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+clear;

+clc;

+

+//Example3.12[Effect of fins on Heat transfer from steam pipes]

+//Given:-

+k_fin=180;//thermal conductivity of aluminium alloy fins[W/m.degree Celcius]

+D_tout=0.03;//Outer diameter of tube[m]

+D_fout=0.06;//Outer diameter of circular fins[m]

+t=0.002;//thickness of fin[m]

+s=0.003;//distance between fins attached to the tube[m]

+n=200;//number of fins per meter of tube

+L=1;//length of tube[m]

+T_surr=25;//Surrounding temperature[degree Celcius]

+T_wall=120;//Temperature of wall of the tube[degree Celcius]

+h=60;//Combined heat transfer coefficient[W/m^2.degree Celcius]

+//Solution:-

+disp("In case of no fins")

+A_nf=%pi*D_tout*L;//Area of tube with no fins attached[m^2]

+//Using Newton's Law of cooling

+Q_nf=h*A_nf*(T_wall-T_surr);//[W]

+disp("W",Q_nf,"Rate of heat transfer when no finis attached")

+//The efficiency of the circular fins attached to a circular tube is plotted in Fig 3.43

+L_fin=(D_fout-D_tout)/2;//[m]

+//In this case we have following corrected parameters

+r2c=(D_fout+t)/2;//[m]

+Lc=L_fin+(t/2);//[m]

+Ap=Lc*t;//[m^2]

+r=r2c/(D_tout/2);

+alpha=(Lc*sqrt(Lc))*sqrt(h/(k_fin*Ap));//efficiency

+disp(alpha)

+//for above value of alpha efficiency is found out from the plot in fig 3.43

+neta=0.96;

+A_f=2*%pi*((r2c^2)-((D_tout/2)^2));//Area of tube with fins attached to it[m^2]

+Q_f_max=h*A_f*(T_wall-T_surr);//maximum rate of heat transfer[W]

+Q_f=neta*Q_f_max;//Heat transfer through tube with fins is efficiency times the maximum rate of heat transfer[W]

+disp("W",Q_f,"Heat transfer due to the finned tube")

+//From unfinned portion

+A_uf=%pi*D_tout*s;//Unfinned area between two consecutive fins[m^2]

+Q_uf=h*A_uf*(T_wall-T_surr);//[W]

+disp("W",Q_uf,"Heat transfer from the unfinned portion of the tube is")

+//Since there are 200 fins per meter of the tube hence 200 interfin spacing 

+Q_tf=n*(Q_f+Q_uf);//[W]

+disp("W",Q_tf,"The total Heat transfer from the finned tube is")

+Q_increase=Q_tf-Q_nf;//[W]

+disp("W",Q_increase,"The increase in heat transfer from the tube per meter of length as a result of the addition of fins is")

+eff=Q_tf/Q_nf;//Effectiveness

+disp(eff,"The rate of heat transfer from the steam tube increases by a factor of")

+disp("as a result of adding fins")