Chapter 12

Irradiation on a semi-transparent medium is at a rate of \(520 \mathrm{~W} / \mathrm{m}^{2}\). If \(160 \mathrm{~W} / \mathrm{m}^{2}\) of the irradiation is reflected from the medium and \(130 \mathrm{~W} / \mathrm{m}^{2}\) is transmitted through the medium, determine the medium's absorptivity, reflectivity, transmissivity, and emissivity.

Consider an opaque horizontal plate that is well insulated on the edges and the lower surface. The plate is uniformly irradiated from above while air at \(T_{\infty}=300 \mathrm{~K}\) flows over the surface providing a uniform convection heat transfer coefficient of \(40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Under steady state conditions the surface has a radiosity of \(4000 \mathrm{~W} / \mathrm{m}^{2}\), and the plate temperature is maintained uniformly at \(350 \mathrm{~K}\). If the total absorptivity of the plate is \(0.40\), determine \((a)\) the irradiation on the plate, \((b)\) the total reflectivity of the plate, \((c)\) the emissive power of the plate, and \((d)\) the total emissivity of the plate.

Consider an opaque plate that is well insulated on the edges and it is heated at the bottom with an electric heater. The plate has an emissivity of \(0.67\), and is situated in an ambient surrounding temperature of \(7^{\circ} \mathrm{C}\) where the natural convection heat transfer coefficient is \(7 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). To maintain a surface temperature of \(80^{\circ} \mathrm{C}\), the electric heater supplies \(1000 \mathrm{~W} / \mathrm{m}^{2}\) of uniform heat flux to the plate. Determine the radiosity of the plate under these conditions.

A horizontal plate is experiencing uniform irradiation on the both upper and lower surfaces. The ambient air temperature surrounding the plate is \(290 \mathrm{~K}\) with a convection heat transfer coefficient of \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). Both upper and lower surfaces of the plate have a radiosity of \(4000 \mathrm{~W} / \mathrm{m}^{2}\), and the plate temperature is maintained uniformly at \(390 \mathrm{~K}\). If the plate is not opaque and has an absorptivity of \(0.527\), determine the irradiation and emissivity of the plate.

A semi-transparent plate \(\left(A_{1}=2 \mathrm{~cm}^{2}\right)\) has an irradiation of \(500 \mathrm{~W} / \mathrm{m}^{2}\), where \(30 \%\) of the irradiation is reflected away from the plate and \(50 \%\) of the irradiation is transmitted through the plate. A radiometer is placed \(0.5 \mathrm{~m}\) above the plate normal to the direction of viewing from the plate. If the temperature of the plate is uniform at \(350 \mathrm{~K}\), determine the irradiation that the radiometer would detect.

When the earth is closest to the sun, we have winter in the northern hemisphere. Explain why. Also explain why we have summer in the northern hemisphere when the earth is farthest away from the sun.

Explain why surfaces usually have quite different absorptivities for solar radiation and for radiation originating from the surrounding bodies.

You have probably noticed warning signs on the highways stating that bridges may be icy even when the roads are not. Explain how this can happen.

What changes would you notice if the sun emitted radiation at an effective temperature of \(2000 \mathrm{~K}\) instead of \(5762 \mathrm{~K}\) ?

What is the solar constant? How is it used to determine the effective surface temperature of the sun? How would the value of the solar constant change if the distance between the earth and the sun doubled?