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

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