Introduction to Heat Transfer
6th Edition
ISBN: 9780470501962
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
Videos
Question
Chapter 3, Problem 3.126P
(a)
To determine
Proposed cooling scheme is satisfactory or not.
(b)
To determine
Rate of heat to transfers the heat from each blade to coolant.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A 1-D conduction heat transfer problem with internal energy generation is governed by the following equation:
+-=
dx2 =0
W
where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that
m-K
T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the
temperature at nodes 3 and 4.
Insulated
Ar
, T
For the answer window, enter the temperature at node 4 in Kelvin (K).
Your Answer:
EN
SORN
Answer
units
Pri
qu) 232 PM
4/27/2022
99+
66°F Sunny a .
20
ENLARGED
oW TEXTURE
PRT SCR
IOS
DEL
F8
F10
F12
BACKSPACE
num
-
%3D
LOCK
HOME
PGUP
170
3. A thin metallic wire of thermal conductivity k, diameter D, and length 2L is annealed by passing
an electrical current through the wire to induce a uniform volumetric heat generation åg. The
ambient air around the wire is at a temperature To, while the ends of the wire at x
A solid cylinder of radius R and length L is made from material with thermal conductivity 2.
Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time).
(a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature
distribution in the cylinder, given that the surface temperature is Ts.
(b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and
length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat
generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The
external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along
the axis of the mouse, as in part a.)
Chapter 3 Solutions
Introduction to Heat 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 - Prob. 3.7PCh. 3 - A t=10-mm-thick horizontal layer of water has a...Ch. 3 - Prob. 3.9PCh. 3 - The wind chill, which is experienced on a cold,...
Ch. 3 - Prob. 3.11PCh. 3 - A thermopane window consists of two pieces of...Ch. 3 - A house has a composite wall of wood, fiberglass...Ch. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 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...Ch. 3 - Prob. 3.21PCh. 3 - In the design of buildings, energy conservation...Ch. 3 - Prob. 3.23PCh. 3 - Prob. 3.24PCh. 3 - Prob. 3.25PCh. 3 - A composite wall separates combustion gases at...Ch. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - Prob. 3.29PCh. 3 - The performance of gas turbine engines may...Ch. 3 - A commercial grade cubical freezer, 3 m on a...Ch. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - A batt of glass fiber insulation is of density...Ch. 3 - Air usually constitutes up to half of the volume...Ch. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - The diagram shows a conical section fabricatedfrom...Ch. 3 - Prob. 3.40PCh. 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 - Prob. 3.43PCh. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - To maximize production and minimize pumping...Ch. 3 - A thin electrical heater is wrapped around the...Ch. 3 - Prob. 3.50PCh. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - A wire of diameter D=2mm and uniform temperatureT...Ch. 3 - Prob. 3.54PCh. 3 - Electric current flows through a long rod...Ch. 3 - Prob. 3.56PCh. 3 - A long, highly polished aluminum rod of diameter...Ch. 3 - Prob. 3.58PCh. 3 - Prob. 3.59PCh. 3 - Prob. 3.60PCh. 3 - Prob. 3.61PCh. 3 - Prob. 3.62PCh. 3 - Consider the series solution, Equation 5.42, for...Ch. 3 - Prob. 3.64PCh. 3 - Copper-coated, epoxy-filled fiberglass circuit...Ch. 3 - Prob. 3.66PCh. 3 - A constant-property, one-dimensional Plane slab of...Ch. 3 - Referring to the semiconductor processing tool of...Ch. 3 - Prob. 3.69PCh. 3 - Prob. 3.70PCh. 3 - Prob. 3.71PCh. 3 - The 150-mm-thick wall of a gas-fired furnace is...Ch. 3 - Steel is sequentially heated and cooled (annealed)...Ch. 3 - Prob. 3.74PCh. 3 - Prob. 3.75PCh. 3 - Prob. 3.76PCh. 3 - Prob. 3.77PCh. 3 - Prob. 3.78PCh. 3 - The strength and stability of tires may be...Ch. 3 - Prob. 3.80PCh. 3 - Prob. 3.81PCh. 3 - A long rod of 60-mm diameter and thermophysical...Ch. 3 - A long cylinder of 30-min diameter, initially at a...Ch. 3 - Work Problem 5.47 for a cylinder of radius r0 and...Ch. 3 - Prob. 3.85PCh. 3 - Prob. 3.86PCh. 3 - Prob. 3.87PCh. 3 - Prob. 3.88PCh. 3 - Prob. 3.89PCh. 3 - Prob. 3.90PCh. 3 - Prob. 3.91PCh. 3 - Prob. 3.92PCh. 3 - In Section 5.2 we noted that the value of the Biot...Ch. 3 - Prob. 3.94PCh. 3 - Prob. 3.95PCh. 3 - Prob. 3.96PCh. 3 - Prob. 3.97PCh. 3 - Prob. 3.98PCh. 3 - Work Problem 5.47 for the case of a sphere of...Ch. 3 - Prob. 3.100PCh. 3 - Prob. 3.101PCh. 3 - Prob. 3.102PCh. 3 - Prob. 3.103PCh. 3 - Consider the plane wall of thickness 2L, the...Ch. 3 - Problem 4.9 addressed radioactive wastes stored...Ch. 3 - Prob. 3.106PCh. 3 - Prob. 3.107PCh. 3 - Prob. 3.108PCh. 3 - Prob. 3.109PCh. 3 - Prob. 3.110PCh. 3 - A one-dimensional slab of thickness 2L is...Ch. 3 - Prob. 3.112PCh. 3 - Prob. 3.113PCh. 3 - Prob. 3.114PCh. 3 - Prob. 3.115PCh. 3 - Derive the transient, two-dimensional...Ch. 3 - Prob. 3.117PCh. 3 - Prob. 3.118PCh. 3 - Prob. 3.119PCh. 3 - Prob. 3.120PCh. 3 - Prob. 3.121PCh. 3 - Prob. 3.122PCh. 3 - Consider two plates, A and B, that are each...Ch. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.125PCh. 3 - Prob. 3.126PCh. 3 - Prob. 3.127PCh. 3 - Prob. 3.128PCh. 3 - Prob. 3.129PCh. 3 - Consider the thick slab of copper in Example 5.12,...Ch. 3 - In Section 5.5, the one-term approximation to the...Ch. 3 - Thermal energy storage systems commonly involve a...Ch. 3 - Prob. 3.133PCh. 3 - Prob. 3.134PCh. 3 - Prob. 3.135PCh. 3 - A tantalum rod of diameter 3 mm and length 120 mm...Ch. 3 - A support rod k=15W/mK,=4.0106m2/s of diameter...Ch. 3 - Prob. 3.138PCh. 3 - Prob. 3.139PCh. 3 - A thin circular disk is subjected to induction...Ch. 3 - An electrical cable, experiencing uniform...Ch. 3 - Prob. 3.142PCh. 3 - Prob. 3.145PCh. 3 - Consider the fuel element of Example 5.11, which...Ch. 3 - Prob. 3.147PCh. 3 - Prob. 3.148PCh. 3 - Prob. 3.149PCh. 3 - Prob. 3.150PCh. 3 - In a manufacturing process, stainless steel...Ch. 3 - Prob. 3.153PCh. 3 - Carbon steel (AISI 1010) shafts of 0.1-m diameter...Ch. 3 - A thermal energy storage unit consists of a large...Ch. 3 - Small spherical particles of diameter D=50m...Ch. 3 - A spherical vessel used as a reactor for producing...Ch. 3 - Batch processes are often used in chemical and...Ch. 3 - Consider a thin electrical heater attached to a...Ch. 3 - An electronic device, such as a power transistor...Ch. 3 - Prob. 3.161PCh. 3 - In a material processing experiment conducted...Ch. 3 - Prob. 3.165PCh. 3 - Prob. 3.166PCh. 3 - Prob. 3.167PCh. 3 - Prob. 3.168PCh. 3 - Prob. 3.173PCh. 3 - Prob. 3.174PCh. 3 - Prob. 3.175PCh. 3 - Prob. 3.176PCh. 3 - Prob. 3.177P
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_forward1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.arrow_forward6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/shas insulated ends and lateral sides. The bar has initial temperature in (C) given by u(x, o) = 10 + 4x 0< x< 10 u( x,0) = = 90 - 4x 10 < x< 20 (a) Model an initial-boundary value problem [IBVP] of the heat equation from the above statement.arrow_forward
- Drive an expression for heat transfer and temperature distribution for steady state one dimensional heat conduction in a plan wall. The temperature is maintained at a temperature Ti at x=0, while the other face X-L is maintained at temperature T2, the thickness of the wall may be taken as L and the energy equation is given by: d²T/dx² = 0. : Sketch a simple diagram for the temperature distribution in plane wall for a steady state one dimensional heat conduction, with heat generation. The surface temperature of the walls Ti and T2, for the cases Ti>T2, T1-T2, and T2>T1. The thickness of the wall may be taken as 2Larrow_forwardFig. 4 illustrates an insulating wall of three homogeneous layers with conductivities k1, k2, and k3 in intimate contact. Under steady state conditions, both right and left surfaces are exposed to a temperature in a steady state condition at ambient temperatures of T and T , respectively, while ß, and BLare the film coefficients respectively. Assume that there is no internal heat generation and that the heat flow is one-dimensional (dT/dy = 0). For the illustrated ambient temperature in Fig. 4, determine the temperature's distribution at each layer. Material 3 Material 1 Material 2 T= 100 T= 35 °C Kı=20 K3=50 (W/m.k) K3=30 (W/m.k) B1= 10 w/m² °K (W/m.k) BR= 15 w/m²°K 50 mm 35 mm 25 cm Fig. 4arrow_forward(a) Consider nodal configuration shown below. (a) Derive the finite-difference equations under steady-state conditions if the boundary is insulated. (b) Find the value of Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k = = W 3 m. k . Ay m-1, n m, n | Δx=" m, n+1 m, n-1 The side insulatedarrow_forward
- Please provide accurate answer with proper steps The wall of the furnace is 30.48 mm thick and is insulated from outside. Thermal conductivity of the wall material is 0.1 W/m K and the insulation material is 0.01 W/m K. The furnace operates at 650 0C and the ambient temperature is 30 0 Allowable temperature on the outer side of the insulation is 1000C. Determine the overall heat transfer by conduction per unit area occurring across a furnace wall made from clay. If the air side heat transfer coefficient is 0.4 W/m2 K, calculate the minimum insulation thickness requirement.arrow_forwardA very long, rectangular cross-section block is made from metal with the following properties: thermal conductivity = 130 W/mK, density = 2771 kg/m³, and specific heat capacity = 703 J/kgK. Initially all 4 sides of the cross section are maintained at 373 K. Then the temperature of one side is suddenly increased to 473 K. The temperature profile in the block will be investigated using an explicit finite difference model. If the time step is fixed at 5.5 seconds, what is the limit for node spacing that should be used to ensure stability of the solution? Give your numerical answer in mm to 1 decimal place.arrow_forward(a) Consider nodal configuration shown below. (a) Derive the finite-difference equations under steady-state conditions if the boundary is insulated. (b) Find the value of Tm,n if you know that Tm, n+1= 12 °C, Tm, n-1 = 8 °C, Tm-1, n = 10 °C, Ax = Ay = 10 mm, and k = W 3 m. k Ay m-1, n 11- m2, 11 m, n+1 m, n-1 The side insulatedarrow_forward
- Consider the square channel shown in the sketch operating under steady state condition. The inner surface of the channel is at a uniform temperature of 600 K and the outer surface is at a uniform temperature of 300 K. From a symmetrical elemental of the channel, a two-dimensional grid has been constructed as in the right figure below. The points are spaced by equal distance. Tout = 300 K k = 1 W/m-K T = 600 K (a) The heat transfer from inside to outside is only by conduction across the channel wall. Beginning with properly defined control volumes, derive the finite difference equations for locations 123. You can also use (n, m) to represent row and column. For example, location Dis (3, 3), location is (3,1), and location 3 is (3,5). (hint: I have already put a control volume around this locations with dashed boarder.) (b) Please use excel to construct the tables of temperatures and finite difference. Solve for the temperatures of each locations. Print out the tables in the spread…arrow_forward2. Consider the temperature distributions associated with a dx differential control volume within the one-dimensional plane walls shown below. T(x,00) T\x,00) * dx * dx (a) (Б) Tx,1) T(x,1) * dx dx (c) (d) (a) Steady-state conditions exist. Is thermal energy being generated within the differential control volume? If so, is the generation rate positive or negative? (b) Steady-state conditions exist as in part (a). Is the volumetric generation rate positive or negative within the differential control volume? (c) Steady-state conditions do not exist, and there is no volumetric thermal energy generation. Is the temperature of the material in the differential control volume increasing or decreasing with time? (d) Transient conditions exist as in part (c). Is the temperature increasing or decreasing with time?arrow_forwardExperiment: A cooling tower uses forced air and column packing to cool downward-flowing water. Inlet water temperature and water flow rate are varied to investigate effects on outlet water temperature, outlet air temperature, and outlet air humidity. The system is first observed operating with ambient room temperature water. A heat load is then applied to the water tank, and the system response is observed. This is to simulate a power plant starting up and placing a cooling load on the cooling water supply. The aim is to compare the system response with and without the load. Data from the Experiment and the make-up water mass flow rate are both shown in the following tables below. For the load cases, determine the net rate of water evaporation from the cooling water to the air using the equation for air flow rate. Compare this with the rate at which make-up water enters the system. For the load cases, determine the rate of work supplied by the pump and compare it to the pump power…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