Question 14.2: An insulated steel pipe with inner and outer diameters di = ......
An insulated steel pipe with inner and outer diameters d_{i} = 100 mm and d_{o} = 110 mm, respectively, and length of 32 m carries steam at a temperature of 150°C while the air temperature is 30°C. The insulation thickness is 50 mm. The thermal conductivities of the pipe and insulation materials are k = 40 W/m K and k_{i} = 0.04 W/m K, respectively. The heat-transfer coefficients are: h_{i} = 50 W/m²K and h_{o} = 13 W/m²K.
Determine the rate of heat loss from steam to air for uninsulated and insulated pipe.
The insulation effect on the pipe heat loss is analyzed in Example 14.2.
Uninsulated pipe ( d_i = 0.1 m and d_o = 0.11 m)
Overall heat-transfer coefficient for the uninsulated pipe
U_{L}=1/[1/({\bf p}\,∗\,0.1\,∗\,50)+\ln\,(0.11/0.1)/(2{\bf p}\,∗\,40)+1/({\bf p}\,∗\,0.11\,∗\,13)]
=3.49\mathrm{~W/mK}
Rate of heat loss of the uninsulated pipe
Q=U_{\mathrm{L}}L~(t_{\mathrm{i}}-t_{\mathrm{o}})=3.49∗32∗(150-30)=13402\,\mathrm{W}Insulated pipe with d_{i}/d_{o} = 0.1 m/0.11 m and d_{oi} = 0.11 + 2∗0.05 = 0.21 m Overall heat-transfer coefficient of the insulated pipe
U_{\mathrm{{L,ins}}}=1/[1/(\mathbf{{p}}d_{\mathrm{{i}}}h_{\mathrm{{i}}})+\ln{(d_{\mathrm{{o}}}/d_{\mathrm{{i}}})/(2\mathbf{{p}}k_{})}+\ln{(d_{\mathrm{{oi}}}/d_{\mathrm{{o}}})/(2\mathbf{{p}}k_{\mathrm{{i}}})+1/(\mathbf{{p}}d_{\mathrm{{oi}}}h_{\mathrm{{o}}})}]U_{\mathrm{L,~ins}}=1/\Big[1/({\bf p}\,∗\,0.1\,∗{50})+\ln\,(0.11/0.1)/(2{\bf p}{}\,∗\,40)+\ln\,(0.21/0.11)\Big]
(2{\bf p}\ ∗\,0.04)+1/({\bf p}\ ∗\,0.21∗\,{ 13})\Big]\ =0.363\;\mathrm{W/mK}
Rate of heat loss of the insulated pipe
Q_{{ins}}=U_{\mathrm{{L,ins}}}L\left(t_{\mathrm{i}}-t_{\mathrm{o}}\right)=0.363\,∗\ 32\,∗\,\left(150-30\right)=1395\,\mathrm{W}Thus, in this case the pipe insulation reduces the heat loss by (1–Q_{ins}/Q) ∗ 100 = 90%.