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 18, Problem 79P
To determine

The soil temperature at distances from 0, 10, 20 and 50 cm from the earth’s surface at the end of the 10h period.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given:

Initial uniform temperature of the furnace (Ti) is 10°C.

Temperature of the area (T) is 10°C.

Convection heat transfer coefficient (h) is 40W/m2K.

Time period (t) is 10h.

Calculation:

Write the given properties of the soil.

  k=0.9W/mKα=1.6×105m2/s

Calculate the one-dimensional transient temperature distribution in the ground.

  T(x,t)TiTTi=erfc(x2αt)exp(hxk+h2αtk2)[erfc(x2αt+hαtk)]={erfc(x2αt)exp(hxk+(40W/m2K)2(1.6×105m2/s)(10×3600s)(0.9W/mK)2)[erfc(x2αt+(40W/m2K)(1.6×105m2/s)(10×3600s)0.9W/mK)]}=erfc(x2αt)[exp(hxk+1138)[erfc(x2αt+33.7)]]

It is concluded that the last term in the temperature distribution relation should be zero irrespective of distance x as the exponential term tends to infinity.

Write the reduced form of one-dimensional transient temperature distribution in the ground.

  T(x,t)TiTTi=erfc(x2αt)T(x,t)=Ti+(TTi)erfc(x2αt)

Calculate the soil temperature at distance from 0 cm from the earth’s surface.

  T(0,10h)=10°C+(10°C10°C)erfc(02(1.6×105m2/s)(10×3600s))=10°C+(20°C)erfc(0)=10°C+(20°C)(1)=10°C

Thus, the soil temperature at distance from 0 cm from the earth’s surface is 10°C.

Calculate the soil temperature at distance from 10 cm from the earth’s surface.

  T(0.1m,10h)=10°C+(10°C10°C)erfc(0.1m2(1.6×105m2/s)(10×3600s))=10°C+(20°C)erfc(0.066)=10°C+(20°C)(0.9257)=8.5°C

Thus, the soil temperature at distance from 10 cm from the earth’s surface is 8.5°C.

Calculate the soil temperature at distance from 20 cm from the earth’s surface.

  T(0.2m,10h)=10°C+(10°C10°C)erfc(0.2m2(1.6×105m2/s)(10×3600s))=10°C+(20°C)erfc(0.132)=10°C+(20°C)(0.8519)=7.0°C

Thus, the soil temperature at distance from 20 cm from the earth’s surface is 7.0°C.

Calculate the soil temperature at distance from 50 cm from the earth’s surface.

  T(0.5m,10h)=10°C+(10°C10°C)erfc(0.5m2(1.6×105m2/s)(10×3600s))=10°C+(20°C)erfc(0.329)=10°C+(20°C)(0.6418)=2.8°C

Thus, the soil temperature at distance from 50 cm from the earth’s surface is 2.8°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 18 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 18 - Prob. 11PCh. 18 - Prob. 12PCh. 18 - Prob. 13PCh. 18 - Prob. 14PCh. 18 - Consider a 1000-W iron whose base plate is made of...Ch. 18 - Metal plates (k = 180 W/m·K, ρ = 2800 kg/m3, and...Ch. 18 - A 5-mm-thick stainless steel strip (k = 21 W/m·K,...Ch. 18 - A long copper rod of diameter 2.0 cm is initially...Ch. 18 - Prob. 21PCh. 18 - Steel rods (ρ = 7832 kg/m3, cp = 434 J/kg·K, and k...Ch. 18 - Prob. 23PCh. 18 - The temperature of a gas stream is to be measured...Ch. 18 - Prob. 25PCh. 18 - A thermocouple, with a spherical junction diameter...Ch. 18 - Prob. 27PCh. 18 - Prob. 28PCh. 18 - Carbon steel balls (ρ = 7833 kg/m3, k = 54 W/m·K,...Ch. 18 - Prob. 31PCh. 18 - Prob. 32PCh. 18 - Prob. 33PCh. 18 - Prob. 34PCh. 18 - Prob. 35PCh. 18 - Prob. 36PCh. 18 - Prob. 37PCh. 18 - Prob. 38PCh. 18 - Prob. 39PCh. 18 - A body at an initial temperature of Ti is brought...Ch. 18 - In a meat processing plant, 2-cm-thick steaks (k =...Ch. 18 - Prob. 42PCh. 18 - Prob. 43PCh. 18 - Prob. 45PCh. 18 - Prob. 46PCh. 18 - Prob. 47PCh. 18 - Prob. 48PCh. 18 - Prob. 49PCh. 18 - A long iron rod (ρ = 7870 kg/m3, cp = 447 J/kg·K,...Ch. 18 - Prob. 51PCh. 18 - A long 35-cm-diameter cylindrical shaft made of...Ch. 18 - Prob. 54PCh. 18 - Prob. 55PCh. 18 - Prob. 56PCh. 18 - A father and son conducted the following simple...Ch. 18 - Prob. 58PCh. 18 - Prob. 59PCh. 18 - Citrus fruits are very susceptible to cold...Ch. 18 - Prob. 61PCh. 18 - Prob. 63PCh. 18 - Prob. 64PCh. 18 - Prob. 65PCh. 18 - White potatoes (k = 0.50 W/m·K and α = 0.13 × 10−6...Ch. 18 - Prob. 67PCh. 18 - Prob. 68PCh. 18 - Prob. 69PCh. 18 - Consider a hot semi-infinite solid at an initial...Ch. 18 - Prob. 71PCh. 18 - Prob. 72PCh. 18 - Prob. 73PCh. 18 - Prob. 74PCh. 18 - Prob. 75PCh. 18 - Prob. 76PCh. 18 - Prob. 77PCh. 18 - Prob. 78PCh. 18 - Prob. 79PCh. 18 - Prob. 81PCh. 18 - Prob. 82PCh. 18 - Prob. 83PCh. 18 - Prob. 84PCh. 18 - Prob. 85PCh. 18 - Prob. 86PCh. 18 - Prob. 88PCh. 18 - Prob. 89PCh. 18 - A 2-cm-high cylindrical ice block (k = 2.22 W/m·K...Ch. 18 - Prob. 91PCh. 18 - Prob. 93PCh. 18 - Prob. 94RQCh. 18 - Large steel plates 1.0-cm in thickness are...Ch. 18 - Prob. 96RQCh. 18 - Prob. 97RQCh. 18 - Prob. 98RQCh. 18 - Prob. 99RQCh. 18 - Prob. 100RQCh. 18 - Prob. 101RQCh. 18 - Prob. 102RQCh. 18 - The water main in the cities must be placed at...Ch. 18 - Prob. 104RQCh. 18 - Prob. 105RQCh. 18 - Prob. 106RQCh. 18 - Prob. 107RQ
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