Problem $3$:

A student performs an experiment to determine the heat transfer

coefficient of an irregularly shaped body which is cooled by natural

convection. The following data are obtained during the first $1000$

seconds of the cooling process:

$T=143\mathrm{.}4$;$131\mathrm{.}4$;$120\mathrm{.}1$;$110\mathrm{.}6$;$102\mathrm{.}6$;$94\mathrm{.}6(C)$

$t=200$;$300$;$400$;$500$;$600$;$700(s)$

Knowing that the process may be adequately modeled by an exponential

relationship, you choose to fit the data to the following simple

expression: $,T(t)=T_{}+$Aexp$(-mt)$

Use the method of least squares to obtain the best $t$ of the data to the

proposed expression. Verify your fit at any three of the data points. The

ambient temperature may be assumed to be $T_{}=20C.$ How would you

determine the heat transfer coefficient from this expression?