Final answer:
The question is concerned with the heat transfer mechanisms involving a material's exposure to hot air and related thermal effects, specifically thermal expansion. The relevant physical principles include conduction, convection, thermal conductivity, and thermal boundary layer.
Step-by-step explanation:
The student's question is related to thermal conduction and the heat transfer through materials. In the scenario described, the material with a temperature of 40°C being heated should not have a temperature change exceeding 5°C across a 1mm thickness to avoid thermal expansion. The convection coefficient is given as 18 W/m^2K, which is part of the heat transfer mechanism by convection. The concepts of thermal conductivity and thermal boundary layer are also relevant as they are involved in the process of heat transfer through conduction.
By understanding the rate at which heat is conducted (Q/t), the thermal conductivity (k) of the material, the surface area (A), and thickness (d), as well as the temperature difference across the material (T₂ - T₁), we can analyze the heat transfer and determine how to control the temperature to prevent damage from excessive thermal expansion.