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+clear;

+clc;

+printf("\t\t\tExample Number 1.8\n\n\n");

+// calculating minimum heat coefficient at the outer surface to maintain outer surface temperature at 100 degree celcius

+// solution

+

+

+T1 =200 ;//[degree celsius] temperature of the inner surface of the insulation layer

+

+

+Tf =20 ;//[degree celsius] temperature of the air

+k=1.5; //[W/m degree celcius] heat conductivity of insulator

+L=0.05;//[m] insulator thickness

+// Let T2 be the temperature of outer layer of the insulator

+// qconv = heat transfer rate from outer layer to the air

+//qcond = heat transfer rate across the insulator

+// if qconv > qcond, then T2 will decrease

+// if qcond > qconv, then T2 will increase

+// for T2 to not go above 100 degree celcius, qcond should be less than equal to qconv , and equality will be when T2 is equal to 100

+//thus qcond = qconv at T2=100

+// qcond = k*(T1-T2)/L = h*(T2-Tf)  = qconv

+//thus

+T2 =100 ;//[degree celsius]maximum permissible temperature of the outer surface 

+

+

+h = k*(T1-T2)/(L*(T2-Tf));// [W/m^2 degree celcius] convection heat trasnfer coefficient between insulator's outer surface and air 

+printf("The minimum convection heat transfer coefficient required to maintain outer surface tempereature below 100 is %f W/m^2 degreee celcius",h);