A hot liquid stream at a temperature of $200C$ flows through a steel pipeline

connecting a reactor to a separating column. The pipe has an internal diameter of

$100mm$ and an external diameter of $110mm.$ In order to reduce heat losses to the

surrounding air at $20C$ the pipe surface is to be covered along its entire length by a

layer of insulation. The internal heat transfer coefficient for the flowing liquid is high

and the thermal resistance of the pipe wall may be neglected.

$($ii$)$ Estimate the required insulation thickness if the heat loss to the surroundings

is not to exceed $100W$ per metre length.

$($iii$)$ An additional layer of insulation, which has a thermal conductivity of $0\mathrm{.}01$

W$/$m$.$K$,$ is to be added to outside of the pipe to reduce heat losses further.

Determine the maximum thickness of this layer of insulation which may be

added if its maximum temperature is to remain below $60C.$

Free convection from the extemal surface of a cylinder is described by the

expression:

$h=1\mathrm{.}32(T_{\text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}}-T_{}{)}^3$

where $h$ is the heat transfer coefficient in the surrounding air $(\frac{W}{m^2}K)$

Data:

Insulation Properties

Thermal Conductivity

$,0\mathrm{.}06\frac{W}{m}.K$A hot liquid stream at a temperature of $200\backslash$deg C flows through a steel pipeline

connecting a reactor to a separating column. The pipe has an internal diameter of

$100$mm and an external diameter of $110$ mm$.$ In order to reduce heat losses to the

surrounding air at $20\backslash$deg C the pipe surface is to be covered along its entire length by a

layer of insulation. The internal heat transfer coefficient for the flowing liquid is high

and the thermal resistance of the pipe wall may be neglected.

$($ii$)$ Estimate the required insulation thickness if the heat loss to the surroundings

is not to exceed $100$ W per metre length.

$($iii$)$ An additional layer of insulation, which has a thermal conductivity of $0\mathrm{.}01$

W$/$m$.$K$,$ is to be added to outside of the pipe to reduce heat losses further.

Determine the maximum thickness of this layer of insulation which may be

added if its maximum temperature is to remain below $60.$