Insulation thickness for steam pipe

[hala.merghani]

hello everybody, I'm new here and i have this homework which i don't know how to solve it, please help me:
Design the thickness of insulation for steam pipe of:
-Pipe diameter 2 in.
-Pipe length 200 m.
-Saturated steam pressure 10 bar.
-Ambient temperature 30°C.
-Steam cost $4.5/MMbtu

i thought about searching for the material first, but the basic problem is that i don't really know where to start with, i do NOT want you to solve my homework, i just wish if someone tells me where to start with!

 

[LawrenceC]

What are the criteria for the design? Maximum outside temperature for safety reasons? We need more information.

 

[LawrenceC]

Given the proper design criteria, you will have to work out the steady state solution in cylindrical coordinates for the LaPlace equation. You'll have to decide on the proper boundary conditions in order to determine outside temperature and heat loss. You must know the thermal conductivity of the insulation material. Is the insulation aluminum sheathed?

 

[hala.merghani]

let's say the maximum outside temperature is 50°C, and knowing the saturated pressure from the steam tables i found that the saturated temperature is 184.154°C. if i chose fiberglass for insulation, which has an emmisivity of 0.75, and a thermal conductivity of 0.06 W/m.K at 184.154°C, and if we assumed that its price per square foot is 0.8$, that's how far I've made it, but you see the main problem is that i don't know which law shall i apply, or should i neglect or consider the radiation? and I forgot to mention that we want to find the economic thickness

 

[LawrenceC]

Whether you consider radiation or not is a consideration you must make. In order to make it, decide which is the stronger boundary condition, radiation or still air. Your result will tell you whether both or only one should be included. Use a natural convection correlation to determine the strength of the still air condition. The radiation heat loss at 50 C is very easy to compute. If the pipe is in an area where it is windy most of the time, then use a forced convection condition instead of natural convection.

 

[RTW69]

This is a one-dimensional, stead-state conduction heat transfer problem. If you do a Google search for "Critical Thickness of cylindrical insulation" you can find the appropriate heat loss equations. Typically you are interested in the conductive and outside convective resistances. You are trying to optimize total costs (energy and material costs) vs. insulation thickness. To get a sense on how to solve this problem I would neglect the outside convective losses to begin with and concentrate on the conductive losses. Assume an insulation thickness, find q and determine energy and insulation costs. Assume a new insulation thickness determine costs. You get the idea. Add the convective heat loss component to get a more accurate solution.

 

[RTW69]

You will also need to know how many hours a year the pipe is heated and the estimated life of the insulation. I would divide the insulation costs by the insulation life and bring the time period to a yearly basis however generally you would calculate over the life of the insulation and account for fuel inflation costs as well.

 

[LawrenceC]

Typically you are interested in the conductive and outside convective resistances.

There are no conductive losses without the radiation and convection losses. The only reason why there is a 'conductive loss' is because the pipe with insulation loses heat via radiation and convection. It creates a temperature gradient across the pipe wall and insulation that equals the heat that is conducted radially. For this instance radiation losses are of the same order of magnitude as convection losses and should be considered.