Consider steady one-dimensional heat conduction in a pin fin of constant diameter
D
with 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.