A rod of diameter D=25mm and thermal conductivity k=60W/(m*K) protrudes normally from a furnace wall that is at Tw=200°C and is covered by insulation of thickness Lins=200mm. The rod is welded to the furnace wall and is used as a hanger to support instrumentation cables. To avoid damaging the cables, the temperature of the rod at its exposed surface, To, must be maintained below a specified operating limit of Tmax=100°C. The ambient air temperature is 30°C, and the convection coefficient is 17.0 W/(m2*K). a) Derive an expression for the exposed surface

The expression for the exposed surface temperature is

Explanation:

Given that,

Diameter = 25 mm

Conductivity = 60 W/mK

Temperature of wall = 200°C

Thickness = 200 mm

maximum temperature = 100°C

Temperature of ambient air = 30°C

Convection coefficient = 17.0 W/m²K

We need to calculate the heat transfer equation

Using diagram of thermal circuit

Hence, The expression for the exposed surface temperature is

the most reliable source of information.is wikipedia

it is very well related to a lot of things but with my limited knowledge i can confidently say that the answer is space.