There is an insulating material with a semi-spherical shape (half hollow sphere) of inner radius R1 and outer radius R2. This insulating material is used for tops of a high-temperature reactor. The temperature of the inner face of the sphere is of T1 and the temperature of the external face is T2, both in stationary state during the process. Find the model that describes the variation of temperature with respect to to the (radial) thickness of the spherical material at steady state. Terms: T1, internal face temperature, 132 C T2, external face temperature, 1430 C R1, internal radius, 1.35 m R2, external radius, 1.75 m q, Heat flux, 175 kW/m2 k, thermal conductivity, 0.015 kW/m*K

The mathematical model that describes the temperature variation is as follows: (DEMOSTRATE and CHECK that it is the one shown in equation 2) (25 points)

T2-T 1 1 (2) T = TS + T. - T 1 R2 R T ( 8 (3) )