Question

IF YOU CANNOT SOLVE THEM ALL THEN PLEASE DONT SOLVE ANY.

A hollow aluminum sphere, with an electrical heater in the center, is used in tests to determine the thermal conductivity of insulating materials. The inner and outer radii of the sphere are 0.15 and 0.18 m, respectively, and testing is done under steady-state conditions with the inner surface of the aluminum maintained at 250°C. In a particular test, a spherical shell of insulation is cast on the outer surface of the sphere to a thickness of 0.12 m. The system is in a room for which the air temperature is 20°C and the convection coefficient at the outer surface of the insulation is 30 W/m2.K. If 75W are dissipated by the heater under steady-state conditions, what is the thermal conductivity of the insulation? k; = i W/m-K Physical Properties Mathematical Functions

Answer 1

Dear student, as per the answering guidelines of Chegg, any expert can answer only one question in the case of multiple questions. So the detailed solution of the first question is given below.

Rinsulation . Sphere section *Cut section view. 9,=0.15m r2 = 0.18m Rg= 0.18+0.12 (outere radères + thickness) = 0.3m Q = AT 99-818 - 45 korurz uski rerz ho U23 Thermal conductivity galuminium at as0% 1 . das Kal= 235 W/ml

6 *75= 250-20 0.18-0.15 40*235x0.18X0us 0.3-0.18 48x kfo.370.18) 30x40X0.32 1 75 = 230 3.762x104 + 0.1768 0.02947 → 0.0298 +0.1768 - 3.067 кі (ke = 0.058 w/mk)