SUMMARY
The continuity condition for heat flux through a boundary separating two media with different thermal conductivities, κ₁ and κ₂, is defined by the equation -κ₁(d[T₁]/dn) = -κ₂(d[T₂]/dn). This indicates that the heat flux, represented by the temperature gradient normal to the boundary, must be continuous across the interface. The temperature distributions in the two media are denoted as T₁(r,θ,φ) and T₂(r,θ,φ), respectively. The correct relationship emphasizes the importance of the normal derivative of temperature at the boundary.
PREREQUISITES
- Understanding of heat conduction principles
- Familiarity with thermal conductivity concepts
- Knowledge of gradient and normal vector mathematics
- Basic grasp of boundary conditions in physics
NEXT STEPS
- Study the derivation of Fourier's law of heat conduction
- Learn about boundary conditions in heat transfer problems
- Explore the implications of thermal conductivity differences in composite materials
- Investigate numerical methods for solving heat conduction equations
USEFUL FOR
Thermal engineers, physicists, and students studying heat transfer principles will benefit from this discussion, particularly those focusing on boundary conditions and heat flux continuity in multi-material systems.