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//Variable declaration:
h = 140 //Convention heat transfer coefficient (W/m^2.K)
D1 = 10/10**3 //Rod diameter (m)
L = 2.5 //Rod length (m)
T1 = 200 //Surface temperature of rod ( C)
T2 = 25 //Fluid temperature ( C)
k = 1.4 //Thermal conductivity of bakellite (W/m.K)
l = 55/10**3 //Insulation thickness (m)
//Calculation:
Q1 = h*%pi*D1*L*(T1-T2) //Rate of heat transfer for the bare rod (W) (part 1)
Bi = 2 //Critical Biot number (part 2)
D2 = Bi*k/h //Critical diameter associated with the bakelite coating (m)
r2 = D2/2 //Critical radius associated with the bakelite coating (m)
r1 = D1/2 //Rod radius (m)
R1 = log(r2/r1)/(2*%pi*k*L) //Insulation conduction resistance ( C/W)
R2 = 1/(h*(2*%pi*r2*L)) //Convection thermal resistance ( C/W)
Rt1 = R1+R2 //Total thermal resistance ( C/W)
Qc = (T1-T2)/Rt1 //Heat transfer rate at the critical radius (W)
r3 = r1+l //New radius associated with the bakelite coating after insulation (m) (part 3)
R3 = log(r3/r1)/(2*%pi*k*L) //Insulation conduction bakelite resistance ( C/W)
R4 = 1/(h*(2*%pi*r3*L)) //Convection bakelite thermal resistance ( C/W)
Rt2 = R3+R4 //Total bakelite thermal resistance ( C/W)
Q2 = (T1-T2)/Rt2 //Heat transfer rate at the bakelite critical radius (W)
Re = ((Q1-Q2)/Q1)*100 //Percent reduction in heat transfer rate relative to the case of a bare rod (%)
//Result:
printf("1. The rate of heat transfer for the bare rod is : %0.f W .",Q1)
printf("2. The critical radius associated with the bakelite coating is : %.0f mm.",r2*10**3)
printf(" & the heat transfer rate at the critical radius is : %.0f W .",Qc)
printf("3. The fractional reduction in heat transfer rate relative to the case of a bare rod is : %.1f ",Re)
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