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
Textbook Question
Chapter 5, Problem 5.101P
To enable cooking a wider range of foods in microwave ovens, thin, metallic packaging materials have been developed that will readily absorb microwave energy. As the packaging material is heated by the microwaves, conduction simultaneously occurs from the hot packaging material to the cold food. Consider the spherical piece of frozen ground beef of Problem 5.33 that is now wrapped in the thin microwave-absorbing packaging material. Determine the time needed for the beef that is immediately adjacent to the packaging material to reach
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Microwave ovens operate by rapidly aligning and reversing water molecules within the food, resulting in volumetric energy generation
and, in turn, cooking of the food. When the food is initially frozen, however, the water molecules do not readily oscillate in response to
the microwaves, and the volumetric generation rates are between one and two orders of magnitude lower than if the water were in
liquid form. (Microwave power that is not absorbed in the food is reflected back to the microwave generator, where it must be
dissipated in the form of heat to prevent damage to the generator.)
(a) Consider a frozen, 0.7-kg spherical piece of ground beef at an initial temperature of T₁ = -20°C placed in a microwave oven with
To = 30°C and h = 15 W/m².K. Determine how long, in min, it will take the beef to reach a uniform temperature of T = 0°C, with all
the water in the form of ice. Assume the properties of the beef are the same as ice, and assume 3% of the oven power (P = 1 kW
total) is…
i. Calculate the heat loss through the furnace wall (all sides) by using conduction shape factor.
ii. Calculate the heat loss through the furnace wall by using thermal resistance from each side (6 sides).
iii. Determine the percentage difference of heat loss between case (i) and case (ii).
iv. Explain why the heat transfer for both cases are different.
PROBLEM 1:
The block of 304 stainless steel shown below is well insulated on the front and back surfaces, and the temperature in the block varies
linearly in both the x- and y-directions. Find:
(a) The heat fluxes and heat flows in the x- and y-directions.
(b) The magnitude and direction of the heat flux vector.
15°C
5°C
5 cm
y
5 cm-
10 cm
The thermal conductivity of 304 stainless steel is 14.4 W/m K.
10°C
0°C
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
- 2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.arrow_forwardA hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are o.18 and o.21 m, respectively, and testing is done under steady-state conditions with the inner surface of the aluminum maintained at 250°C. In a particular test, a spherical shell of insulation is cast on the outer surface of the sphere to a thickness of o.15 m. The system is in a room for which the air temperature is 20°C and the convection coefficient at the outer surface of the insulation is 30 W/m2. K. If 80 W is dissipated by the heater under steady-state conditions, what is the thermal conductivity of the insulation?arrow_forwardpartbarrow_forward
- As a researcher in the field of heat transfer, how will you distinguish between radiation by black body and a real body? Explain briefly Point out and briefly explain the various factors affect the thermal conductivity of a material. What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness t1, t2, t3 respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab. Based upon the reradiating properties of absorptivity, reflectivity and transmissivity, how would you distinguish between the following:Black body, white body, transparent body and opaque body. The nature of surfaces affects the absorption and the reflection of…arrow_forwardA warehouse is being built that will have neither heating nor cooling. Depending on the amount of insulation, the time constant for the building may range from 1 to 4 hr. To illustrate the effect insulation will have on the temperature inside the warehouse, assume the outside temperature varies as a sine wave, with a minimum of 12°C at 2:00 A.M. and a maximum of 32°C at 2:00 P.M. Assuming the exponential term (which involves the initial temperature To) has died off, what is the lowest temperature inside the building if the time constant is 1 hr? If it is 4 hr? What is the highest temperature inside the building if the time constant is 1 hr? If it is 4 hr? If the time constant is 1 hr, then the lowest temperature inside the building is about °C. (Round to the nearest tenth as needed.)arrow_forward1. A simple cavity wall consists of two brick layers separated by an air gap of 50 mm. If the inside air temperature is 20oC and the ambient outside temperature is 5 oC, calculate the heat flux through the wall. Bricks are 100 mm thick with thermal conductivity kbrick = 0.5 W/m K, hin = 10 W/m2 K, hout = 20 W/m2 K. The internal air cavity can be considered still (no convection) with kair = 0.015 W/m K. 2. On a day in winter, the outside air temperature drops to -5 oC and the outside convective heat transfer changes to hout = (2 x V) + 8.9 W/m2 K. If the outside wind speed gusts at 50 kph, calculate the change in heat flux for the wall in question 3.arrow_forward
- Pravinbhaiarrow_forwardQuestion 3: An electronic device with a temperature of 84°C (shown in golden colour) is embedded inside a composite plastic tube which is equipped with three fins (shown in blue) to enhance the convective heat transfer with the surrounding air. The composite tube is held horizontally. The temperature drop along the fins can be ignored due to their high thermal conductivity. The outer ring of the fins (shown in brown) is insulated. The ambient temperature is 20°C. 3d. Calculate the heat transfer coefficients across the cylinder 3e. Calculate the heat transfer coefficients across the fins by assuming fins as vertical planes 31. Calculate the heat loss across the system Aluminium fins Diameter = 30 cm Insulated ring Thickness = 5 mm Composite tube Thickness = 5 mm Thermal conductivity = 25 W/mk Tube is held horizontally. Air 20°C Hot electronic device Temperature = 84°C Diameter = 10 cm Length = 100 cm %3Darrow_forwardA heat-conducting rod, that is wrapped in insulation, is constructed with a 0.15-m length of alloy A and a 0.40-m length of alloy B, joined end-to-end. Both pieces have a cross-sectional area of 0.0020 m2. The thermal conductivity of alloy B is known to be 1.8 times as great as that of alloy A. The end of the rod in alloy A is maintained at a temperature of 10 degrees Celcius, and the other end of the rod is maintained at an unknown temperature. When the steady-state flow has been established, the temperature at the junction of the alloys is measured to be 40 degrees Celcius, and the rate of heat flow in the rod is measured at 56 W. What is the temperature of the end of the rod in alloy B.arrow_forward
- 2. Two bars are conducting heat from a region of higher temperature to a region of lower temperature. The bars have identical lengths and cross-sectional areas, but are made from different materials. In the draw- ing they are placed “in parallel" between the two temperature regions in arrangement A, whereas they are placed end to end in arrangement B. In which arrangement is the heat that is conducted the greatest? (a) The heat conducted is the same in both arrangements. (b) Arrangement A (c) Arrangement B (d) It is not possible to determine which arrangement conducts more heat. 100 °C ´Aluminum 0 °C 0 °C 100 °C Aluminum Соpper Copperarrow_forwardi need the answer quicklyarrow_forwardA sphere of radioactive material of radius aR is wrapped with a ceramic casing of outer radius R.The heat flux density emitted by the sphere radioactive on its surface is qaR. Find the temperature profile of the spherical shell if the thermal conductivity of the housing material varieswith its radius according to k = Kr (where K is a constant and r is the distance from the center of thesphere) and the temperature outside the casing is keeps T constant Rarrow_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