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Develop and explain each step the general equation of heat transfer by conduction in a constructive way...

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Mechanical Engineering

Develop and explain each step thegeneral equation of heat transfer by conduction ina constructive way starting from an element general differential inthe cartesian coordinate system and then reduce to get:
1) Laplace's equation (in R3)
Δ? = 0
2) The Poisson equation (with constant thermal conductivity?)
Δ? + ? '''= 0

Δ is the Laplacian operator and ? ''' is a source term.


Note: start the analysis from a differential element with volume??????. Make a energy balance over this volume considering that itcan increase if temperature in time according to its thermalcapacity. Give more generality to the model assuming there is asource term ? ''' which can be a source that produces thermalenergy or consume it.

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