What is the continuity condition for the heat flux through a boundary?

  • #1
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Assume there is a boundary seperates two medium with different heat conductivity [κ][/1] and [κ][/2]. In one medium, the temperature distribution is [T][/1](r,θ,φ) and on the other medium is [T][/2](r,θ,φ). What is the relationship between [T][/1] and [T][/2] ?
Is it - [κ][/1]grad [T][/1]=- [κ][/2]grad [T][/2] or - [κ][/1](d[T][/1]/dn)=- [κ][/2](d[T][/2]/dn) ?
 

Answers and Replies

  • #2
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Assume there is a boundary seperates two medium with different heat conductivity [κ][/1] and [κ][/2]. In one medium, the temperature distribution is [T][/1](r,θ,φ) and on the other medium is [T][/2](r,θ,φ). What is the relationship between [T][/1] and [T][/2] ?
Is it - [κ][/1]grad [T][/1]=- [κ][/2]grad [T][/2] or - [κ][/1](d[T][/1]/dn)=- [κ][/2](d[T][/2]/dn) ?
If n signifies the normal to the boundary, then the latter is correct.
 

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