Consider a surface of area \(A\) at which the convection and radiation heat transfer coefficients are \(h_{\text {conv }}\) and \(h_{\mathrm{rad}}\), respectively. Explain how you would determine \((a)\) the single equivalent heat transfer coefficient, and \((b)\) the equivalent thermal resistance. Assume the medium and the surrounding surfaces are at the same temperature.

Question: Calculate the single equivalent heat transfer coefficient and the equivalent thermal resistance for a surface with a convection heat transfer coefficient of \(h_{\text {conv }} = 10 \, W/m^2K\) and a radiation heat transfer coefficient of \(h_{\mathrm{rad}} = 5 \, W/m^2K\). The surface area is \(A = 2 \, m^2\). Answer: The single equivalent heat transfer coefficient, \(h\), is the sum of the convection and radiation heat transfer coefficients, so \(h = h_{\text {conv }} + h_{\mathrm{rad}} = 10 + 5 = 15 \, W/m^2K\). To find the equivalent thermal resistance, \(R_{\text{eq}}\), use the formula \(R_{\text{eq}} = \frac{1}{h \cdot A} = \frac{1}{15 \cdot 2} = 0.0333 \, K/W\). Therefore, the single equivalent heat transfer coefficient is \(15 \, W/m^2K\) and the equivalent thermal resistance is \(0.0333 \, K/W\).