Question

A three layer insulation is proposed for a computer room to be maintained at 20ºC. The materials chosen are 10mm layer finishing material inside with k = 0.12 W/mk and a 20 mm layer of weathering material on the outside with k = 0.25 W/mK. The heat gain is limited to 7 W/m2 . Determine the conductivity of the material required for the middle layer if the thickness is restricted to 100 mm. The convection coefficient on the inside is 30 W/m2 K. The outside air is at 39ºC with convection coefficient of 60 W/m2 K.

Answer 1

Answer:

Explanation:

Concept:

In order to provide effective insulation, the radius of insulation must be greater than the critical radius of insulation as at a critical radius of insulation maximum heat loss takes place.

The critical radius of insulation for a cylindrical pipe

Where k is the thermal conductivity of the insulating material and h is the heat transfer coefficient of the surrounding medium.

Critical radius for sphere is given by

Calculation:

Given:

k = 0.12 W/mK, h = 4 W/m2K,

Critical radius =

Minimum diameter = 2 × radius = 60 mm