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

[LordGfcd]

Assume there is a boundary separates 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) ?

 

[Chestermiller]

Assume there is a boundary separates 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.