A cylinder of radius r and thermal conductivity K 1 is surrounded by a cylindrical shell of linear radius r and outer radius 2 r , whose thermal conductivity is K 2 . There is no loss of heat across cylindrical surfaces, when the ends of th

Question

A cylinder of radius r and thermal conductivity K 1 is surrounded by a cylindrical shell of linear radius r and outer radius 2 r , whose thermal conductivity is K 2 . There is no loss of heat across cylindrical surfaces, when the ends of the combined system are maintained at temperatures T 1 a n d T 2 . The effective thermal conductivity of the system, in the steady state is

Quantrex Academy · Accepted Answer

Correct answer: C. K 1 + 3 K 2 4

∆ Q ∆ t i n n e r + ∆ Q ∆ t o u t e r = ∆ Q ∆ t t o t a l K 1 π r 2 ( T 2 - T 1 ) l + K 2 π 2 r 2 - r 2 ( T 2 - T 1 ) l = K π 2 r 2 T 2 - T 1 l or K 1 + 3 K 2 π r 2 T 2 - T 1 l = K π 4 r 2 ( T 2 - T 1 ) l ∴ K = K 1 + 3 K 2 4

Options

Correct answer

Step-by-step solution

More from Thermal Properties of Matter