One side of a 2-m-high and 3-m-wide vertical plate at 80°C is to be cooled by attaching aluminum fins (k= 237 W/m-K) of a rectangular profile in an environment at 35°C. The fins are 2 cm long, 0.3 cm thick, and 0.4 cm apart. The heat transfer coefficient between the fins and the surrounding air for combined convection and radiation is estimated to be 30 W/m2·K. Assuming steady one-dimensional heat transfer along the fin and taking the nodal spacing to be 0.5 cm, determine
(a) the finite difference formulation of this problem,
(b) the nodal temperatures along the fin by solving these equations,
(c) the rate of heat transfer from a Single fin, and
(d) the rate of heat transfer from the entire finned surface of the plate.