$1.(30$ points$)$ see Figure below $-$ In order to improve the quality of life at your remote cabin, you would like to use the waste heat from the chimney of a wood burning stove to heat water. The water will enter thin copper tubing that you will encircle around the chimney pipe. Assume the chimney provides a uniform heat flux to the entire surface area of the copper tubing.

a$.$ What is the average temperature of the water $\backslash ([\backslash$mathrm$\{$K$\}]\backslash )?$

b$.$ What length $[$m$]$ of copper tubing is required to provide the desired exit temperature?

c$.$ Assuming each coil length is simply the outer perimeter of the chimney, and accounting for the gap between coils, what length $[$m$]$ of chimney would be required for the coils? $($hint: round up the number of coils and consider how many gaps there are for n coils$).$

d$.$ Is the flow of water laminar or turbulent? Explain.

e$.$ What is the average heat transfer coefficient $\backslash (\backslash$left$[\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$cdot $\backslash$mathrm$\{$~K$\}\backslash$right$]\backslash )?$