Question
In: Mechanical Engineering
Develop and explain each step the general equation of heat transfer by conduction in a constructive...
Develop and explain each step the
general equation of heat transfer by conduction in
a constructive way starting from an element general differential in
the 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 it
can increase if temperature in time according to its thermal
capacity. Give more generality to the model assuming there is a
source term ? ''' which can be a source that produces thermal
energy or consume it.
Solutions
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