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+clear;
+clc;
+
+//Example3.7[Heat Transfer to a Spherical Container]
+//Radiation effect is being considered. For the black tank emissivity=1
+//Given:-
+k=15;//thermal conductivity of stainless steel[W/m.degree Celcius]
+T_ice=0+273;//temeperature of iced water[K]
+T_tank=22+273;//temperature of tank stored at room temperature[K]
+h_in=80;//Heat Transfer Coefficient at the inner surface of the tank[W/m^2.degree Celcius]
+h_out=10;//Heat Transfer Coefficient at the outer surface of the tank[W/m^2.degree Celcius]
+heat_f=333.7;//Heat of fusion of water at atmospheric pressure[kJ/kg]
+e=1;//emissivity of tank
+sigma=5.67*(10^(-8));//Stefan's [W/m^2.K^4]
+D1=3;//inner diameter[m]
+D2=3.04;//Outer diameter[m]
+//Solution:-
+//a)
+A1=(%pi)*(D1^2);//Inner Surface area of the tank[m^2]
+A2=(%pi)*(D2^2);//outer Surface area of the tank[m^2]
+disp("The radiation heat transfer coefficient is given by ")
+disp("h_rad=e*sigma*((T2^2)+(T_tank^2))*(T2+T_tank)")
+disp("But we dont know the outer surface temperature T2 of the tank. hence we assume a T2 value")
+disp("since heat transfer inside the tank is larger ")
+T2=5+273;//[K]
+disp("K",T2,"Therefore taking T2 =")
+h_rad=e*sigma*((T2^2)+(T_tank^2))*(T2+T_tank);//[W/m^2.K]
+disp("W/m^2.degree Celcius",h_rad,"The radiation heat transfer coefficient is determined to be")
+//Individual Thermal Resistances Offered
+R_in=1/(h_in*A1);//Resistance to convetion from inner side of tank[degree Celcius/W]
+R_sphere=((D2-D1)/2)/(4*%pi*k*(D1/2)*(D2/2));//Resistance to conduction due to ice sphere[degree Celcius/W]
+R_out=1/(h_out*A2);//Resistance to convection from outer side of tank[degree Celcius/W]
+R_rad=1/(h_rad*A2);//Resistance to radiation heat transfer[degree Celcius/W]
+//R_out and R_rad are in parallel connection,
+R_eq=(1/((1/R_out)+(1/R_rad)));//[degree Celcius/W]
+//R_in,R_sphere and R_eq are connected in series
+R_total=R_in+R_sphere+R_eq;//[degree Celcius/W]
+Q_=(T_tank-T_ice)/R_total;//[W]
+disp("W",Q_,"The steady rate of heat transfer to the iced water is")
+disp("We determine outer surface temperature to check the validity of assumption")
+T2=T_tank-(Q_*R_eq);//[K]
+disp("K",T2)
+disp("which is sufficiently close to 278 K")
+//b)
+delta_t=24;//Time duration[h]
+Q=Q_*delta_t*(3600/1000);//[kJ]
+disp("kJ",Q,"The total amount of heat transfer during a 24 hour period is")
+//It takes 333.7 kJ of energy to melt 1kg of ice at 0 degree Celcius
+m_ice=Q/heat_f;//[kg]
+disp("kg",m_ice,"The amount of ice that will melt during 24h period is")