An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly W } mk k = 0.6 overall density of p = 1000 kg and heat capacity of C₂ = m² = 90°C The egg is initially at a uniform temperature of T₁ = 10°C and is dropped into boiling water at T Taking the convective heat transfer coefficient to be h = 10- -determine how long it will take for the egg to W m²K reach T = 70°C. In solving this problem, please use the lump model method (ignoring the requirement of small Biot number and discuss the outcomes, In solving the problem, please follow the steps below. For the Lump Model 3000 = 3000K 1. Compute the volume and surface area of the sphere (as the egg model) 2. Compute the characteristic length Lc Vol As 3. Compute the diffusivity a = k PCp =

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Chapter8: Natural Convection
Section: Chapter Questions
Problem 8.28P
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An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly
k = 0.6-
W
mk
overall density of p = 1000; and heat capacity of C₂ = 3000-
kg
m²
The egg is initially at a uniform temperature of T₂ = 10°C and is dropped into boiling water at T..
= 90°C
W
- determine how long it will take for the egg to
m²K
Taking the convective heat transfer coefficient to be h
reach T = 70°C.
In solving the problem, please follow the steps below.
For the Lump Model
In solving this problem, please use the lump model method (ignoring the requirement of small Biot
number and discuss the outcomes,
1.
2. Compute the characteristic length Lc
Compute the volume and surface area of the sphere (as the egg model)
Vol
As
3. Compute the diffusivity α =
= 10-
k
p Cp
=
J
kgk
Compute non-dimensional excessive temperature 0
=
h Lc
k
4. Compute the Biot number using the characteristic length found above Bi
=
T-Too
5.
Ti-Too
6.
Calculate the Fourier number from the equation =
exp(-Bi * Fo)
7. Calculate the time to achieve the target temperature T from the Fourier number Fo =
(at)/Lc²
Transcribed Image Text:An ordinary egg can be approximated as a 5.5-cm-diameter sphere whose thermal conductivity of roughly k = 0.6- W mk overall density of p = 1000; and heat capacity of C₂ = 3000- kg m² The egg is initially at a uniform temperature of T₂ = 10°C and is dropped into boiling water at T.. = 90°C W - determine how long it will take for the egg to m²K Taking the convective heat transfer coefficient to be h reach T = 70°C. In solving the problem, please follow the steps below. For the Lump Model In solving this problem, please use the lump model method (ignoring the requirement of small Biot number and discuss the outcomes, 1. 2. Compute the characteristic length Lc Compute the volume and surface area of the sphere (as the egg model) Vol As 3. Compute the diffusivity α = = 10- k p Cp = J kgk Compute non-dimensional excessive temperature 0 = h Lc k 4. Compute the Biot number using the characteristic length found above Bi = T-Too 5. Ti-Too 6. Calculate the Fourier number from the equation = exp(-Bi * Fo) 7. Calculate the time to achieve the target temperature T from the Fourier number Fo = (at)/Lc²
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