The density and specific heat of a plastic material are known (p = 950 kg/m³, c_p = 1100 J/kg ∙ K), but its thermal conductivity is unknown. To determine the thermal conductivity, an experiment is performed in which a thick sample of the material is heated to a uniform temperature of 100°C and then cooled by passing air a 25°C over one surface. A thermocouple embedded a distance of X m = 10 mm below the surface records the thermal response of the plastic during cooling.

If the convection coefficient associated with the air flow is h = 200 W/m² ∙ K and a temperature of 60°C is recorded 5 min after the onset of cooling, what is the thermal conductivity of the material?

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Air T h Thermocouple, TCr, ) -Material of unknown thermal conductivity (p. Cp. T)