Chapter 5, Problem 5.103P

The structural components of modem aircraft are commonly fabricated of high-performance composite materials. These materials are fabricated by impregnating mats of extremely strong fibers that are held within a form with an epoxy or thermoplastic liquid. After the liquid cures or cools, the resulting component is of extremely high strength and low weight. Periodically, these components must be inspected to ensure that the fiber mats and bonding material do not become delaminated and. in turn, the component loses its airworthiness. One inspection method involves application of auniform. constant radiation heat flux to the surface being inspected. The thermal response of the surface is measured with an infrared imaging system, which captures the emission from the surface and converts it to a color-coded map of the surface temperature distribution. Consider the case where a uniform flux of $5{\text{kW/m}}^{\text{2}}$ is applied to the top skin of an airplane wing initially at $20°\text{C}\text{.}$ ne opposite side of the 15-mm-thick skin is adjacent to stagnant air and can be treated as well insulated. The density and specific heat of the skin material are $1200{\text{kg/m}}^{\text{3}}$ and $1200\text{J/kg}\cdot \text{K,}$ respectively. effective thermal conductivity of the intact skin material is $k_1=1.6\text{W/m}\cdot \text{K}\text{.}$ Contact resistances develop internal to the structure as a result of delamination between the fiber mats and the bonding material, leading to a reduced effective thermal conductivity of $k_2=1.1\text{W/m}\cdot \text{K}\text{.}$ Determine the surface temperature of the component after 10 and 100 s of irradiation for (i) an area where the material is structurally intact and (ii) an adjacent area where delamination has occurred within the wing.