Answers.

A $=249\mathrm{.}6$ W$/$m

B$=189\mathrm{.}4$ W$/$m$.\%$error $+31\mathrm{.}8$A boilerhouse flue is constructed of two layers of brick, each $80mm$ thick, separated by a $60mm$ air gap. The internal diameter of the flue is $780mm.$ Assume the coefficients of thermal conductivity to be as follows: inner layer of brick, $1*15\frac{W}{m}K$; outer layer of brick, $1*33\frac{W}{m}K$; air, $0*034\frac{W}{m}K.$

The Temperature of the flue gasses and the ambient temperature around the flue are monitored regularly and on a particular afternoon are found to be $170C$ and $19C,$ respectively. It has always been company policy to estimate the heat loss from the flue, based on the on the assumption that the surface temperatures of the brick are the same as the temperatures of the flue gasses and the ambient air temperature.

$($a$)$ Calculate the heat loss per unit length of the flue pipe, following company policy.

$($b$)$ It has now been decided to check the accuracy of the heat loss estimation, taking into account the surface heat transfer. If the surface transfer coefficients for the internal and external surfaces of the flue are $3*1\frac{W}{m^2}K$ and $4*3\frac{W}{m^2}K,$ respectively, determine the percentage error of your answer to question $($a$).$

$($c$)$ What are the actual internal and external surface temperatures of the flue?$\%$

C $=145\mathrm{.}1$ degrees. $30\mathrm{.}5$ degrees