Both ends of an aluminum rod of length 20 cm and cross-sectional area 4 cm² are kept at a temperature $0^{0}C$.  Thermal conductivity of aluminum is 205  $W/(m-k)$.  The initial distribution of temperature along the rod can be expressed as. $T=25\sin {\left(15.7x\right)}^{o}C$  Here length of the rod has been considered to be along the X direction and one of the ends as the origin so that  '$x$' in the initial temperature distribution equation refers to the $x$ position of any point on the rod. Also the angle in the sine term is in radian provided that  $x$ is expressed in the SI system. 
Answer the following questions.