The temperature T at the wall of a furnace varies periodically over the day as T t( ) = + 125 50 sin (t − ) 2 24 6 π where t is the time in hours measured from midnight and T is in °C. The ambient temperature Ta is 25°C, and the surface area A of the wall is 10 m2. If the heat transfer coefficient h is given as 20 W/m2°C, the heat transfer from the wall is given by ∫[ ( T t) ] − T hA t a d . Using the trapezoidal rule, compute this integral as accurately as possible for the time interval t = 6 to t = 12. Also evaluate the integral analytically and compare the result with the computed value. Use the quad function in MATLAB to verify the results obtained.
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