Derivation of boiling an egg formula using laplace transformation

crazystuff
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I have been set a challenge to derive the formula for boiling a “perfect” soft-boiled egg, (essentially a thermal diffusion equation), in terms of the mass of the egg, the specific heat capacity and thermal conductivity of an egg, the initial temperature of the egg and the temperature of the boiling water using Laplace Transformation. Is it even possible, if so, is it published anywhere or does anyone know someone who has succeeded so that I can work through it?

I have done a lot of background reading about the materials and make up of an egg and the transfer of heat and energy. I have done my introduction, but unfortunately I am not very good at mathematics. Therefore I have taught myself the Laplace transformation, but now I am completely stuck. Can anyone point me in the right direction please or is there anyone else I can contact who might be able to help me. I would be very grateful for any help given to me on this challenging subject.

Many Thanks
 
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what asumptions are you making? the mass of the egg is evenly distributed through out the egg? or are you seperating the yoke? is this egg spherical?
 

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