# A steel frame (K = 45 W m–1 °C–1) of total length 60 cm and cross-sectional area 0.20 cm2, forms three sides of a square. The free ends are maintained at 20°C and 40°C. Find the rate of heat flow through a cross-section of the frame.

Given:
Thermal conductivity of steel frame: K=45 W m–1 °C–1.
Length of the steel frame : x = 60 cm = 0.6 m
Area of cross section : A = 0.20 cm2 = 0.2 × 10-4 m2.
Temperature difference between the free ends :
ΔT = 40-20= 20°C.
Formula used:
Rate of amount of heat flowing is given as:

Here, Δθ is the amount of heat transferred, ΔT is the temperature difference, K is the thermal conductivity of the material, A is the area of cross section of the material and x is the thickness of the material.
Substituting the values we get,

Hence, the rate of heat flow through a cross-section of the frame is 0.03 J/s.

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