It is proved from the below that the temperature of the egg varies from the shell to the center of the egg.
Using the 2-dimensional finite element method, we will need to find the Biot number of the system by using the formula:
[tex]\mathbf{Bi = \dfrac{h_c r_o}{k} }[/tex]
According to the Heisler chart, the curves in the graph represent a range of values for the inverse of the Biot number,
where;
[tex]\mathbf{Bi = \dfrac{h_c r_o}{k} }[/tex]
here;
By developing nodes based on assumptions;
[tex]\mathbf{Bi = \dfrac{1700 \times 0.025}{0.682} }[/tex]
Bi = 62.32
The inverse of Biot number is:
[tex]\mathbf{=\dfrac{1}{Bi}}[/tex]
[tex]\mathbf{=\dfrac{1}{62.32}}[/tex]
= 0.016
Similarly, the Fourier number [tex]\mathbf{F_o}}[/tex] is calculated by using the expression;
[tex]\mathbf{F_o = \dfrac{\alpha t }{r_o^2} }[/tex]
[tex]\mathbf{F_o = \dfrac{k t }{\rho c_pr_o^2} }[/tex]
where;
[tex]\mathbf{F_o = \dfrac{0.682 \times 15 \times 60 }{958.4 \times 4211 \times 0.025^2} }[/tex]
[tex]\mathbf{F_o = 0.243}[/tex]
Using the 2-dimensional finite element method, the temperature ratio is:
[tex]\mathbf{\dfrac{T(0,t) -T_{\infty}}{T_o -T_{\infty}} = 0.1 }[/tex]
T(0,t) = 100 + 0.1(4-100)
T(0,t) = 100 + 0.1(-96)
T(0,t) = 100 - 9.6
T(0, t) = 90.4° C
Therefore, we can conclude that it is proved that the temperature of the egg varies from the shell to the center of the egg.
Learn more about the Heisler chart here:
https://brainly.com/question/14839677?referrer=searchResults
