Fundamentals Of Thermal-fluid Sciences In Si Units
Fundamentals Of Thermal-fluid Sciences In Si Units
5th Edition
ISBN: 9789814720953
Author: Yunus Cengel, Robert Turner, John Cimbala
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 19, Problem 102P

(a)

To determine

The exit temperature of the hot air leaving the basement.

(a)

Expert Solution
Check Mark

Explanation of Solution

Given:

The length (L) of the duct is 12m.

The cross section area (Ac) of the duct is 20cm×20cm.

The average velocity (V) of the hot air in the duct is 4m/s

The temperature (T1) of the hot air leaving the furnace is 60°C.

The emissivity (ε) of the outer surface of duct is 0.3.

The temperature (T0) of the cold air is 10°C.

Calculation:

Refer to the table A22 “Properties of air at 1atm pressure.”

Obtain the following properties of air corresponding to the bulk mean temperature of 50°C as follows:

cp=1007J/kgK

k=0.02735W/mK

ν=1.798×105m2/s

ρ=1.092kg/m3

Pr=0.7228

Calculate the cross sectional area of the duct by using the relation.

    As=4aL=4(0.2m)(12m)=9.6m2

Calculate the hydrodynamic diameter by using the relation.

    Dh=4AcP=4(0.2m×0.2m)4(0.2m)=0.2m

Calculate the Reynolds number by using the relation.

    Re=VDhν=(4m/s)(20cm×1m100cm)1.798×105m2/s=44494

The Reynolds number is greater than 10000 so the flow in the tube is turbulent.

Calculate the length of hydrodynamic layer by using the relation.

    Lh=10Dh=10(0.2m)=2m

Calculate the length of thermal boundary layer by using the relation.

    Lt=10Dh=10(0.2m)=2m

The length of hydrodynamic layer and thermal boundary layer is less than the length of duct.

Calculate the heat transfer coefficient by using the relation.

    Nu=0.023Re0.8Pr0.4hDk=0.023(44494)0.8(0.7228)0.4h=(105.68)(0.02735W/mK0.2m)=14.45W/m2K

Calculate the mass flow rate by using the relation.

    m˙=ρAcV=(1.092kg/m3)((20cm×1m100cm)×(20cm×1m100cm))(4m/s)=0.1747kg/s

Calculate the heat transfer due to convection by using the relation.

    Qcon=h1As(ΔTlm)=h1As[(T2T1)ln(TsT2TsT1)]=(14.45W/m2K)(9.6m2)[(T260°C)ln(TsT2Ts60°C)]=138.72W/K[(T260°C)ln(TsT2Ts60°C)]

Calculate the heat transfer due to convection and radiation by using the relation.

    Qcon+rad=h2As(TsTo)+εAsσ(Ts4To4)=[(10W/m2K)(9.6m2)(Ts10°C)+(0.3)(9.6m2)(5.67×108W/m2K4)[(Ts)4(10°C+273)4K4]]

Calculate the total heat transfer by using the relation.

    Qt=m˙cp(T2T1)=(0.1747kg/s)(1007J/kgK)(60°CT1)

In the steady operation heat transfer from the hot air to duct must be equal to heat transfer due to convection and radiation, which also equal to energy loss of the hot air in the duct.

    Qcon=Qcon+rad=Qt

From above condition

Q=2622W

T2=45.1°C

Ts=33.3°C

Thus, the exit temperature of the hot air leaving the basement is 45.1°C.

(b)

To determine

The rate of heat loss from the hot air in the duct.

(b)

Expert Solution
Check Mark

Explanation of Solution

Calculation:

Calculate the total heat transfer by using the relation.

    Qt=m˙cp(T2T1)=(0.1747kg/s)(1007J/kgK)((60°C+273)K(45.1°C+273)K)=2621.25W

Thus, the rate of heat loss from the hot air in the duct is 2621.25W.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 19 Solutions

Fundamentals Of Thermal-fluid Sciences In Si Units

Ch. 19 - The upper surface of a 50-cm-thick solid plate (k...Ch. 19 - Prob. 12PCh. 19 - During air cooling of oranges, grapefruit, and...Ch. 19 - During air cooling of steel balls, the convection...Ch. 19 - Prob. 15PCh. 19 - Water at 43.3°C flows over a large plate at a...Ch. 19 - Prob. 17PCh. 19 - Hot engine oil at 150°C is flowing in parallel...Ch. 19 - Prob. 19PCh. 19 - Prob. 22PCh. 19 - Prob. 23PCh. 19 - Prob. 24PCh. 19 - Prob. 25PCh. 19 - Prob. 27PCh. 19 - Prob. 28PCh. 19 - Prob. 30PCh. 19 - Prob. 31PCh. 19 - Solar radiation is incident on the glass cover of...Ch. 19 - Liquid mercury at 250°C is flowing with a velocity...Ch. 19 - Prob. 35PCh. 19 - Prob. 36PCh. 19 - Air is flowing in parallel over the upper surface...Ch. 19 - Prob. 40PCh. 19 - Consider laminar flow of air across a hot circular...Ch. 19 - Prob. 42PCh. 19 - A heated long cylindrical rod is placed in a cross...Ch. 19 - A person extends his uncovered arms into the windy...Ch. 19 - Prob. 46PCh. 19 - Prob. 47PCh. 19 - Prob. 49PCh. 19 - Consider a person who is trying to keep cool on a...Ch. 19 - A 12-ft-long, 1.5-kW electrical resistance wire is...Ch. 19 - Prob. 52PCh. 19 - Prob. 53PCh. 19 - Prob. 55PCh. 19 - Prob. 56PCh. 19 - A 10-cm-diameter, 30-cm-high cylindrical bottle...Ch. 19 - Prob. 58PCh. 19 - An incandescent lightbulb is an inexpensive but...Ch. 19 - Prob. 60PCh. 19 - Prob. 61PCh. 19 - Prob. 62PCh. 19 - A coated sheet is being dried with hot air blowing...Ch. 19 - Prob. 65PCh. 19 - Consider laminar forced convection in a circular...Ch. 19 - Consider turbulent forced convection in a circular...Ch. 19 - What does the logarithmic mean temperature...Ch. 19 - Prob. 69PCh. 19 - Prob. 70PCh. 19 - Prob. 71PCh. 19 - Prob. 72PCh. 19 - Prob. 73PCh. 19 - Cooling water available at 10°C is used to...Ch. 19 - Prob. 75PCh. 19 - Inside a condenser, there is a bank of seven...Ch. 19 - Prob. 79PCh. 19 - Prob. 81PCh. 19 - Prob. 82PCh. 19 - In a thermal system, water enters a 25-mm-diameter...Ch. 19 - Prob. 84PCh. 19 - Prob. 85PCh. 19 - Prob. 86PCh. 19 - Prob. 88PCh. 19 - Prob. 89PCh. 19 - Prob. 90PCh. 19 - Glycerin is being heated by flowing between two...Ch. 19 - Determine the convection heat transfer coefficient...Ch. 19 - Prob. 94PCh. 19 - Water is to be heated from 10°C to 80°C as it...Ch. 19 - Consider a fluid with a Prandtl number of 7...Ch. 19 - The hot water needs of a household are to be met...Ch. 19 - Prob. 98PCh. 19 - Prob. 99PCh. 19 - Hot air at atmospheric pressure and 85°C enters a...Ch. 19 - Prob. 102PCh. 19 - Prob. 104PCh. 19 - Prob. 105PCh. 19 - Prob. 106PCh. 19 - Prob. 107RQCh. 19 - Prob. 108RQCh. 19 - The passenger compartment of a minivan traveling...Ch. 19 - Prob. 110RQCh. 19 - Prob. 111RQCh. 19 - Prob. 112RQCh. 19 - Prob. 113RQCh. 19 - Prob. 114RQCh. 19 - Prob. 115RQCh. 19 - Prob. 116RQCh. 19 - Airstream at 1 atm flows, with a velocity of 15...Ch. 19 - Prob. 118RQCh. 19 - Prob. 119RQCh. 19 - Prob. 120RQCh. 19 - Prob. 121RQCh. 19 - A 3-m-internal-diameter spherical tank made of...Ch. 19 - Prob. 123RQCh. 19 - Prob. 124RQCh. 19 - Prob. 125RQCh. 19 - Prob. 126RQCh. 19 - Prob. 127RQCh. 19 - Prob. 128RQCh. 19 - Prob. 129RQCh. 19 - Prob. 130RQCh. 19 - Prob. 131RQCh. 19 - Prob. 132RQCh. 19 - Prob. 133RQCh. 19 - Prob. 134RQCh. 19 - Prob. 135RQCh. 19 - Prob. 136RQCh. 19 - Prob. 137RQCh. 19 - Prob. 138RQCh. 19 - Prob. 139RQCh. 19 - Prob. 140RQCh. 19 - Liquid water enters a 10-m-long smooth rectangular...
Knowledge Booster
Background pattern image
Mechanical Engineering
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.
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Heat Transfer – Conduction, Convection and Radiation; Author: NG Science;https://www.youtube.com/watch?v=Me60Ti0E_rY;License: Standard youtube license