Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5- cm-thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the per cent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
GIVEN
• Wood wall
• Two layers 0.025-m-thick each
• Nail cross sectional area of nails = 0.5% of wall area
• Temperature difference (?T) = 25°C
FIND
(a) The unit thermal conductance (k/L) of the wall (b) Percent of total heat flow that passes through the wall
ASSUMPTIONS
• One dimensional heat transfer through the wall
• Steady state prevails
• Contact resistance between the wall layers is negligible
SKETCH
PROPERTIES AND CONSTANTS
? Wood (Pine) (kw) = 0.15 W/(m K)
? Mild steel (1% C) (ks) = 43 W/(m K)
(a) The thermal circuit for the wall is
The individual resistances are
The total resistance of the wood and steel in parallel is
The unit thermal conductance (k/L) is
(b) The total heat flow through the wood and nails is given by
The heat flow through the nails alone is
Therefore the per cent of the total heat flow that passes through the nails is
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