A composite wall is composed of an insulating material of thermal conductivity (k_{text {ins }}=1.5 mathrm{~W} /

Question:

A composite wall is composed of an insulating material of thermal conductivity \(k_{\text {ins }}=1.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\) sandwiched between two 1-mm-thick stainless steel sheets of thermal conductivity \(k_{\mathrm{ss}}=15 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). The wall separates two fluids of temperatures \(T_{\infty, 1}=50^{\circ} \mathrm{C}\) and \(T_{\infty, 2}=25^{\circ} \mathrm{C}\), respectively. Determine the thickness of insulation required to limit the heat flux through the composite wall to \(60 \mathrm{~W} / \mathrm{m}^{2}\) for the cases shown in the table. The convection heat transfer coefficients are \(h=5 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) for gas free convection, \(h=50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) for gas forced convection, \(h=500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) for liquid forced convection, and \(h=5000 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) for either boiling or condensation.

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