A small dam, which may be idealized by a large slab 1.2 m thick, is to be completely poured in a short period of time. The hydration of the concrete results in the equivalent of a distributed source of constant strength of 100 W/m3 . If both dam surfaces are at 16°C, determine the maximum temperature to which the concrete will be subjected, assuming steady-state conditions. The thermal conductivity of the wet concrete may be taken as 0.84 W/(m K).
GIVEN
FIND
The maximum temperature (Tmax)
ASSUMPTIONS
Steady state conditions prevail
SKETCH
The dam is symmetric. Therefore, x will be measured from the centerline of the dam. The equation for one
dimensional conduction is given
This is subject to the following boundary conditions
The constant C1 can be evaluated using the first boundary condition
Integrating once again
The constant C2 can be evaluated using the second boundary condition
Therefore, the temperature distribution in the dam is
The maximum temperature occurs at x = 0
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