Space shuttles are exposed to temperatures of up to 1600°C during reentry. However, the aluminum shell of the spacecraft cannot withstand temperatures higher than 175°C. In order to protect the...

Space shuttles are exposed to temperatures of up to 1600°C during reentry. However, the aluminum shell of the spacecraft cannot withstand temperatures higher than 175°C. In order to protect the structural integrity of the craft, the shuttle is covered by over 24,000 ceramic tiles that protect the aluminum shell from overheating. The tiles are made of two layers. The outer layer has a thickness of 1 mm and a thermal conductivity of 15 W/mK. The inner layer has a thickness of 0.5 mm and a conductivity of 20 W/mK. Calculate the temperature at the interface of the layers and find the temperature gradient in both layers.