Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 4, Problem 4.54P
A flue passing hot exhaust gases has a square cross section, 300 mm to a side. The walls are constructed of refractory brick 150 mm thick with a thermal conductivity of
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Problem 1
A hot water pipe is used for domestic applications is insulated with a layer of calcium silicate. If the
insulation is 25 mm thick and its inner and outer surfaces are maintained at Ts,1 = 800 K and Ts,2 = 400 K,
respectively. The outside diameter is 0.12 m. Given the thermal conductivity calcium silicate insulation
equals to 0.09 W/m.K.
A. Define the difference between lagged and unlagged pipes.
B. Calculate the heat loss per unit length for this pipe.
A steel tube having k =46W/m•C has an inside diameter of 3.0 cm and a tube wall thickness of 2 mm
is covered with a 3-cm layer of asbestos insulation [k =0.2 WN/m•C]. A fluid flows maintains inside tube
surface temperature 223•C while the outside surface insulation temperature is 57 C. Calculate the
heat lost by the tube per meter of length and what in the tube-insulator interface temperature?
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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- need fastarrow_forwardAn overhead 65-m-long, uninsulated industrial steam pipe of 80 mm diameter is routed through a building whose walls and air are at 30 °C. Pressurized steam maintains a pipe surface temperature of 200 "C, and the coefficient associated with natural convection is h = 15 W/m'K. The surface emissivity is e= steam line? 0.6. What is the rate of heat loss from thearrow_forwardHEAT TRANSFER: A thick-walled nuclear coolant pipe (k = 12.5 Btu/hr-ft-°F) with 10 in. inside diameter and 12 in. outside diameter is covered with a 3 in. layer of asbestos insulation (k 0.14 = Btu/hr-ft-°F). If the inside wall temperature of the pipe is maintained at 550°F, (a) calculate the heat loss per foot of length. The outside temperature is 100°F. (b) Find the interface temperature between the pipe and the insulation.arrow_forward
- I need the answer as soon as possiblearrow_forwardW m.K W m².K' W An insulation material of thermal conductivity k = 0.05; is sandwiched between thin metal sheets of negligible thickness. It is used as the material of the wall of a drying oven. The air inside the oven is 300°C with a convection heat transfer coefficient of 30 The inner wall surface is subjected to a constant radiant heat flux of 100 from hotter objects inside the oven. The air inside the room where the oven is situated has a temperature of 25°C and the combined heat transfer coefficient for W convection and radiation from the outer surface is 10- If the outer surface temperature of the oven m².K is safe to touch at a temperature of 40°C, what is the required rate of heat loss from the wall in ₂? W m²arrow_forwardDetermine the optimum thickness from an economic point of view, of insulation for a steam pipe 100 mm dia. at 465°C. The insulation conductivity is 1.55 x 10 kW/mK, the natural convection coefficient -4 on the insulation outer surface is 0.0112 kW/m2K, the insulation cost is £70/m³ plus a fixed charge of 160p. per metre run of pipe and the cost is to be spread over 5 veres. The oil fuel, of density 900 kg/m³, costs 1.lp. per litre and is used to raise steam in a boiler of 90% efficiency. The fuel calorific value is 41,000 kJ/Kg and the air temperature surrounding the insulation is 27°c.arrow_forward
- 1. A simple cavity wall consists of two brick layers separated by an air gap of 50 mm. If the inside air temperature is 20oC and the ambient outside temperature is 5 oC, calculate the heat flux through the wall. Bricks are 100 mm thick with thermal conductivity kbrick = 0.5 W/m K, hin = 10 W/m2 K, hout = 20 W/m2 K. The internal air cavity can be considered still (no convection) with kair = 0.015 W/m K. 2. On a day in winter, the outside air temperature drops to -5 oC and the outside convective heat transfer changes to hout = (2 x V) + 8.9 W/m2 K. If the outside wind speed gusts at 50 kph, calculate the change in heat flux for the wall in question 3.arrow_forwardCalculate the overall heat loss and the temperature profile for each interface if the length of the cylinder is 50 m.Please write your answers legibly.arrow_forwardIf the length of the cylinder is 50 m, calculate the overall heat loss and the temperature profile at each interface. Please write the solution legibly.arrow_forward
- Q8/ A 1.0mm diameter wire is maintained at a temperature of 400 C and exposed to a convection environment at 40°C. with h=20W/m.C. Calculate the thermal conductivity which will just cause an insulation thickness of 0.2mm to reduce a "critical radius". How much of this insulation must be added to reduce the heat transfer by 75% from that which would be experienced by the bare wire?arrow_forward6. Air flows at 120 o C in a thin-walled tube (k = 18 W/m o C) with h = 65 w/m 2 - o C. The inside diameter of the tube is 2.5 cm tand the thickness is 0.4 mm. The tube is exposed to an environment with h = 6.5 W/m 2 - o C and temperature of 15 o C. Calculate the the heat loss for 1 m length. What thickness of insulation having k = 40 W/m- 0 C should be added to reduce heat loss by 90 %.arrow_forward1. Heat Loss from saturated steam at 121.1°C. The line is covered with 25.4 mm of insulation. Assuming that the inside surface temperature of the metal wall is at 121.1°C and the outer sur- face of the insulation is at 26.7°C, calculate the heat loss for 30.5 m of pipe. Also, calculate the kg of steam condensed per hour in the pipe due to the heat loss. The average k for steel from Appendix A.3 is 45 W/m K and the k for the insulation is 0.182. a Steam Pipeline. A steel pipeline, 2-in. Schedule 40 pipe, contains A 381 Stearrow_forward
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