Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 19, Problem 82P
To determine

The tube surface temperature necessary to heat water.

The tube surface temperature necessary to heat engine oil.

The tube surface temperature necessary to heat liquid mercury.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

The diameter of tube is (D) is 25mm.

The length of tube is (L) is 15m.

The inlet temperature (Ti) of fluid is 50oC.

The outlet temperature (Te) of fluid is 150oC.

The mass flow rate (m˙) is 0.01kg/s.

Calculation:

Calculate the average temperature.

    Tavg=Ti+Te2=50°C+150°C2=100°C

For water:

Refer Table A-15 “Properties of saturated water”.

Obtain the following properties of water corresponding to the temperature of 100°C as follows:

ρ=957.9kg/m3

k=0.679W/mK

Pr=1.75

μ=0.282×103kg/ms

Calculate the Reynolds number for water.

    Re=4m˙πDμ=4×0.01kg/sπ(25mm103m1mm)(0.282×103kg/ms)=1806.01

The value of Reynolds number is less than 2000. Therefore the flow is laminar flow.

Calculate the hydrodynamic entry length for water.

    LH=0.05ReD=0.05×1806.01×25mm103m1mm=0.05×1806.01×0.025m=2.2575m

Calculate the thermal entry length for water.

    LT=Pr×LH=1.75×2.2575m=3.9506m

The value of hydrodynamic entry length and thermal entry length is less than 15m. Therefore the flow is fully developed flow.

The value of Nusselt number for fully developed laminar flow is 3.66.

    Nu=3.66

Calculate the heat transfer coefficient.

    h=Nu(kD)=3.66(0.679W/mK25mm103m1mm)=99.41W/m2K

Calculate the surface area of tube.

    As=πDL=π(25mm103m1mm)(15m)=1.178m2

Calculate the exit temperature of fluid.

    Ts=TeTiexp[hAsm˙cp]1exp[hAsm˙cp]=150°C(50°C)exp[(99.41W/m2°C)×(1.178m2)(0.01kg/s)(4217J/kgK)]1exp[(99.41W/m2°C)×(1.178m2)(0.01kg/s)(4217J/kgK)]=150°C(50°C)exp[2.7769]1exp[2.7769]=156.6°C

Thus, the tube surface temperature is 156.6°C.

For engine oil:

Refer Table A-19 “Properties of liquids”.

Obtain the following properties of the engine oil corresponding to the temperature of 100°C as follows:

k=0.1367W/mK

cp=2220J/kgK

Pr=279.1

μ=0.01718kg/ms

Calculate the Reynolds number for engine oil.

    Re=4m˙πDμ=4×0.01kg/sπ(25mm103m1mm)(0.01718kg/ms)=29.64

The value of Reynolds number is less than 2000. Therefore the flow is laminar flow.

Calculate the hydrodynamic entry length for engine oil.

    LH=0.05ReD=0.05×29.64×25mm103m1mm=0.037m

Calculate the thermal entry length for engine oil.

    LT=Pr×LH=279.1×0.037m=10.34m

Calculate the heat transfer coefficient for engine oil.

    h=Nu(kD)=3.66(0.1367W/mk25mm103m1mm)=20.01W/m2°C

Calculate the exit temperature of fluid.

    Ts=TeTiexp[hAsm˙cp]1exp[hAsm˙cp]=150°C(50°C)exp[(20.01W/m2°C)×(1.178m2)(0.01kg/s)(2220J/kgK)]1exp[(20.01W/m2°C)×(1.178m2)(0.01kg/s)(2220J/kgK)]=150°C(50°C)exp[1.06126]1exp[1.06126]=202.9°C

Thus, the tube surface temperature is 202.9°C.

For liquid mercury:

Refer Table A-20 "Properties of liquid metals”.

Obtain the following properties of liquid mercury corresponding to the temperature of 100°C as follows:

k=9.467W/mK

cp=137.1J/kgK

Pr=0.018

μ=1.245×103kg/ms

Calculate the Reynolds number for liquid mercury.

    Re=4m˙πDμ=4×0.01kg/sπ(25mm103m1mm)(1.245×103kg/ms)=409.07

The value of Reynolds number is less than 2000. Therefore the flow is laminar flow.

Calculate the hydrodynamic entry length for liquid mercury.

    LH=0.05ReD=0.05×409.07×25mm103m1mm=0.05×1806.01×0.025m=0.511m

Calculate the thermal entry length for liquid mercury.

    LT=Pr×LH=0.018×0.511m=0.0092m

Calculate the heat transfer coefficient for liquid mercury.

    h=Nu(kD)=3.66(9.467W/mk25mm103m1mm)=1385.98W/m2°C

Calculate the exit temperature of fluid.

    Ts=TeTiexp[hAsm˙cp]1exp[hAsm˙cp]=150°C(50°C)exp[(1385.98W/m2°C)×(1.178m2)(0.01kg/s)(137.1J/kgK)]1exp[(1385.98W/m2°C)×(1.178m2)(0.01kg/s)(137.1J/kgK)]=150°C(50°C)exp[1190.87]1exp[1190.87]=150°C

Thus, the tube surface temperature is 150°C.

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

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