Consider a stainless steel spoon (k = 15.1 W/m K, = 0.6) that is partially

Consider a stainless steel spoon (k = 15.1 W/m · K, ε = 0.6) that is partially immersed in boiling water at 95°C in a kitchen at 25°C. The handle of the spoon has a cross section of about 0.2 cm × 1 cm and extends 18 cm in the air from the free surface of the water. The spoon loses heat by convection to the ambient air with an average heat transfer coefficient of h = 13 W/m² · K as well as by radiation to the surrounding surfaces at an average temperature of T_surr = 295 K. Assuming steady one-dimensional heat transfer along the spoon and taking the nodal spacing to be 3 cm,
(a) Obtain the finite difference formulation for all nodes,

(b) Determine the temperature of the tip of the spoon by solving those equations,

(c) Determine the rate of heat transfer from the exposed surfaces of the spoon.