Since the correlation given in the textbook is so complicated, for convection over a sphere. proposes the correlation to be NUD = 2+ C Re Pr¹/3 used a steel sphere (conductivity of 42 W/m-K) of 20 cm diameter that generates steady 40 W heat. placed it in air flow with 1 m/s where air temperature is 20°C. then measured the steady state tempera- ture of the sphere surface to be 30°C. Based on come up with a new correlation 2 measurements, what is the convection coefficient? 318 W/m²K Using properties at film temperature, what should the value of C be as per assumes m = 0.8? 0.142 What is the temperature at the center of the sphere? 30'38 ℃ calculations if
Since the correlation given in the textbook is so complicated, for convection over a sphere. proposes the correlation to be NUD = 2+ C Re Pr¹/3 used a steel sphere (conductivity of 42 W/m-K) of 20 cm diameter that generates steady 40 W heat. placed it in air flow with 1 m/s where air temperature is 20°C. then measured the steady state tempera- ture of the sphere surface to be 30°C. Based on come up with a new correlation 2 measurements, what is the convection coefficient? 318 W/m²K Using properties at film temperature, what should the value of C be as per assumes m = 0.8? 0.142 What is the temperature at the center of the sphere? 30'38 ℃ calculations if
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Correlation for Convection Over a Sphere**
Since the correlation given in the textbook is so complicated, a new correlation is proposed for convection over a sphere:
\[ \overline{NU_D} = 2 + C \, \text{Re}_D^m \, \text{Pr}^{1/3} \]
A steel sphere with a conductivity of 42 W/m·K and a diameter of 20 cm generates a steady 40 W of heat. It is placed in an airflow with a speed of 1 m/s where the air temperature is 20°C. The steady-state temperature of the sphere surface is then measured to be 30°C.
1. **Based on these measurements, what is the convection coefficient?**
**31.8 W/m²·K**
2. **Using properties at film temperature, what should the value of C be as per calculations if m = 0.8?**
**0.142**
3. **What is the temperature at the center of the sphere?**
**30.38°C**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20000a63-5a8a-4b5e-adbd-85ecbf6c298b%2F41fb0189-3b4d-4bf1-a132-355e8d2cd009%2F13m4x7j_processed.png&w=3840&q=75)
Transcribed Image Text:**Correlation for Convection Over a Sphere**
Since the correlation given in the textbook is so complicated, a new correlation is proposed for convection over a sphere:
\[ \overline{NU_D} = 2 + C \, \text{Re}_D^m \, \text{Pr}^{1/3} \]
A steel sphere with a conductivity of 42 W/m·K and a diameter of 20 cm generates a steady 40 W of heat. It is placed in an airflow with a speed of 1 m/s where the air temperature is 20°C. The steady-state temperature of the sphere surface is then measured to be 30°C.
1. **Based on these measurements, what is the convection coefficient?**
**31.8 W/m²·K**
2. **Using properties at film temperature, what should the value of C be as per calculations if m = 0.8?**
**0.142**
3. **What is the temperature at the center of the sphere?**
**30.38°C**
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