A firefighter's protective clothing, referred to as a turnout coat, is typically constructed as an ensemble of three layers separated by air gaps, as shown schematically.

Representative dimensions and thermal conductivities for the layers are as follows.

Layer                                       Thickness (mm)     k (W/m. K)

Shell (s)                                               0.8                    0.047

Moisture barrier (mb)                    0.55                    0.012

Thermal liner (tl)                               3.5                    0.038

The air gaps between the layers are 1 mm thick, and heat is transferred by conduction and radiation exchange through the stagnant air. The linearized radiation coefficient for a gap may be approximated as, h_rad = σ(T₁ + T₂)(T2/1 + T2/2) = 4σT³_avg where T_avg represents the average temperature of the' surfaces comprising the gap, and the radiation flux across the gap may be expressed as q_rad = h _rad (T₁ - T₂).

(a) Represent the turnout coat by a thermal circuit, labeling all the thermal resistances. Calculate and tabulate the thermal resistances per unit area (m² ∙ K/W) for each of the layers, as well as for the conduction and radiation processes in the gaps. Assume that a value of T_avg = 470 K may be used to approximate the radiation resistance of both gaps. Comment on the relative magnitudes of the resistances.

(b) For a pre-flash-over fire environment in which firefighters often work, the typical radiant heat flux On the fire-side of the turnout coat is 0.25 W/cm². What is the outer surface temperature of the turnout coat if the inner surface temperature is 66°C, a condition that would result in burn injury?

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Thermal liner (ti) Moisture Shell (s) barrier (mb) mm Fitefighter mm Fn-side kmb Air gap Air gap