Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470501979
Author: Frank P. Incropera, David P. DeWitt, Theodore L. Bergman, Adrienne S. Lavine
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 3, Problem 3.34P
Ring-porous woods, such as oak, are characterized by grains. dark grains consist of very low-density material that forms early in the springtime. The surrounding lighter-colored wood is composed of high-density material that forms slowly throughout most of the growing season.
Assuming the low-density material is highly porous and the oak is dry, determine the fraction of the oak cross-section that appears as being grained. Hint: Assume the thermal conductivity parallel to the grains is the same as the radial conductivity of Table A.3.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Problem 1. (Taken from Bergman et.al. 2011*) An igloo is built in the shape of a hemisphere,
with an inner radius of 1.8 m and walls of compacted snow that are 0.5 m thick. On the inside of
the igloo the surface heat transfer coefficient is 6 W/m².K; on the outside, under normal wind
conditions, it is 15 W/m².K. The thermal conductivity of compacted snow is 0.15 W/m.K. The
temperature of the ice cap on which the igloo sits is -20 °C and has the same thermal conductivity
as the compacted snow.
Artic wind Too
Tair
Ice cap Tice
Igloo
Assuming that the occupants' body heat provides a continuous source of 320 W within the igloo,
calculate the inside air temperature when the outside air temperature is T∞ = -40 °C draw a thermal
circuit for the heat transfer from the igloo. Be sure to consider heat losses through the floor of igloo
where the heat transfer coefficient is 6 W/m²K.
I need answers with clear hand writing or using Microsoft word . ASAP
PROCEDURE: for (HEAT TRANSFER THROUGH COMPOSITE WALLS)
2. One end of a 40 cm metal rod 2.0 cm2
in cross section is in a steam bath while the other
end is embedded in ice. It is observed that 13.3 grams of ice melted in 15 minutes from the heat conducted by the rod. What is the thermal conductivity of the rod.
Chapter 3 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 3 - Consider the plane wall of Figure 3.1, separating...Ch. 3 - A new building to be located in a cold climate is...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - The rear window of an automobile is defogged by...Ch. 3 - A dormitory at a large university, built 50 years...Ch. 3 - In a manufacturing process, a transparent film is...Ch. 3 - The walls of a refrigerator are typically...Ch. 3 - A t=10-mm -thick horizontal layer of water has a...Ch. 3 - A technique for measuring convection heat transfer...Ch. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Determine the thermal conductivity of the carbon...Ch. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Consider the composite wall of Problem 3.13 under...Ch. 3 - Consider a composite wall that includes an...Ch. 3 - Work Problem 3.15 assuming surfaces parallel to...Ch. 3 - Consider the oven of Problem 1.54. The walls of...Ch. 3 - The composite wall of an oven consists of three...Ch. 3 - The wall of a drying oven is constructed by...Ch. 3 - The t=4-mm-thick glass windows of an automobile...Ch. 3 - The thermal characteristics of a small, dormitory...Ch. 3 - In the design of buildings, energy conservation...Ch. 3 - When raised to very high temperatures. many...Ch. 3 - A firefighter's protective clothing, referred to...Ch. 3 - A particular thermal system involves three objects...Ch. 3 - A composite wall separates combustion gases at...Ch. 3 - Approximately 106 discrete electrical components...Ch. 3 - Two stainless steel plates 10 mm thick are...Ch. 3 - Consider a plane composite wall that is composed...Ch. 3 - The performance of gas turbine engines may be...Ch. 3 - A commercial grade cubical freezer, 3 m on a side,...Ch. 3 - Physicists have determined the theoretical value...Ch. 3 - Consider a power transistor encapsulated in an...Ch. 3 - Ring-porous woods, such as oak, are characterized...Ch. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Determine the density, specific heat, and thermal...Ch. 3 - A one-dimensional plane wall of thickness L is...Ch. 3 - The diagram shows a conical section fabricated...Ch. 3 - A truncated solid cone is of circular cross...Ch. 3 - From Figure 2.5 it is evident that, over a wide...Ch. 3 - Consider a tube wall of inner and outer radii ri...Ch. 3 - Measurements show that steady-state conduction...Ch. 3 - A device used to measure the surface temperature...Ch. 3 - A steam pipe of 0.12-m outside diameter is...Ch. 3 - Consider the water heater described in Problem...Ch. 3 - To maximize production and minimize pumping costs....Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - A stainless steel (AISI 304) tube used to...Ch. 3 - A thin electrical heater is inserted between a...Ch. 3 - A 2-mm-diameter electrical wire is insulated by a...Ch. 3 - Electric current flows through a long rod...Ch. 3 - A composite cylindrical wall is composed of two...Ch. 3 - An electrical current of 700 A flows through a...Ch. 3 - A 0.20-m-diameter. thin-walled steel pipe is used...Ch. 3 - An uninsulated. thin-walled pipe of 100-mm...Ch. 3 - Steam flowing through a long. thin-walled pipe...Ch. 3 - A storage tank consists of a cylindrical section...Ch. 3 - Consider the liquid oxygen storage system and the...Ch. 3 - A spherical Pyrex glass shell has inside and...Ch. 3 - In Example 3.6. an expression was derived for the...Ch. 3 - A hollow aluminum sphere. with an electrical...Ch. 3 - A spherical tank for storing liquid oxygen on the...Ch. 3 - A spherical, cryosurgical probe may be imbedded in...Ch. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - A composite spherical shell of inner radius...Ch. 3 - The energy transferred from the anterior chamber...Ch. 3 - The outer surface of a hollow sphere of radius r2...Ch. 3 - A spherical shell of inner and outer radii r1 and...Ch. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The air inside a chamber at T,i=50C is heated...Ch. 3 - Prob. 3.80PCh. 3 - A plane wall of thickness 0.1 m and thermal...Ch. 3 - Large, cylindrical bales of hay used to feed...Ch. 3 - Prob. 3.83PCh. 3 - Consider one-dimensional conduction in a plane...Ch. 3 - Consider a plane composite wall that is composed...Ch. 3 - An air heater may be fabricated by coiling...Ch. 3 - Prob. 3.87PCh. 3 - Consider uniform thermal energy generation inside...Ch. 3 - A plane wall of thickness and thermal conductivity...Ch. 3 - A nuclear fuel element of thickness 21, is covered...Ch. 3 - In Problem 3.79 the strip heater acts to guard...Ch. 3 - The exposed surface (x=0) of a plane wall of...Ch. 3 - A quartz window of thickness L serves as a viewing...Ch. 3 - For the conditions described in Problem 1.44....Ch. 3 - A cylindrical shell of inner and outer radii, ri...Ch. 3 - The cross section of a long cylindrical fuel...Ch. 3 - A long cylindrical rod of diameter 200 mm with...Ch. 3 - A radioactive material of thermal conductivity k...Ch. 3 - Radioactive wastes are packed in a thin-walled...Ch. 3 - Radioactive wastes (ktw=20W/mK) are stored in a...Ch. 3 - Unique characteristics of biologically active...Ch. 3 - Consider the plane wall, long cylinder, and sphere...Ch. 3 - One method that is used to grow nanowires...Ch. 3 - Consider the manufacture of photovoltaic silicon,...Ch. 3 - Copper tubing is joined to a solar collector plate...Ch. 3 - A thin flat plate of length L thickness t. and...Ch. 3 - The temperature of a flowing gas is to be measured...Ch. 3 - A thin metallic wire of thermal conductivity k,...Ch. 3 - A motor draws electric power Pelec from a supply...Ch. 3 - Consider the fuel cell stack of Problem 158. The...Ch. 3 - Consider a rod of diameter D, thermal conductivity...Ch. 3 - A carbon nanotube is suspended across a trench of...Ch. 3 - A probe of overall length L=200mm and diameter...Ch. 3 - A metal rod of length 2L diameter D, and thermal...Ch. 3 - A very long rod of 5-mm diameter and uniform...Ch. 3 - From Problem 1.71, consider the wire leads...Ch. 3 - Turbine blades mounted to a rotating disc in a...Ch. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - A brass rod 100 mm long and 5 mm in diameter...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A pin fin of uniform. cross-sectional area is...Ch. 3 - The extent to which the tip condition affects the...Ch. 3 - A straight tin fabricated from 2024 aluminum alloy...Ch. 3 - Triangular and parabolic straight tins are...Ch. 3 - Two long copper rods of diameter D=10mm are...Ch. 3 - Circular copper rods of diameter D=1mm and length...Ch. 3 - During the initial stages of the growth of the...Ch. 3 - Consider two long, slender rods of the same...Ch. 3 - A 40-mm-long, 2-mm-diameter pin fin is fabricated...Ch. 3 - An experimental arrangement for measuring the...Ch. 3 - Finned passages are frequently formed between...Ch. 3 - The fin array of Problem 3.142 is commonly found...Ch. 3 - An isothermal silicon chip of width W=20mm on a...Ch. 3 - As seen in Problem 3.109, silicon carbide...Ch. 3 - A homeowner's wood stove is equipped with a top...Ch. 3 - Water is heated by submerging 50-mm-diameter,...Ch. 3 - As a means of enhancing heat transfer from...Ch. 3 - Consider design B of Problem 3.151. Over time....Ch. 3 - Determine the percentage increase in heat transfer...Ch. 3 - Aluminum fins of triangular profile are attached...Ch. 3 - An annular aluminum fin of rectangular profile is...Ch. 3 - Annular aluminum fins of rectangular profile are...Ch. 3 - It is proposed to air-cool the cylinders of a...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - A nanolaminated material is fabricated with an...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- I need answers with clear hand writing or using Microsoft word . ASAP INTRODUCTION: for (HEAT TRANSFER THROUGH COMPOSITE WALLS) note: i want a lot of informationarrow_forwardAn electrical resistance wire made of tungsten dissipates heat to the surroundings at a constant rate. Which of the following equations are you going to use to compute for the temperature at any point within the wire when the temperature throughout the whole wire no longer changes with time? Assume that the wire can be approximated as a thin cylinder. a. Fourier-Biot equation b. Poisson equation c. Diffusion equation d. Laplace equationarrow_forwardA square piece is initially at 10 degrees Celsius everywhere. Each side is 0.05 m long. Then the four sides are instantly heated up to 25 degrees Celsius, 50 degrees Celsius, 30 degrees Celsius, and 0 degrees Celsius. a. Find how long it takes for the temperature profile of this square to become steady if the material is copper. What is the final temperature at the center of the square? b. Find how long it takes for the temperature profile of this square to become steady if the material is air. What is the final temperature at the center of the square? c. Which material takes longer to reach steady state and why?arrow_forward
- Refer to Table 3.2 in the lecture and take the data for air, water (steam), and four other gases listed in the table. Plot the data in a graph with the thermal conductivity on the vertical axis and the temperature range from 200 K to 600 K on the horizontal axis. Use colors or different dashed lines to make the graph presentable and understandable. The graph should look like the graph in Figure 3.1 in the lecture. Provide a short explanation of the graph in three to five sentences.arrow_forwardBebang owns a 830-mm-thick concrete brick table top that has an area of 10,000,000 mm^2 and a 0.750-cm-thick glass plate that has an area of 20,000 cm^2. Assuming the same temperature difference across each, what is the ratio of the rate of heat conduction through the plate with respect to the rate of heat conduction through the table top? Use Table 10.1(given below) for the value of Thermal Conductivity k. Table 10.1 Thermat Conductivities of Common Substances Values are given for temperatures near o °C. Substance Thermal Conductivity k (W/m-O Diamond 2000 Silver 420 Copper 390 Gold 318 Aluminum 220 Steel iron Steel (stainless) 14 Ice 2.2 Glass (average) 0.84 Concrete brick O.84 water 0.6 Fatty tissue (without blood) 0.2 Asbestos 0.16 Plasterboard 0.16 wood 0.08-0.16 Snow (dry) 0.10 Cork 0.042 Glass wool 0.042 wool 0.04 Down feathers 0.025 Air 0.023 Polystyrene foam 0.010arrow_forwardQuestion 1 An industrial cold room has four 200 mm thick walls made of concrete. The walls are insulated on the outside with a layer of foam 60 mm thick. Cladding with a thickness of 15 mm protects the foam on the outside from the elements. The composite wall surface temperatures are -3 °C on the inside and 18 °C on the outside of the room respectively. The thermal conductivities of concrete, foam and cladding are 0.75, 0.35 and 0.5 W/m K respectively. a) Assuming perfect thermal contact between the layers of the composite walls, draw the typical temperature distribution across the layers and determine the heat energy gained per hour through all 4 walls of the room with a total surface area of 20 m². What does this heat energy represent in terms of the refrigeration system of the cold room? b) c) Without any calculations, how would you expect the internal and external air temperatures to be relative to the wall surface temperatures? Explain your answer. How do you expect the heat gain…arrow_forward
- I need answers with clear hand writing or using Microsoft word . ASAP INTRODUCTION: for (HEAT TRANSFER THROUGH COMPOSITE WALLS)arrow_forwardThe heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.arrow_forwardYou are asked to design an insulated stud timber wall and have the following materials available: Outer skin materials. ● Plasterboard 8 mm thick (k= 0.3 W/m.K) Plasterboard 12.5 mm thick (k = 0.3 W/m.K) Insulated Plasterboard 25 mm thick (k = 0.2 W/m.K) Timber studs available (k = 0.1 W/m.K) 50 mm x 100 mm 50 mm x 120 mm 50 mm x 150 mm Insulation layers Glass fibre insulation (k= 0.05 W/m.K) ● Polyisocyanurate insulation (k= 0.025 W/m.K) Sheeps wool insulation (k= 0.04 W/m.K) ● Wall construction should consist of two outer plasterboard skins, followed by an appropriate stud/insulation infill layer. Studs can be placed vertically at 400 mm or 600 mm intervals and you may ignore any requirement for horizontal studding. 1) Draw a plan (top view) cross section of your wall indicating dimensions, spacing and material choices. 2) Calculate the thermal resistance of your wall. 3) If the internal convective heat transfer coefficient in room one is 10 W/m²K and in the second room it is 15…arrow_forward
- Question 1 An industrial cold room has four 200 mm thick walls made of concrete. The walls are insulated on the outside with a layer of foam 60 mm thick. Cladding with a thickness of 15 mm protects the foam on the outside from the elements. The composite wall surface temperatures are -3 °C on the inside and 18 °C on the outside of the room respectively. The thermal conductivities of concrete, foam and cladding are 0.75, 0.35 and 0.5 W/m K respectively. a) Assuming perfect thermal contact between the layers of the composite walls, draw the typical temperature distribution across the layers and determine the heat energy gained per hour through all 4 walls of the room with a total surface area of 20 m². What does this heat energy represent in terms of the refrigeration system of the cold room?arrow_forwardMetal spheres, 10 mm in diameter, are to be annealed by heating them to 827°C then allowing them to cool slowly in air at 27°C to the point where they are in thermal equilibrium with the air. 2000 balls are annealed in one hour’s time. What is the total rate of their heat transfer if they are made of steel, lead, or copper? a.Sketch the problem. b.Draw lines identifying the control volume, or control mass. c.Identify the states with numbers, letters, or descriptions such as “in” and “out”. d.Write down the knowns and unknowns. e.Identify what is being asked for. f.State all assumptions.arrow_forwardAyy 1. For a brick in the shape of a finite cylinder with a triangular cross section (as is used at the junction of two orthogonal walls), with vertices at (0, 0, 0) m, (0, 0, 0.10) m, (0, 0.20, 0) m, (0, 0.20, 0.10) m. (0.20, 0, 0) m, and (0.20, 0, 0.10) m, the temperature distribution (in Cartesian coordinates) is I(z,y,z,1)= (8xy m-¹ +12yz m-¹ +9zts-¹) Cm-¹ Compute the heat transfer rate to the brick as a function of time. (Using the ME 300 sign convention, this will be a positive quantity if the net flow of heat is into the brick.) Use = 0.60 W/(m K).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning
Principles of Heat Transfer (Activate Learning wi...
Mechanical Engineering
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Cengage Learning
Understanding Conduction and the Heat Equation; Author: The Efficient Engineer;https://www.youtube.com/watch?v=6jQsLAqrZGQ;License: Standard youtube license