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+//Display mode

+mode(0);

+// Display warning for floating point exception

+ieee(1);

+clear;

+clc;

+disp("Introduction to heat transfer by S.K.Som, Chapter 2, Example 09")

+//A thin walled copper tube of outside metal radius r=0.01m carries steam at temprature, T1=400K.It is inside a room where the surrounding air temprature is Tinf=300K.

+T1=400;

+Tinf=300;

+r=0.01;

+//The tube is insulated with magnesia insulation of an approximate thermal conductivity of k=0.07W/(m*K)

+k=0.07;

+//External convective Coefficient h=4W/(m^2*K)

+h=4;

+//Critical thickness(rc) is given by k/h

+disp("The critical thickness of insulation in metre is")

+rc=k/h

+//We use the rate of heat transfer per metre of tube length as Q=(Ti-Tinf)/((ln(r2/r1)/(2*%pi*L*k))+(1/(h*2*%pi*r2*L))) where length,L=1m

+L=1;

+//When 0.002m thick layer of insulation r1=0.01m,r2=0.01+0.002=0.012m

+r1=0.01;//inner radius

+r2=0.012;//outer radius

+//Let ln(r2/r1)=X

+X=log(r2/r1)/log(2.718);

+//The heat transfer rate per metre of tube length is Q

+disp("The heat transfer rate Q per metre of tube length in W/m is ")

+Q=(T1-Tinf)/(((X)/(2*%pi*L*k))+(1/(h*2*%pi*r2*L)))

+//When critical thickness of insulation r1=0.01m,r2=0.0175m

+r2=0.0175;//outer radius

+r1=0.01;//inner radius

+//Let ln(r2/r1)=X

+X=log(r2/r1)/log(2.718);

+//The heat transfer rate per metre of tube length is Q 

+disp("The heat transfer rate per metre of tube length Q in W/m is ")

+Q=(T1-Tinf)/(((X)/(2*%pi*L*k))+(1/(h*2*%pi*r2*L)))

+//When there is a 0.05 m thick layer of insulation r1=0.01m,r2=.01+0.05=0.06m

+r1=0.01;//inner radius

+r2=0.06;//outer radius

+//Let ln(r2/r1)=X

+X=log(r2/r1)/log(2.718);

+//The heat transfer rate per metre of tube length is Q 

+disp("The heat transfer rate per metre of tube length Q in W/m is ")

+Q=(T1-Tinf)/(((X)/(2*%pi*L*k))+(1/(h*2*%pi*r2*L)))

+//It is important to note that Q increases by 5.2% when the insulation thickness increases from 0.002m to critical thickness. 

+//Addition of insulation beyond the critical thickness decreases the value of Q (The heat loss).

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