Process Plant Layout, 2nd Edition

Example B.12

(a) Consider a large steel vessel, wall thickness 16 mm protected by 40 mm of vermiculite cement. Find the metal temperature after 1 and 2 h in a flux of 100 kW m⁻² for surface emissivities of 1 (~black), 0.3 (~aluminum paint), and 0.1 (~white). Properties of steel are density 7800 kg m⁻³, specific heat 0.5 kJ kg⁻¹ K⁻¹ and properties of vermiculite are density 430 kg m⁻³, specific heat 0.84 kJ kg⁻¹ K⁻¹ and thermal conductivity 9.5 × 10⁻⁵ kW m⁻¹ K⁻¹.

ANSWER

Surface temperature	$\begin{array}{ll}100\hfill & =5.6697\times {10}^{-11}({T_{\mathrm{s}}}^4-{293}^4)+\frac{0.01}{\epsilon }(T_{\mathrm{s}}-293)\hfill \\ T_{\mathrm{s}}\hfill & =856,797,640°\mathrm{C}\mathrm{for}\epsilon =1,0.3,\mathrm{and}0.1\hfill \end{array}$
Insulation time constant	$\begin{array}{ll}{t}_{\mathrm{c}}\hfill & =\left(\frac{W_{\mathrm{R}}{s}_{\mathrm{R}}}{A_{\mathrm{R}}}+\frac{x_{\mathrm{I}}{\rho }_{\mathrm{I}}{s}_{\mathrm{I}}}{2}\right)\frac{x_{\mathrm{I}}}{k_{\mathrm{I}}}\hfill \\ =(\frac{7,800\times 0.016A_{\mathrm{R}}\times 0.5}{}\hfill \end{array}$