Calculating Heat Loss in Long Pipe Transfer with Octave

[Philip West]

Homework Statement

Hello everyone, I hope that you guys could lend me a hand.
I need to calculate the heat loss at any point over a long pipe while considering lambda of the pipe. I am trying to use octave to find a reasonable flow-rate to keep the temperature loss to a minimum at a reasonable pressure.

lambda= 0.02
inner radius=0.1m
outer radius=0.2m
Distance=4000m
initial inside temperature 100C
outside temperature=10C

Assumptions:
laminar flow.
no vertical variations.

Homework Equations

The Attempt at a Solution

%Heat loss long distance transfer
%Initial Settings
PipeRadiusInside=0.1;
PipeRadiusOutside=0.2;
TotalPipeDistance=1000;
Time=1;
PipeSegmentLength=16;
OutsideTemperature=10;
InsulatingCapacity=0.020;
Temperature=[];
CurrentTemperature=100;
i=0;
%%
PipeThickness=PipeRadiusOutside-PipeRadiusInside;
Resistance=((PipeThickness*log(PipeRadiusOutside/PipeRadiusInside))/InsulatingCapacity); U=1/Resistance;
TemperatureDifference=CurrentTemperature-OutsideTemperature; SegmentVolume=2*pi*PipeSegmentLength; EnergyOfWater=4.2*TemperatureDifference*SegmentVolume*0.9982;
while i<TotalPipeDistance/Time i=i+PipeSegmentLength; Temperature=[Temperature CurrentTemperature]; HeatLoss=2*pi*PipeRadiusOutside*U*TemperatureDifference*PipeSegmentLength; EnergyOfWater=EnergyOfWater-HeatLoss; CurrentTemperature=((EnergyOfWater-HeatLoss)/(4.2*SegmentVolume*0.9982))+OutsideTemperature; TemperatureDifference=CurrentTemperature-OutsideTemperature;
end plot(Temperature)It gives me results which look like the could be right as it reacts to changes in variables correctly but it is definitely incorrect. Also I do not know how to relate it to flow rate.
I really need help and would be thankful for an example.

Thank you for your time.

 

[SteamKing]

Does lambda have any units associated with it?

 

[Philip West]

Does lambda have any units associated with it?

Yes. Sorry I forgot to mention that. (w/mK)