In metal processing plants, workers often operate near hot metal surfaces.
Exposed hot surfaces are hazards that can potentially cause thermal burns on
human skin tissue. Metallic surface with a temperature above 70°C is considered
extremely hot. Damage to skin tissue can occur instantaneously upon
contact with metallic surface at that temperature. In a plant that processes
metal plates, a plate is conveyed through a series of fans to cool its surface
in an ambient temperature of 30°C, as shown in Figure 2-47. The plate is
25 mm thick and has a thermal conductivity of 13.5 W/m∙K. Temperature at
the bottom surface of the plate is monitored by an infrared (IR) thermometer.
Obtain an expression for the variation of temperature in the metal plate. The
IR thermometer measures the bottom surface of the plate to be 60°C. Determine
the minimum value of the convection heat transfer coefficient necessary
to keep the top surface below 47°C to avoid instantaneous thermal burn upon
accidental contact of hot metal surface with skin tissue.