A 30-cm-radius metallic sphere is having thermal conductivity of k = 100. overall density ofW7mkp = 1500-kgm²and heat capacity of C₂ = 3000The sphere is initially at a uniform temperature ofkgkCOT₁ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient isassumed to be only h = 50;Wm²KUsing lump model, compute the temperature of the sphere after t = 1200 seconds.In solving this problem, please use and show the following steps (do not use EES)1. Compute the volume and surface area2. Compute the characteristic length Lc=kp Cph Lc4. Compute the Biot number Bik5. Calculate the Fourier number Fo= (at)/Lc²6. Calculate the excess temperature using 0 = exp(-Bi * Fo)T-Too7. Compute the target temperature T using 0 =Ti-Too3. Compute the diffusivity a ==the sphere VolVolAs==3r³ and А¸ = 4πr²

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W A 30-cm-radius metallic sphere is having thermal conductivity of k = 100; , overall density of mk kg = 1500- and heat capacity of C₂ = 3000; . The sphere is initially at a uniform temperature of kgk T¡ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient is assumed to be only h = 50- W m²K Jsing lump model, compute the temperature of the sphere after t = 1200 seconds. n solving this problem, please use and show the following steps (do not use EES) 1. Compute the volume and surface area of the sphere Vol = Vol 2. Compute the characteristic length Lc = As k 3. Compute the diffusivity a pCp h Lc k 5. Calculate the Fourier number Fo= (at)/Lc² 6. Calculate the excess temperature using 8 = exp(-Bi * Fo) T-Too 7. Compute the target temperature T using 8 = Ti-Too 4. Compute the Biot number Bi = ³ and A² = 4²

W A 30-cm-radius metallic sphere is having thermal conductivity of k = 100; , overall density of mk kg = 1500- and heat capacity of C₂ = 3000; . The sphere is initially at a uniform temperature of kgk T¡ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient is assumed to be only h = 50- W m²K Jsing lump model, compute the temperature of the sphere after t = 1200 seconds. n solving this problem, please use and show the following steps (do not use EES) 1. Compute the volume and surface area of the sphere Vol = Vol 2. Compute the characteristic length Lc = As k 3. Compute the diffusivity a pCp h Lc k 5. Calculate the Fourier number Fo= (at)/Lc² 6. Calculate the excess temperature using 8 = exp(-Bi * Fo) T-Too 7. Compute the target temperature T using 8 = Ti-Too 4. Compute the Biot number Bi = ³ and A² = 4²

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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Question

A 30-cm-radius metallic sphere is having thermal conductivity of k = 100. overall density of
W
7
mk
p = 1500-
kg
m²
and heat capacity of C₂ = 3000
The sphere is initially at a uniform temperature of
kgk
CO
T₁ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient is
assumed to be only h = 50;
W
m²K
Using lump model, compute the temperature of the sphere after t = 1200 seconds.
In solving this problem, please use and show the following steps (do not use EES)
1. Compute the volume and surface area
2. Compute the characteristic length Lc
=
k
p Cp
h Lc
4. Compute the Biot number Bi
k
5. Calculate the Fourier number Fo= (at)/Lc²
6. Calculate the excess temperature using 0 = exp(-Bi * Fo)
T-Too
7. Compute the target temperature T using 0 =
Ti-Too
3. Compute the diffusivity a =
=
the sphere Vol
Vol
As
==
3
r³ and А¸ = 4πr²

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