Heat dissipated from a machine in operation can cause hot spots on its surface. Exposed hot spots can cause thermal burns when in contact with human skin tissue and are considered to be hazards at the workplace. Consider a machine surface that is made of a 5-mm thick aluminum with a thermal conductivity of 237 W/m∙K. During operation the machine dissipates about 300 W/m² of heat to the surroundings, and the inner aluminum surface is at 150°C. To prevent machine operators from thermal burns, the machine surface can be covered with insulation. The aluminum/ insulation interface has a thermal contact conductance of 3000 W/m²∙K. What is the thickness required for the insulation layer with a thermal conductivity of 0.06 W/m∙K in order to maintain the surface temperature at 45°C or lower?

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Aluminum machine surface k = 237 W/m-K Insulation 150°C