Thermodynamics - time to cook an egg

[FEAnalyst]

Hi,

as Easter is slowly approaching, I came up with an egg cooking thermodynamics problem that I would like to solve. My formulation of the problem including necessary simplifications is as follows:

Let's assume that an egg is a sphere-shaped solid body made of homogenous material (ignoring the fact that its actually made of yolk and white). During cooking its outer surface is heated to 95 °C (initial temperature about 5 °C). How long will it take to heat the inside of that egg to 50 °C ?

I know how to solve this problem using Finite Element Analysis (numerical analysis claims the time is about 860 s) but how can I do it using hand calculations ? There are some examples about conduction (Fourier's law) in spherical coordinates but they all refer to shells. There's also a complex derivation of equation for egg cooking time based on thermal diffusion equation but it's not what I want too. Is it possible to do it for homogenous solid body assuming conduction only ? Could you show the subsequent steps required to solve it ? I'm not good at differential equations solved analytically so I would be grateful for help.

P.S. It may sound like a homework task but it's definitely not the case. Just a real-life problem.

 

[hutchphd]

Hi,

as Easter is slowly approaching, I came up with an egg cooking thermodynamics problem that I would like to solve. My formulation of the problem including necessary simplifications is as follows:

Let's assume that an egg is a sphere-shaped solid body made of homogenous material (ignoring the fact that its actually made of yolk and white). During cooking its outer surface is heated to 95 °C (initial temperature about 5 °C). How long will it take to heat the inside of that egg to 50 °C ?

I know how to solve this problem using Finite Element Analysis (numerical analysis claims the time is about 860 s) but how can I do it using hand calculations ? There are some examples about conduction (Fourier's law) in spherical coordinates but they all refer to shells. There's also a complex derivation of equation for egg cooking time based on thermal diffusion equation but it's not what I want too. Is it possible to do it for homogenous solid body assuming conduction only ? Could you show the subsequent steps required to solve it ? I'm not good at differential equations solved analytically so I would be grateful for help.

P.S. It may sound like a homework task but it's definitely not the case. Just a real-life problem.

What is the difference, in your reckoning, between conduction and diffusion of heat??
I believe you need to solve the heat diffusion equation for a homogeneous sphere with a step in the surface temperature at time zero. I'm sure this can be found. It may be solvable for an ellipsoid as well...