Problem 6A pipe (see figure for data) carrying hot water through a covered section of a chemical processing plant has been identified for extra insulation in order to save money on energy expenditure. The water heats the wall to 95 ºC. You are the plant engineer who is to decide on the insulation specification for the job. Your first step is to identify the heat energy lost per m length of the existing pipe set-up. Identify a simple thermal circuit. Calculate the thermal resistances. Calculate the heat loss per m length of pipe. Assume that ambient temperature to be 12 ºC

Figure. Original pipe and lagging with convective cooling to air at 12 ºC

12 ºC95 ºC

Identify a simple thermal circuit

95 ºC 12 ºC

conduction conduction convection

pipeR laggingR convectionR

Calculate the thermal resistances.

kHabRconduction 2)/ln(

surfaceconvection AhR

1

0007254.01402)10/12ln(

pipeR

45786.011.02)12/16ln(

laggingR

205026.0

1008.0212

008.01000/)2/16(

m

rA

mr

outersurface

outer

97887.305026.051

convectionR in K/W per m length

Calculate the heat loss per m length of pipe.

7044.1843746.4

)1295(

43746.497887.345786.00007254.0

Q

R

RRRR

RTQ

equivalent

convectionlaggingpipeequivalent

equivalent

W per m length

Heat loss for the original pipe and lagging

The heat loss is to be reduced by replacing the lagging on the pipe. Your plant manager suggests that the budget available will be sufficient to give a total of 10 mm thickness of insulation of poly vinyl acetate / cork spray-on foam (thermal conductivity k=0.1 W/K m). You are to demonstrate the predicted energy savings. Calculate the new heat loss per m length of pipe.

Calculate the thermal resistances.

kHabRconduction 2)/ln(

surfaceconvection AhR

1

0007254.01402)10/12ln(

pipeR

56104.111.02)12/32ln(

laggingR

2100531.0

1016.0212

016.01000/)2/32(

m

rA

mr

outersurface

outer

98944.1100531.051

convectionR in K/W per m length

Calculate the heat loss per m length of pipe.

3724.235512.3

)1295(

5512.398944.156104.10007254.0

Q

R

RRRR

RTQ

equivalent

convectionlaggingpipeequivalent

equivalent

W per m length

Heat loss for the new pipe and lagging

Increasing the lagging thickness increases the surface area for convective heat loss more than the conductive heat loss is reduced by increasing the lagging thickness. Recommend to the plant manager that if this is all the extra lagging that can be afforded, it is not worth re-lagging the pipe.