Fundamentals of Heat and Mass Transfer
7th Edition
ISBN: 9780470917855
Author: Bergman, Theodore L./
Publisher: John Wiley & Sons Inc
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Chapter 5, Problem 5S.9P
To determine
The time required for the billet to reach
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6. a. The heat flux applied to the walls of the biomass combustion furnace is 20 W/m2. The furnace walls have a thickness of 10 mm and a thermal conductivity of 12 W/m.K. If the wall surface temperature is measured to be 50oC on the left and 30oC on the right, prove that conduction heat transfer occurs at a steady state!b. Heating the iron cylinder on the bottom side is done by placing the iron on the hotplate. This iron has a length of 20 cm. The surface temperature of the hotplate is set at 300oC while the top side of the iron is in contact with the still outside air. To reach the desired hotplate temperature, it takes 5 minutes. Then it takes 15 minutes to measure the temperature of the upper side of the iron cylinder at 300oC. Show 3 proofs that heat transfer occurs transiently
1. For a steam pipe with a given diameter of 10 cm covered by two (2) layers of
insulation. The first insulation has a thickness of 4 cm and a coefficient of thermal
conductivity of 0.08 W/m.K. and the second insulation has a thickness of 3 cm and
a thermal conductivity of 0.15 W/m.K. The steam main conveys steam at a
pressure of 1.70 MPa with 25°C superheat. Outside temperature is 27°C. The pipe
is 30 meters in length. (tsat @ 1.70 MPa = 204°C). Determine the following:
a) The heat loss in KW
b) Explain the concepts/principles that were considered and the factors that
affected the condition of the above mentioned items (a & b).
2. A steel plate of k=50w/mk and thickness 10cm passes a heat flux by conduction of 25kW/m² . If the
temperature of hot surface of plate is 100C, then what is the temperature of the cooler side of plate?
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
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- 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_forwardA plane wall, 7.5 cm thick, generates heat internally at the rate of 105 W/m3. One side of the wall is insulated, and the other side is exposed to an environment at 90C. The convection heat transfer coefficient between the wall and the environment is 500 W/m2 K. If the thermal conductivity of the wall is 12 W/m K, calculate the maximum temperature in the wall.arrow_forwardA 5cm copper plate has a thermal conductivity of 395??−?is used as a heat sink for a semiconductor. A 1mm layer of thermal paste lies in between the two and it has a thermal conductivity of 10??−?. Solve for the heat transferred at a 5cmx5cm area if the semiconductor is 80C, while the copper plate has a temperature of 30C since it is exposed to ambient air temperature.arrow_forward
- 3. The wall of a storage system contents of a 10cm layer of common brick (k=0.69w/m. °C) and a 2.5cm layer of glass (k=0.15w/m. °C). The outside wall and environmental temperature are 25°C and 30°C, respectively. If the heat transfer coefficient between the storage system and this environment is 2.4w/m2. °C, What is the inside wall temperature of the storage system? a. 22.16°C b. 21.26°C с. 23.46°C d. 20.16°Carrow_forward2. A steel plate of k=50W/mK and thickness 10cm passes a heat flux by conduction of 25kW/m2. If the temperature of hot surface of plate is 100 C, then what is the temperature of the cooler side of plate? 1. 30 C 2. 40 C 3. 50 C 4. 60 Carrow_forwardConsider a heat conductor in the form of a long cylinder, with inner and outer radii R1 and R2, respectively. Heat is generated within the cylinder, where the temperature O(r, t) at position r and time t satisfies the modified heat equation = DV0 + H, where D is the thermal diffusivity, and H is proportional to the rate of heat production. The inner and outer surfaces of the cylinder are cooled by a fluid maintained at constant temperature Oo. (a) If the temperature is in a steady state and depends only on the distance r from the centre of the cylinder, use cylindrical coordinates (r, 0, 2) to write down an ordinary differential equation for O(r) valid in the region R1arrow_forward1 - A square chip, with side w = 5 mm, operates under isothermal conditions.The chip is positioned on a substrate so that its side and bottom surfaces are thermally insulated, while its top surface is exposed to theflow of a refrigerant at T∞ = 15°C. From reliability considerations, the chip temperature cannot exceed T = 85°C. 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When the person is in still air at T = 282 K, what is the skin surface temperature and rate of heat loss to the environment? Convection heat transfer to the air is characterized by a free convection coefficient of h 2 m2 -K b). When the person is in water at T = 282,…arrow_forwardThe inside wall of a furnace is at 2100oF and the outside wall is at 300oF. The wall of a furnace must be designed to transmit no more than 220 Btu/hr-ft2. Two types of bricks are available for construction:TYPE A: k = 0.38 Btu/ hr-ft-R with an allowable maximum temperature of 1400oFTYPE B: k = 0.98 Btu/ hr-ft-R with an allowable maximum temperature of 2300oF Both types of bricks have the same dimensions (9” x 4.5” x 3”) but the cost for Type B brick is twice the cost of Type A brick. Illustrate the order of arrangement of bricks A and B in the furnace wall (with thickness, estimated temperatures at the interface between walls A and B and at the interior and exterior surface, the transport area and direction of transfer included)arrow_forwardThe inside wall of a furnace is at 2100oF and the outside wall is at 300oF. The wall of a furnace must be designed to transmit no more than 220 Btu/hr-ft2. Two types of bricks are available for construction:TYPE A: k = 0.38 Btu/ hr-ft-R with an allowable maximum temperature of 1400oFTYPE B: k = 0.98 Btu/ hr-ft-R with an allowable maximum temperature of 2300oF Both types of bricks have the same dimensions (9” x 4.5” x 3”) but the cost for Type B brick is twice the cost of Type A brick. If a 15 ft2 wall is to be constructed, how many bricks will be used? how many brick A and how many brick B?arrow_forwardThe inside wall of a furnace is at 2100oF and the outside wall is at 300oF. The wall of a furnace must be designed to transmit no more than 220 Btu/hr-ft2. Two types of bricks are available for construction:TYPE A: k = 0.38 Btu/ hr-ft-R with an allowable maximum temperature of 1400oFTYPE B: k = 0.98 Btu/ hr-ft-R with an allowable maximum temperature of 2300oF Both types of bricks have the same dimensions (9” x 4.5” x 3”) but the cost for Type B brick is twice the cost of Type A brick. Model the wall as one-dimensional and determine the most economical arrangement of the bricks. Include:a drawing labeled with all given informationthe variables used in the appropriate places on the drawing (along with values and units, if provided)a thermal circuit showing the paths for heat transmissionequations and calculationsCalculations that show that the maximum temperature for Type A brick does not exceed 1400oFA recommendation for the number and orientation of the bricks. The inside temp is 2100f…arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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