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
Videos
Textbook Question
Chapter 5, Problem 5.109P
A thin rod of diameter D is initially in equilibrium with its surroundings, a large vacuum enclosure at temperature
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
2. 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?
(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 insulated
(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 insulated
Chapter 5 Solutions
Fundamentals of Heat and Mass Transfer
Ch. 5 - Consider a thin electrical heater attached to a...Ch. 5 - The inner surface of a plane wall is insulated...Ch. 5 - A microwave oven operates on the principle that...Ch. 5 - A plate of thickness 2L, surface area As, mass M,...Ch. 5 - For each of the following cases, determine an...Ch. 5 - Steel balls 12 mm in diameter are annealed by...Ch. 5 - Consider the steel balls of Problem 5.6, except...Ch. 5 - The heat transfer coefficient for air flowing over...Ch. 5 - A solid steel sphere (AISI 1010), 300 mm in...Ch. 5 - A flaked cereal is of thickness 2L=1.2mm. The...
Ch. 5 - The base plate of an iron has a thickness of L=7mm...Ch. 5 - Thermal energy storage systems commonly involve a...Ch. 5 - A tool used for fabricating semiconductor devices...Ch. 5 - A copper sheet of thickness 2L=2mm has an initial...Ch. 5 - Carbon steel (AISI 1010) shafts of 0.1-m diameter...Ch. 5 - A thermal energy storage unit consists of a large...Ch. 5 - Small spherical particles of diameter D=50m...Ch. 5 - A spherical vessel used as a reactor for producing...Ch. 5 - Batch processes are often used in chemical and...Ch. 5 - An electronic device. such as a power transistor...Ch. 5 - Molecular electronics is an emerging field...Ch. 5 - A plane wall of a furnace is fabricated from plain...Ch. 5 - A steel strip of thickness =12mm is annealed by...Ch. 5 - In a material processing experiment conducted...Ch. 5 - Plasma spray-coating processes are often used to...Ch. 5 - The plasma spray-coating process of Problem 5.25...Ch. 5 - A chip that is of length L=5mm on a side and...Ch. 5 - Consider the conditions of Problem 5.27. In...Ch. 5 - A long wire of diameter D=1mm is submerged in an...Ch. 5 - Consider the system of Problem 5.1 where the...Ch. 5 - Shape memory alloys (SMAs) are metals that undergo...Ch. 5 - Before being injected into a furnace, pulverized...Ch. 5 - As noted in Problem 5.3, microwave ovens operate...Ch. 5 - A metal sphere of diameter D, which is at a...Ch. 5 - A horizontal structure consists of an LA=10...Ch. 5 - As permanent space stations increase in size....Ch. 5 - Thin film coatings characterized by high...Ch. 5 - A long. highly polished aluminum rod of diameter...Ch. 5 - Thermal stress testing is a common procedure used...Ch. 5 - The objective of this problem is to develop...Ch. 5 - In thermomechanical data storage, a processing...Ch. 5 - The melting of water initially at the fusion...Ch. 5 - Consider the series solution, Equation 5.42, for...Ch. 5 - Consider the one-dimensional wall shown in the...Ch. 5 - Copper-coated, epoxy-tilled fiberglass circuit...Ch. 5 - Circuit boards are treated by heating a stack of...Ch. 5 - A constant-property, one-dimensional plane slab of...Ch. 5 - Referring to the semiconductor processing tool of...Ch. 5 - Annealing is a process by which steel is reheated...Ch. 5 - Consider an acrylic sheet of thickness L=5mm that...Ch. 5 - The 150-mm-thick wall of a gas-fired furnace is...Ch. 5 - Steel is sequentially heated and cooled (annealed)...Ch. 5 - Stone mix concrete slabs are used to absorb...Ch. 5 - During transient operation, the steel nozzle of a...Ch. 5 - Two plates of the same material and thickness L...Ch. 5 - In a tempering process, glass plate, which is...Ch. 5 - The strength and stability of tires may be...Ch. 5 - A plastic coating is applied to wood panels by...Ch. 5 - A long rod of 60-mm diameter and thermophysical...Ch. 5 - A long cylinder of 30-mm diameter, initially at a...Ch. 5 - A long pyroceram rod of diameter 20 mm is clad...Ch. 5 - A long rod 40 mm in diameter, fabricated from...Ch. 5 - A cylindrical stone mix concrete beam of diameter...Ch. 5 - A long plastic rod of 30-mm diameter...Ch. 5 - As part of a heat treatment process, cylindrical,...Ch. 5 - In a manufacturing process, long rods of different...Ch. 5 - The density and specific heat of a particular...Ch. 5 - In heat treating to harden steel ball bearings...Ch. 5 - A cold air chamber is proposed for quenching steel...Ch. 5 - Stainless steel (AISI 304) ball bearings. which...Ch. 5 - A sphere 30 mm in diameter initially at 800K is...Ch. 5 - Spheres A and B are initially at 800K. and they...Ch. 5 - Spheres of 40-mm diameter heated to a uniform...Ch. 5 - To determine which parts of a spider's brain are...Ch. 5 - Consider the packed bed operating conditions of...Ch. 5 - Two large blocks of different materials. such as...Ch. 5 - A plane wall of thickness 0.6 m (L=0.3m) is made...Ch. 5 - Asphalt pavement may achieve temperatures as high...Ch. 5 - A thick steel slab...Ch. 5 - A tile-iron consists of a massive plate maintained...Ch. 5 - A simple procedure for measuring surface...Ch. 5 - An insurance company has hired you as a consultant...Ch. 5 - A procedure for determining the thermal...Ch. 5 - A very thick slab with thermal diffusivity...Ch. 5 - Standards for firewalls may be based on their...Ch. 5 - It is well known that, although two materials are...Ch. 5 - Two stainless steel plates...Ch. 5 - Special coatings are often formed by depositing...Ch. 5 - When a molten metal is cast in a mold that is a...Ch. 5 - Joints of high quality can be formed by friction...Ch. 5 - A rewritable optical disc (DVD) is formed by...Ch. 5 - Ground source heat pumps operate by using the...Ch. 5 - To enable cooking a wider range of foods in...Ch. 5 - Derive an expression for the ratio of the total...Ch. 5 - The structural components of modem aircraft are...Ch. 5 - Consider the plane wall of thickness 2L, the...Ch. 5 - Problem 4.9 addressed radioactive wastes stored...Ch. 5 - Derive an expression for the ratio of the total...Ch. 5 - Prob. 5.107PCh. 5 - Prob. 5.108PCh. 5 - A thin rod of diameter D is initially in...Ch. 5 - A one-dimensional slab of thickness 2L is...Ch. 5 - Prob. 5.114PCh. 5 - Prob. 5.115PCh. 5 - A molded plastic product...Ch. 5 - Prob. 5.133PCh. 5 - A thin circular disk is subjected to induction...Ch. 5 - Two very long (in the direction normal to the...Ch. 5 - Prob. 5S.2PCh. 5 - Prob. 5S.3PCh. 5 - Estimate the time required to cook a hot dog in...Ch. 5 - Prob. 5S.7PCh. 5 - Prob. 5S.9PCh. 5 - Prob. 5S.10PCh. 5 - Prob. 5S.11PCh. 5 - Prob. 5S.13P
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
- Fig. 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_forwardFor each of the following cases, determine an appropriate characteristic length Lc and the corresponding Biot Bi number that is associated with the transient thermal response of the solid object. Say if the global capacitance approximation is va lid. If temperature information is not provided, evaluate properties T = 300K a)oroidal shape with diameter D = 50mm and cross-sectional area AC = 5 mm², with thermal conductivity k = 2.3W / (mK) The surface of the toroid is exposed to a refrigerant corresponding to a convective coefficient eta = 50 W/( m2.k) b)A long stainless steel heated bar (AISI 304), with rectangular cross section, and dimensions w = 3mm , W = 5mm and L = 100mm . the bar issubjected to a refrigerant that provides a heat transfer coefficient of h =15 W/(m2 K) on all exposed surfaces. c)A long extruded aluminum tube (2024 Alloy) with internal dimensions and external w = 20 mm and W = 24 mm , respectively, suddenly submerged in water, with a convective coefficient of h =…arrow_forwardConsider 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_forward
- 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.)arrow_forwardQ1 Passage of an electric current through a long conducting rod of radius r; and thermal conductivity k, results in uniform volumetric heating at a rate of ġ. The conduct- ing rod is wrapped in an electrically nonconducting cladding material of outer radius r, and thermal conduc- tivity k, and convection cooling is provided by an adjoining fluid. Conducting rod, ġ, k, 11 To Čladding, ke For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express ap- propriate boundary conditions for the solution of these equations.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
- Free Response problems 1. 2 moles of a monatomic ideal gas is placed under a piston in a cylindrical container. The piston can move freely up and down without friction and its diameter is 20 cm. A 50 kg weight is placed on the top of the piston. The initial temperature of the gas is O C. a. Calculate the absolute pressure in the container. b.Calculate the volume of the gas. The gas is heated to a temperature of a 100 C at the constant pressure. c. Calculate the new volume of the gas. d. Calculate the amount of work done by the gas during its expansion. e. Calculate the change in internal energy of the gas. f. Calculate the amount of heat added to the gas.arrow_forwardShow detailed step by step solution. Topic: Thermodynamicsarrow_forwardHi, kindly solve this problem and show the solution. Thank youarrow_forward
- 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 xarrow_forwardPlease help me answer question 1, show all the steps taken.arrow_forwardNuclear fuel rods. A typical nuclear fuel rod contains circular uranium oxide (UO2) fuel pellets 10 mm in diameter and 5-mm thick stacked in a column to a length of 4 m inside a thin zirconium alloy tube, as shown below. The pellets generate heat uniformly throughout their volume due to nuclear fission, with a power density a (i.e., the heat power produced per unit volume of the pellet) that depends on their 235U enrichment. This heats up the water in the reactor to produce steam to drive the turbine. Assuming that the rim of the fuel pellet is maintained at a constant temperature Trim due to water cooling, show that the steady-state temperature profile T(r), where r is the radial distance from the centre of the pellet and fuel rod, 4. P(R? -r²; is given by: T(r) = Tim + 4k where k is the thermal conductivity of the pellet and R is its radius. partial stacked column of fuel pellets in rodarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_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