Determine the temperature distribution and heat flow rate per meter length in a long concrete block having the shape shown below. The cross-sectional area of the block is square and the hole is centered.
GIVEN
A long concrete block having the shape shown below
The cross-sectional area of the block is square
The hole is centered
FIND
(a) The temperature distribution in the block
(b) The heat flow rate per meter length
ASSUMPTIONS
The heat flow is two dimensional and in steady state
The thermal conductivity in the block is uniform
SKETCH
The temperature distribution and heat flow rate may be estimated with a flux plot
(a) The temperature distribution is given by the isotherms in the flux plot.
(b) The number of flow lanes (M) = 2 ? 21 = 42
The number of squares per lane (N) = 4
Therefore, the shape factor is
From the rate of heat flow per unit length is
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