Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 2, Problem 2.46P
To determine
The condition of heat conduction and the variation of heat flux and heat rate with radius.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
PROBLEM 3
In the given schematic of heat transfer for a wall, there is heat conduction through the wall
and the outer surface of the wall is subject to both convection and radiation.
T₁ = 308 K
k = 0.3 W/m-K
L = 3 mm
-T₁
-ε = 0.95
111
Air
Tsur = 297 K
T = 297 K
h = 2 W/m² K (Air)
(a) Write the energy conservation equation for the system in terms of the three heat
transfer modes.
(b) Find the surface temperature Ts in °C.
Shown in the figure below is an insulated copper block that receives energy at a rate of 200 W from an
embedded resistor. The temperature of the resistor is 34°C above the temperature of the copper block.
Insulation
Δt =
Resistor
5000000000000000000000
oooooooooooooo.......
Copper block
If the block has a volume of 10-3 m³ and an initial temperature of 20°C, how long
would it take, in minutes, for the temperature to reach 88°C?
-V=10-³ m³
T₁ = 20°C
min
The 1-4-7 surface in the section shown in the figure is insulated. The heat transfer coefficient on the
surface 1-2-3 is 28W /m? °C. The thermal conductivity of the solid material is 5.2W / m°C. Calculate the
temperatures of the points 1, 2, 4 and 5 using the finite difference method.
insulated
T = 0°C
30 cm
h = 28 W/m?. C+
30 cm
T, = T3 = T, = 38°C
T3 = T6 = 10°C
00
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
- 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_forward1.10 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_forward1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.arrow_forward
- 1.4 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_forwardI am struggling with this question. Part a and barrow_forwardA bar of thermal conductivity k = 140 W/m ⋅ K is of a trapezoidal cross section asshown in the schematic. The left and right faces are at temperatures Th = 100°Cand Tc = 0°C, respectively. Determine the heat transfer rate per unit bar lengthusing a finite difference approach with ∆X = ∆y = 10 mm. Compare the heat rate tothat of a bar of a 20 mm × 30 mm rectangular cross section where the height of thedomain is 20 mm.arrow_forward
- ähäi 100 Q1: Consider a long resistance wire of radius r1 = 0.3 cm and thermal conductivity kwire = %3D 17 W/m•°C in which heat is generated uniformly as a result of resistance heating at a constant rate of q = 100 W/cm3 (see Figure below). The wire is embedded in a 1-cm- thick layer of ceramic whose thermal conductivity is kceramic =1 W/m.°C. If the center temperature of the resistance wire is measured to be Tc= 705°C, determine the temperatures at the surface of ceramic and the interface of the wire and the ceramic layer under steady conditions.arrow_forward1250 W/m and a = 90 W/m2 and the ég An infinite wall that has a thickness of L = 0.22 m has a uniform heat generation of thermal conductivity of k = 20 W/m-°C. At x = 0 the heat flux going into the wall is temperature of the surface at x = L is T = 42 °C. Find an equation for the steady state temperature distribution in this wall as a function of the position x. Also find the value of the temperature at x = 0. ég k do x= 0 x = Larrow_forwardwhat is the temperature T at distance X = L1 = 8 cm under the steady-state condition?arrow_forward
- Q1: Consider one-dimensional conduction in a plane composite wall (Im x Im) as shown in the figure below. The outer surfaces are exposed to a fluid at 25°C and a convection heat transfer coefficient of 1000 W/m K. The middle wall B experiences uniform heat generation dg, while there is no generation in walls A and C. The temperatures at the interfaces are T=261°C and T; -211°C. Assuming negligible contact resistance at the interfaces: A) Determine the outside surface temperature of walls A and C? B) Compute the value of dg? (20 M) A B. ーム k= 25 Wim-K A = 50 W/m-K L = 30 mm Le= 30 mm L = 20 mm %3Darrow_forwardThe temperature distribution across a wall 0.25 m thick at a certain instant of time is T(x) = a + bx + cx², where T is in degrees Celsius and x is in meters, a = 200 C, b = -200 C/m, and c = 30 C/m². The wall has a thermal conductivity of 2.5 W/m.K. (a) Determine the heat flux into and out of the wall (q"in and q'out). (b) If the cold surface is exposed to a fluid at 100 C, what is the convection coefficient h? - Degree Celsius 200°C q" In- q'in q'out= h = Choose... Choose.... Choose... L₂x K = 2.5 W/m.k T(x)-200-200 x +30x² q" Out 142.7 C 11 L=0.25 m Fluid Too = 100 °C harrow_forward(A) Consider a plane wall of thickness L and thermal conductivity k. The two sides of the wall are maintained at constant temperatures of T1 and T2 respectively. Show that the temperature distribution through the wall is represented as Т, - Т, T = - x + x+T| L Assume one dimensional steady state heat conductionarrow_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