Explanation Given: The thickness of concrete slab = 15 cm Thermal conductivity of concrete slab k c = 2 W/mK The dimensions of the slab = 15 m wide and 20 m long. The convection coefficient on the inner surface of the roof h i = 5W/m 2 K The convection coefficient on the outer surface of the roof h o = 12W/m 2 K The temperature of the air T ∞ = 10 ° C The temperature of the sky at night T s = 100 K The constant temperature of house and interior surface of the wall T h = 20 o C The emissivity of both the surface of the roof = 0.9 The efficiency of the furnace = 80% The price of natural gas = $1.20/therm (1 therm = 105,500 kJ) Calculation: First, assume the steady-state operation of the heat transfer. The heat transfer takes place from the room to the roof by both conduction and convection. The roof also transmits heat to the surrounding by both conduction and convection process. It is to be noted that the heat transferred from the room to the roof will be equal to the heat transferred from the roof to the surrounding. This heat transferred by the conduction and convection process will be equal to the heat transferred through the roof by conduction only. In mathematical terms, the equation can be written as Q = Q r o o m t o r o o f , c o n d + r a d = Q r o o f , c o n d = Q r o o f t o s u r r , c o n v + r a d The inner surface temperature = T i n The outer surface temperature = T o u t Now, calculate the individual terms of heat transfer. Q r o o m t o r o o f , c o n v + r a d = h i A ( T r o o m − T s , i n ) + ε A σ ( T r o o m 4 − T i n 4 ) Q r o o m t o r o o f , c o n v + r a d = ( 5 × 300 × ( 20 − T i n ) ) + 0.9 × ( 300 × 5.67 × 10 − 8 ) ( ( 20 + 273 ) 4 − ( T i n + 273 ) 4 ) Q r o o m t o r o o f , c o n v + r a d = ( 1500 × ( 20 − T i n ) ) + 1.53 × 10 − 5 × ( 7370050801 − ( T i n + 273 ) 4 ) Q r o o f , c o n d = k A ( T i n − T o u t L ) Q r o o f , c o n d = ( 2 × 300 ) × ( T i n − T o u t 0.15 ) Q r o o f , c o n d = 4000 × ( T i n − T o u t ) Q r o o f t o s u r r , c o n v + r a d = h o A ( T o u t − T s u r r ) + ε A σ ( T o u t 4 − T s u r r 4 ) Q r o o f t o s u r r , c o n v + r a d = ( ( 12 × 300 ) ( T o u t − 10 ) ) + ( 0

6th Edition

ISBN: 9780073398198

Author: CENGEL

Publisher: RENT MCG

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Question

Chapter 3, Problem 32P

To determine

The rate of heat transfer through the roof and the inner surface temperature of the roof also, the money lost through the roof during the 14-hour period.

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Chapter 3, Problem 31P

Chapter 3, Problem 33P

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Chapter 3 Solutions

HEAT+MASS TRANSFER:FUND.+APPL.

Ch. 3 - Consider heat conduction through a wall of...Ch. 3 - Consider heat conduction through a plane wall....Ch. 3 - What does the thermal resistance of a medium...Ch. 3 - Can we defme the convection resistance for a unit...Ch. 3 - Consider steady heat transfer through the wall of...Ch. 3 - How is the combined heat transfer coefficient...Ch. 3 - Why are the convection and the radiation...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Someone comments that a microwave oven can be...Ch. 3 - Consider two cold canned drinks, one wrapped in a...

Ch. 3 - The bottom of a pan is made of a 4-mm-thick...Ch. 3 - Consider a surface of area A at which the...Ch. 3 - How does the thermal resistance network associated...Ch. 3 - Consider steady one-dimensional heat transfer...Ch. 3 - Consider a window glass consisting of two...Ch. 3 - Prob. 16P Ch. 3 - Consider a person standing in a room at 20C with...Ch. 3 - Consider an electrically heated brick house...Ch. 3 - A12-cm18-cm circuit board houses on its surface...Ch. 3 - Water is boiling in a 25-cm-diameter aluminum pan...Ch. 3 - A cylindrical resistor element on a circuit board...Ch. 3 - Prob. 22P Ch. 3 - A1.0m1.5m double-pane window consists of two...Ch. 3 - Prob. 24P Ch. 3 - Prob. 25P Ch. 3 - Prob. 26P Ch. 3 - Prob. 27P Ch. 3 - Prob. 28EP Ch. 3 - To defog the rear window of an automobile, a very...Ch. 3 - A transparent film is to be bonded onto the top...Ch. 3 - To defrost ice accumulated on the outer surface of...Ch. 3 - Prob. 32P Ch. 3 - Prob. 33P Ch. 3 - Prob. 34P Ch. 3 - Prob. 35P Ch. 3 - Heat is to be conducted along a circuit board that...Ch. 3 - Prob. 37EP Ch. 3 - Consider a house that has a 10m20-m base and a...Ch. 3 - Prob. 39EP Ch. 3 - Prob. 40P Ch. 3 - Prob. 41P Ch. 3 - Prob. 42P Ch. 3 - Prob. 43P Ch. 3 - What is thermal contact resistance? How is it...Ch. 3 - Will the thermal contact resistance be greater for...Ch. 3 - Explain how the thermal contact resistance can be...Ch. 3 - A waII consists of two layers of insulation...Ch. 3 - Prob. 48CP Ch. 3 - Consider two surfaces pressed against each other....Ch. 3 - Prob. 50P Ch. 3 - Two 5-cm-diameter, 15-cm-long aluminum bars...Ch. 3 - Prob. 52P Ch. 3 - Two identical aluminum plates with thickness of 30...Ch. 3 - A tvolayer wall is made of two metal plates, with...Ch. 3 - Prob. 55P Ch. 3 - An aluminum plate and a stainless steel plate are...Ch. 3 - Prob. 57P Ch. 3 - Prob. 58P Ch. 3 - Prob. 59P Ch. 3 - Prob. 60P Ch. 3 - Prob. 61P Ch. 3 - What are the two approaches used in the...Ch. 3 - The thermal resistance networks can also be used...Ch. 3 - When plotting the thermal resistance network...Ch. 3 - A 10-cm-thick vall is to be constructed with...Ch. 3 - Prob. 66EP Ch. 3 - Prob. 67P Ch. 3 - Prob. 68P Ch. 3 - Prob. 69P Ch. 3 - Prob. 70P Ch. 3 - Prob. 71P Ch. 3 - Prob. 72P Ch. 3 - A 12-m-long and 5-m-high wall is constructed of...Ch. 3 - Prob. 74EP Ch. 3 - Prob. 75P Ch. 3 - Prob. 76P Ch. 3 - Prob. 77P Ch. 3 - What is an infinitely long cylinder? When is it...Ch. 3 - Can the thermal resistance concept be used for a...Ch. 3 - Consider a short cylinder whose top and bottom...Ch. 3 - Prob. 81P Ch. 3 - Prob. 82P Ch. 3 - Prob. 83P Ch. 3 - Superheated steam at an average temperature 20C is...Ch. 3 - Prob. 85P Ch. 3 - Prob. 86P Ch. 3 - Prob. 87EP Ch. 3 - Prob. 88EP Ch. 3 - Prob. 89EP Ch. 3 - Prob. 90P Ch. 3 - Prob. 91P Ch. 3 - Prob. 92P Ch. 3 - Prob. 93EP Ch. 3 - Prob. 94P Ch. 3 - Prob. 95P Ch. 3 - Prob. 96P Ch. 3 - Liquid hydrogen is flowing through an insulated...Ch. 3 - Exposure to high concentrations of gaseous ammonia...Ch. 3 - A mixture of chemicals is flowing in a pipe...Ch. 3 - Ice slurry is being transported in a pipe...Ch. 3 - Prob. 101P Ch. 3 - Prob. 102P Ch. 3 - Prob. 103P Ch. 3 - What is the critical radius of insulation? How is...Ch. 3 - Prob. 105CP Ch. 3 - Prob. 106CP Ch. 3 - Prob. 107CP Ch. 3 - A pipe is insulated such that the outer radius of...Ch. 3 - A 0.083-in-diameter electrical wire at 90F is...Ch. 3 - Repeat Prob. 3-109E, assuming a thermal contact...Ch. 3 - Prob. 111P Ch. 3 - Prob. 112P Ch. 3 - Hot air is to be cooled as it is forced to flow...Ch. 3 - Prob. 114CP Ch. 3 - Prob. 115CP Ch. 3 - The fins attached to a surface are determined to...Ch. 3 - Explain how the fins enhance heat transfer from a...Ch. 3 - How does the overall effectiveness of a finned...Ch. 3 - Hot water is to be cooled as it flows through the...Ch. 3 - Consider two finned surfaces that are identical...Ch. 3 - The heat transfer surface area of a fin is equal...Ch. 3 - Does the (a) efficiency and (b) effectiveness of a...Ch. 3 - Two pin fins are identical, except that the...Ch. 3 - Two plate fins of constant rectangular cross...Ch. 3 - Two finned surfaces are identical, except that the...Ch. 3 - Obtain a relation for the fin efficiency for a fin...Ch. 3 - Prob. 127P Ch. 3 - Consider a very long rectangular fin attached to a...Ch. 3 - Prob. 129P Ch. 3 - Prob. 130P Ch. 3 - Prob. 131P Ch. 3 - Prob. 132P Ch. 3 - Prob. 133EP Ch. 3 - Prob. 134EP Ch. 3 - Prob. 135P Ch. 3 - Prob. 136P Ch. 3 - Prob. 137P Ch. 3 - Prob. 138P Ch. 3 - Prob. 139P Ch. 3 - Prob. 140P Ch. 3 - Prob. 141P Ch. 3 - Prob. 142P Ch. 3 - Prob. 143P Ch. 3 - Prob. 144P Ch. 3 - Prob. 145P Ch. 3 - Prob. 146P Ch. 3 - The human body is adaptable to extreme climatic...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Consider the conditions of Example 3-14 in the...Ch. 3 - Prob. 150P Ch. 3 - What is a conduction shape factor? How is it...Ch. 3 - What is the value of conduction shape factors in...Ch. 3 - Prob. 153P Ch. 3 - A thin-walled cylindrical container is placed...Ch. 3 - Prob. 155P Ch. 3 - Prob. 156P Ch. 3 - Prob. 157P Ch. 3 - Prob. 158EP Ch. 3 - Prob. 159P Ch. 3 - Prob. 160P Ch. 3 - Prob. 161P Ch. 3 - Prob. 162P Ch. 3 - Prob. 163P Ch. 3 - Prob. 164P Ch. 3 - Consider a house with a flat roof whose outer...Ch. 3 - Prob. 166P Ch. 3 - Radioactive material, stored in a spherical vessel...Ch. 3 - What is the R-value of a wall? How does it differ...Ch. 3 - What is effective emissivity for a plane-parallel...Ch. 3 - Prob. 170CP Ch. 3 - What is a radiant barrier? What kinds of materials...Ch. 3 - Consider a house whose attic space is ventilated...Ch. 3 - Prob. 173P Ch. 3 - Prob. 174P Ch. 3 - Prob. 175P Ch. 3 - Prob. 176P Ch. 3 - Prob. 177P Ch. 3 - Prob. 178P Ch. 3 - Determine the winter R-value and the U-factor of a...Ch. 3 - The overall heat transfer coefficient (the...Ch. 3 - Prob. 181EP Ch. 3 - Determine the summer and winter R-values. in m2 ....Ch. 3 - The overall heat transfer coefficient of a wall is...Ch. 3 - Two homes are identical, except that the walls of...Ch. 3 - Prob. 185P Ch. 3 - Consider two identical people each generating 60 V...Ch. 3 - Cold conditioned air at 12C is flowing inside a...Ch. 3 - Hot water is flowing at an average velocity of 1.5...Ch. 3 - Prob. 189P Ch. 3 - Prob. 190P Ch. 3 - Prob. 191P Ch. 3 - Prob. 192P Ch. 3 - Prob. 193P Ch. 3 - Prob. 194P Ch. 3 - Prob. 195P Ch. 3 - Prob. 196P Ch. 3 - Prob. 197P Ch. 3 - A total of 10 rectangular aluminum fins...Ch. 3 - Prob. 199P Ch. 3 - A plane wall surface at 200C is to be cooled with...Ch. 3 - Prob. 201P Ch. 3 - Prob. 202P Ch. 3 - Prob. 203P Ch. 3 - Prob. 204P Ch. 3 - A 0.6-rn-diameter, 1.9-rn-long cylindrical tank...Ch. 3 - Prob. 206P Ch. 3 - Prob. 207P Ch. 3 - A thin-walled spherical tank is buried in the...Ch. 3 - Heat is lost at a rate of 275 W per m2 area of a 1...Ch. 3 - Prob. 210P Ch. 3 - Heat is generated steadily in a 3-cm-diameter...Ch. 3 - Prob. 212P Ch. 3 - Prob. 213P Ch. 3 - Prob. 214P Ch. 3 - Prob. 215P Ch. 3 - Prob. 216P Ch. 3 - Consider two walls. A and B, with the same surface...Ch. 3 - Prob. 218P Ch. 3 - A room at 20C air temperature is losing heat to...Ch. 3 - Prob. 220P Ch. 3 - A 1-cm-diameter, 30cm-long fin made of aluminum...Ch. 3 - A hot surface at 80C in air at 20C is to be cooled...Ch. 3 - A cylindrical pin fin of diameter 0.6 cm and...Ch. 3 - A 3-cm-long. 2-nuti x 2-mm rectangular...Ch. 3 - Two finned surfaces with long fins are identical,...Ch. 3 - A 20-cm-diameter hot sphere at 120C is buried in...Ch. 3 - A 25-cm-diameter, 2.4-rn-long vertical cylinder...Ch. 3 - Prob. 228P Ch. 3 - The walls of a food storage facility are made of a...Ch. 3 - The equivalent thermal resistance for the thermal...Ch. 3 - Prob. 231P Ch. 3 - Prob. 232P Ch. 3 - Prob. 233P Ch. 3 - The fin efficiency is defined as the ratio of the...Ch. 3 - Prob. 235P Ch. 3 - In the United States, building insulation is...Ch. 3 - Prob. 237P Ch. 3 - A plane brick wall (k=0.7W/m.K) and is 10 cm...Ch. 3 - The temperature in deep space is close to absolute...Ch. 3 - In the design of electronic components, it is...Ch. 3 - Using cylindrical samples of the same material,...Ch. 3 - Find out about the wall construction of the cabins...Ch. 3 - Prob. 243P Ch. 3 - A house with 200-m2 floor space is to be heated...

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