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+clear;

+clc;

+

+//Example3.8[Heat Loss through an Insulated Steam Pipe]

+//Given:-

+T_steam=320;//[degree Celcius]

+T_surr=5;//[degree Celcius]

+k_iron=80;//Thermal conductivity of cast iron[W/m.degree Celcius]

+k_insu=0.05;//Thermal conductivity of glass wool insulation[W/m.degree Celcius]

+h_out=18;//Covection heat transfer coefficient outside the pipe[w/m^2.degree Celcius]

+h_in=60;//Covection heat transfer coefficient insideside the pipe[w/m^2.degree Celcius]

+D_in=0.05;//Inner diameter of pipe[m]

+D_out=0.055;//Outer diameter of pipe[m]

+t=0.03;//Thickness of insulation[m]

+r=(D_out/2)+t;//Effective outer radius[m]

+L=1;//Length of pipe[m]

+//Solution:-

+//Areas of surfaces exposed to convection

+A1=2*%pi*(D_in/2)*L;//Inner Area of pipe[m^2]

+A2=2*%pi*(r)*L;//Outer Area of pipe[m^2

+//Individual Thermal Resistances

+R_conv_in=1/(h_in*A1);//Resistance to convetion from inner surface of pipe[degree Celcius/W]

+R_pipe=(log(D_out/D_in))/(2*%pi*k_iron*L);//Resitance to conduction through iron pipe[degree Celcius/W]

+R_insu=(log(r/(D_out/2)))/(2*%pi*k_insu*L);//Resistance to conduction through insulation[degree Celcius/W]

+R_conv_out=1/(h_out*A2);//Resistance to convetion from outer surface of insulation on pipe[degree Celcius/W]

+//All resistances are in series

+R_total=R_conv_in+R_pipe+R_insu+R_conv_out;//Total Resistance[degree Celcius]

+Q_=(T_steam-T_surr)/R_total;//[W]

+disp("W",Q_,"The Steady rate of heat loss from the steam per m length of pipe is")

+delta_T_pipe=Q_*R_pipe;//[degree Celcius]

+delta_T_insu=Q_*R_insu;//[degree Celcius]

+disp("degree Celcius",delta_T_insu,"and",delta_T_pipe,,"The temperature drop across the pipe and the insulation is respectively")
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