Question $6(11$ points$)$

A $0\mathrm{.}8$ mm diameter copper wire $(k=373\frac{W}{m}.C$;$C_p=380\frac{J}{k}g.C$;$=9000k\frac{g}{m^3})$ at an initial temperature of $150C$ is quenched in water at $35C,$ with heat transfer coefficient, $h=85\mathrm{.}5\frac{W}{m^2}.C.$ Show step by step calculations to determine the following;

a$.$ Characteristic length of the copper wire, $L_c$ in m $.$

b$.$ Biot number, Bi$.$

c$.$ Reciprocal of time constant, $b.$

d$.$ Time required $($in seconds$)$ by the wire to reach a temperature of $95C.$