A cylinder, initially at $300$ K $,$ is plunged into a large melt of a low melting point metal maintained at $810$ K ; the heat transfer coefficient may be taken to be infinity. The dimensions of the cylinder are $230$ mm diameter and $150$ mm length.

a$)$ After $100$ s of heating in the melt, what is the temperature in the geometric center of the cylinder?

b$)$ After $5$ s $,$ what is the temperature at the centre of the circular surface?

Data: $k=5\mathrm{.}2W*m^{-1}*K^{-1}$;$=4810kg*m^{-3}$;$Cp=420J*k{g}^{-1}*K^{-1}.$