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
Textbook Question
Chapter 2, Problem 2.20P
Consider a small but known volume of metal that has a large thermal conductivity.
- Since the thermal conductivity is large, spatial temperature gradients that develop within the metal in response to mild heating are small. Neglecting spatial temperature gradients, derive a differential equation that could be solved for the temperature of the metal versus time T(t) if the metal is subjected to a fixed surface heat rate q supplied by an electric heater.
- A student proposes to identify the unknown metal by comparing measured and predicted thermal responses. Once a match is made, relevant thermo-physical properties might be determined, and, in turn. the metal may be identified by comparison to published property data. Will this approach work? Consider aluminum, gold. and silver as the candidate metals.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The composite wall of an oven consists of three materials, two of which are of knownthermal conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and known thickness, LA =0.30 m and LC = 0.15 m. The third material, B, which is sandwiched between materialsA and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB.Under steady – state operating conditions, measurements reveal an outer surfacetemperature of 600 oC, and an oven air temperature of 800 oC. The inside convectioncoefficient h is known to be 25 W/m2 – K. total rate of heat transfer = 550 W/m2.What is the value of kB?
Write one dimensional steady state conduction heat transfer equation. By using this equation derive the expression of one dimensional heat transfer rate across a Wall of thickness "t" and isothermal surface temperatures T1 and T2 on both sides of the wall considering thermal conductivity "k" as constant . Also tell what effect comes on the temperature distribution across the wall if the thermal conductivity varies with temperature.
: Consider a perfectly insulated thin rod of arbitrary finite length, rod is heated with extenal heat
source q(t), assuming that temperature in the rod is uniformly distributed and initially the rod has constant
room temperature.
a) Model the problem mentioned in the statement
b) Solve the modeled problem by suitable method
c) Classify the resulting pde and its boundary conditions
Chapter 2 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - Assume steady-state, one-dimensional conduction in...Ch. 2 - A hot water pipe with outside radius r, has a...Ch. 2 - A spherical shell with inner radius r1 and outer...Ch. 2 - Assume steady-state, one-dimensional heat...Ch. 2 - A composite rod consists of two different...Ch. 2 - A solid, truncated cone serves as a support for a...Ch. 2 - To determine the effect of the temperature...Ch. 2 - A young engineer is asked to design a thermal...Ch. 2 - A one-dimensional plane wall of thickness 2L=100mm...
Ch. 2 - Consider steady-state conditions for...Ch. 2 - Consider a plane wall 100 mm thick and of thermal...Ch. 2 - A cylinder of radius ro, length L, and thermal...Ch. 2 - In the two-dimensional body illustrated, the...Ch. 2 - Consider the geometry of Problem 2.14 for the case...Ch. 2 - Steady-state, one-dimensional conduction occurs in...Ch. 2 - An apparatus for measuring thermal conductivity...Ch. 2 - An engineer desires to measure the thermal...Ch. 2 - Consider a 300mm300mm window in an aircraft. For a...Ch. 2 - Consider a small but known volume of metal that...Ch. 2 - Use INT to perform the following tasks. Graph the...Ch. 2 - Calculate the thermal conductivity of air,...Ch. 2 - A method for determining the thermal conductivity...Ch. 2 - Compare and contrast the heat capacity cp of...Ch. 2 - A cylindrical rod of stainless steel is insulated...Ch. 2 - At a given instant of time, the temperature...Ch. 2 - A pan is used to boil water by placing it on a...Ch. 2 - Uniform internal heat generation at q=5107W/m3 is...Ch. 2 - Consider a one-dimensional plane wall with...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - The temperature distribution across a wall 0.3 m...Ch. 2 - Prob. 2.33PCh. 2 - One-dimensional, steady-state conduction with...Ch. 2 - Derive the heat diffusion equation, Equation 2.26,...Ch. 2 - Derive the heat diffusion equation, Equation 2.29....Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - One-dimensional, steady-state conduction with no...Ch. 2 - The steady-state temperature distribution in a...Ch. 2 - Prob. 2.41PCh. 2 - Prob. 2.42PCh. 2 - cylindrical system illustrated has negligible...Ch. 2 - Beginning with a differential control volume in...Ch. 2 - Prob. 2.45PCh. 2 - Prob. 2.46PCh. 2 - For a long circular tube of inner and outer radii...Ch. 2 - Passage of an electric current through a long...Ch. 2 - Two-dimensional. steady-state conduction occurs in...Ch. 2 - An electric cable of radius r1 and thermal...Ch. 2 - A spherical shell of inner and outer radii ri and...Ch. 2 - A chemically reacting mixture is stored in a...Ch. 2 - A thin electrical heater dissipating 4000W/m2 is...Ch. 2 - The one-dimensional system of mass M with constant...Ch. 2 - Consider a one-dimensional plane wall of thickness...Ch. 2 - A large plate of thickness 2L is at a uniform...Ch. 2 - The plane wall with constant properties and no...Ch. 2 - Consider the steady-state temperature...Ch. 2 - A plane wall has constant properties, no internal...Ch. 2 - A plane wall with constant properties is initially...Ch. 2 - Consider the conditions associated with Problem...Ch. 2 - Consider the steady-state temperature distribution...Ch. 2 - A spherical particle of radius r1 experiences...Ch. 2 - Prob. 2.64PCh. 2 - A plane wall of thickness L=0.1m experiences...Ch. 2 - Prob. 2.66PCh. 2 - A composite one-dimensional plane wall is of...Ch. 2 - Typically, air is heated in a hair dryer by...Ch. 2 - Prob. 2.69P
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
- 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?arrow_forwardA plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.arrow_forward3.9 The heat transfer coefficients for the flow of 26.6°C air over a sphere of 1.25 cm in diameter are measured by observing the temperature-time history of a copper ball the same dimension. The temperature of the copper ball was measured by two thermocouples, one located in the center and the other near the surface. The two thermocouples registered, within the accuracy of the recording instruments, the same temperature at any given instant. In one test run, the initial temperature of the ball was 66°C, and the temperature decreased by 7°C in 1.15 min. Calculate the heat transfer coefficient for this case.arrow_forward
- A food product containing a water content of 85% is frozen. Estimate the heat type products at -10 °C when 82% of the water is in its frozen state. Hot product type dry is 2.5 kJ/(kg °C) is assumed to heat this type of water at -10 °C is equal to heat water type at 0 °C, and the heat of the types of ice follow function Cp ice = 0 0062 x T frozen + 2 0649. a. Cp frozen products kJ/kg °C.arrow_forwardA vertical cylinder 6 ft tall and 1 ft in diameter might be used to approximate a man for heat-transfer purposes. Suppose the surface temperature of the cylinder is 78°F, h=2 Btu/h · ft2 . °F, the surface emissivity is 0.9, and the cylinder is placed in a large room where the air temperature is 68°F and the wall temperature is 45°F. Calculate the heat lost from the cylinder. Repeat for a wall temperature of 80°F. What do you conclude from these calculations?arrow_forwardYou are tasked to design a cooling system for an ice rink. A standard ice rink has surface area ofArink = 1580 m2 . In this design, a technologically advanced solid state thermoelectric generatingcooling plate is placed in between concrete slabs. The following diagram contains the dimensionalparameters of the design (a) In the space below, with your best effort to correspond to the above diagram, draw a thermalcircuit that establishes the relationship between the cooling plate’s heat rate, Q, and the system’stemperatures and thermal resistances. Label the appropriate dimensions, thermal conductivities,convection coefficient, and temperatures. Ignore effects from contact resistance. (b) Given that the temperature at the top surface of the ice must be T ice = -5°C, obtain the requiredheat rate Q that must be drawn by the cooling plate in units Kilowatts. Be careful of +/- sign.Answer: ____________________________ [kW] c) Using the thermal circuit you established in Part (a), obtain the…arrow_forward
- Question 2: The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA 20 W/m K and kC50 W/m K, and known thickness, LA 0.30 m and LC 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o 20°C, an inner surface temperature of Ts,i 600°C, and an oven air temperature of T 800°C. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of kB?arrow_forwardUsing Gauss-Seidel iteration method, determine the temperatures at nodes 1, 2, 3 and 4.Estimate the midpoint temperature.arrow_forwardb. A large potato is dropped into a pot of boiling water and allowed to boil for half an hour. Which type of system does this represent Lumped or distributed parameter? Provide a reason for your choice .. Comment on temperature distributions. (ii.)arrow_forward
arrow_back_ios
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
Power Plant Explained | Working Principles; Author: RealPars;https://www.youtube.com/watch?v=HGVDu1z5YQ8;License: Standard YouTube License, CC-BY