transported from a cogeneration power...Ch. 4 - A long constantan wire of 1-mm diameter is butt...Ch. 4 - A hole of diameter D=0.25m is drilled through the...Ch. 4 - In Chapter 3 we that, whenever fins are attached...Ch. 4 - An igloo is built in the shape of a hemisphere,...Ch. 4 - Prob. 4.34PCh. 4 - An electronic device, in the form of a disk 20 mm...Ch. 4 - The elemental unit of an air heater consists of a...Ch. 4 - Prob. 4.37PCh. 4 - Prob. 4.38PCh. 4 - Prob. 4.39PCh. 4 - Prob. 4.40PCh. 4 - One of the strengths of numerical methods is their...Ch. 4 - Determine expressionsfor...Ch. 4 - Consider heat transfer in a one-dimensional...Ch. 4 - In a two-dimensional cylindrical configuration,...Ch. 4 - Upper and lower surfaces of a bus bar are...Ch. 4 - Derive the nodal finite-difference equations for...Ch. 4 - Consider the nodal point 0 located on the boundary...Ch. 4 - Prob. 4.48PCh. 4 - Prob. 4.49PCh. 4 - Consider the network for a two-dimensional system...Ch. 4 - An ancient myth describes how a wooden ship was...Ch. 4 - Consider the square channel shown in the sketch...Ch. 4 - A long conducting rod of rectangular cross section...Ch. 4 - A flue passing hot exhaust gases has a square...Ch. 4 - Steady-state temperatures (K) at three nodal...Ch. 4 - Functionally graded materials are intentionally...Ch. 4 - Steady-state temperatures at selected nodal points...Ch. 4 - Consider an aluminum heat sink (k=240W/mK), such...Ch. 4 - Conduction within relatively complex geometries...Ch. 4 - Prob. 4.60PCh. 4 - The steady-state temperatures (°C) associated with...Ch. 4 - A steady-state, finite-difference analysis has...Ch. 4 - Prob. 4.63PCh. 4 - Prob. 4.64PCh. 4 - Consider a two-dimensional. straight triangular...Ch. 4 - A common arrangement for heating a large surface...Ch. 4 - A long, solid cylinder of diameter D=25mm is...Ch. 4 - Consider Problem 4.69. An engineer desires to...Ch. 4 - Prob. 4.71PCh. 4 - Prob. 4.72PCh. 4 - Prob. 4.73PCh. 4 - Refer to the two-dimensional rectangular plate of...Ch. 4 - The shape factor for conduction through the edge...Ch. 4 - Prob. 4.77PCh. 4 - A simplified representation for cooling in very...Ch. 4 - Prob. 4.84PCh. 4 - A long trapezoidal bar is subjected to uniform...Ch. 4 - Consider the system of Problem 4.54. The interior...Ch. 4 - A long furnace. constructed from refractory brick...Ch. 4 - A hot pipe is embedded eccentrically as shown in a...Ch. 4 - A hot liquid flows along a V-groove in a solid...Ch. 4 - Prob. 4S.5PCh. 4 - Hollow prismatic bars fabricated from plain carbon...
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- 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_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_forward1.10 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_forward
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- 8--The reactor from uniform carbide and graphite as a cylinder rod with diameter of 12 mm. The volumetric heat liberationis 3.88x108 W/m3 The thermal conductivity of the rod material is 85 W/mC.. Determine the heat losses from the rod and the surface temperature if the maximum temperature of the rod is 200C...Ans Tw=1940 C,,Heat losses=1.164 MW/m2.arrow_forwardPlease include a fbd of the problemarrow_forwardA pipe wall with inner and outer radii r, and ro, whose temperatures are kept in Tj and To, is discussed. The heat transfer coefficient of the cylinder depends on the temperature, and k = ko (1 + aT) relationship can be written, where k, and a are constant. Subtract an equation for the heat passing through the unit length of the pipe. What is the thermal resistance of the pipe wall.arrow_forward
- As a researcher in the field of heat transfer, how will you distinguish between radiation by black body and a real body? Explain briefly Point out and briefly explain the various factors affect the thermal conductivity of a material. What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness t1, t2, t3 respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab. Based upon the reradiating properties of absorptivity, reflectivity and transmissivity, how would you distinguish between the following:Black body, white body, transparent body and opaque body. The nature of surfaces affects the absorption and the reflection of…arrow_forwardI need the answer as soon as possiblearrow_forwardDiagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.arrow_forward
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