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Consider steady one-dimensional heat conduction in a pin fin of constant diameter
Dwith constant thermal conductivity k and surface emissivity
\epsi . The fin is losing heat by convection to the ambient air at
T_(\infty )with a convection coefficient of
h, and by radiation to the surrounding surfaces at an average temperature of
T_(surr ). The nodal network of the fin consists of nodes 0 (at the base), 1 (in the middle), and 2 (at the fin tip) with uniform nodal spacing of
\Delta x. Using the Finite Volume Method (energy balance method), obtain the discretized equations of this problem to determine node
1(T_(1)), node
2(T_(2)), for the specified temperature
T_(0)at the fin base and negligible heat transfer at the fin tip.