Conduction in concentric spheres models heat transfer in which geometry?

Conduction in concentric spheres models heat transfer in which geometry?

• A. Spherical geometry
• B. Cylindrical geometry
• C. Planar geometry
• D. Toroidal geometry

Answer: (A)

Conduction in concentric spheres models heat transfer in spherical geometry because the temperature is assumed to depend only on the distance from the center, reflecting perfect radial symmetry. In this setup, the heat crossing any spherical shell must pass through a surface whose area scales with r^2 (4πr^2). That area scaling leads to the steady-state equation (1/r^2) d/dr (r^2 dT/dr) = 0, whose solution is T(r) = A + B/r. The temperature therefore changes with 1/r in spherical geometry. This contrasts with cylindrical geometry, where the area scales with r and the solution involves a logarithm, and planar geometry, which yields a linear temperature profile. So concentric spheres specifically correspond to spherical geometry.

Conduction in concentric spheres models heat transfer in spherical geometry because the temperature is assumed to depend only on the distance from the center, reflecting perfect radial symmetry. In this setup, the heat crossing any spherical shell must pass through a surface whose area scales with r^2 (4πr^2). That area scaling leads to the steady-state equation (1/r^2) d/dr (r^2 dT/dr) = 0, whose solution is T(r) = A + B/r. The temperature therefore changes with 1/r in spherical geometry. This contrasts with cylindrical geometry, where the area scales with r and the solution involves a logarithm, and planar geometry, which yields a linear temperature profile. So concentric spheres specifically correspond to spherical geometry.