A \(0.2 \mathrm{~m} \times 0.2 \mathrm{~m}\) street sign surface has an absorptivity of \(0.6\) and an emissivity of \(0.7\), while the street sign is subjected to a cross flow wind at \(20^{\circ} \mathrm{C}\) with a velocity of \(1 \mathrm{~m} / \mathrm{s}\). Solar radiation is incident on the street sign at a rate of \(1100 \mathrm{~W} / \mathrm{m}^{2}\), and the surrounding temperature is \(20^{\circ} \mathrm{C}\). Determine the surface temperature of the street sign. Evaluate the air properties at \(30^{\circ} \mathrm{C}\). Treat the sign surface as a vertical plate in cross flow.

Question: Determine the temperature on the surface of a street sign subjected to solar radiation and cross-flow wind, given that the sign dimensions are \(0.2m \times 0.2m\), sign surface absorptivity is \(\alpha = 0.6\), sign surface emissivity is \(\varepsilon = 0.7\), wind temperature is \(T_{wind} = 20^{\circ}C\), wind velocity is \(1 m/s\), solar radiation is \(1100 \, W/m^2\), surrounding temperature is \(20^{\circ}\)C, and air properties are evaluated at \(30^{\circ}\)C. Answer: To determine the temperature on the surface of the street sign, follow these steps: 1. Find the radiative heat transfer: \(q''_{rad} = 660 \, W/m^2\). 2. Find the convective heat transfer coefficient using the empirical correlation for a vertical plate in cross-flow. 3. Calculate the convective heat transfer: \(q''_{conv} = h(T_s-T_{wind})\). 4. Apply the energy balance equation: \(q''_{rad} = q''_{conv}\). 5. Evaluate air properties at the specified temperature, \(30^{\circ}\)C. 6. Solve for the surface temperature, \(T_s\), of the street sign.