Consider the plane wall of a building made of concrete with thermal diffusivity a 1.03 10-...

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Consider the plane wall of a building made of concrete with thermal diffusivity a 1.03 10- [m2/s] and thermal conductivity k 0.52 [W/mK]. The wall is exposed to the external environment. Assume that the width of the wall is very large so that we can approximate the solid as a semi-infinite medium in the direction normal to the wall. The temperature of the wall is initially a uniform and equal to Ti = 10°C. Due to a snowstorm, the temperature on the external surface of the wall suddenly drops to T 9°C During the day, the temperature on the external surface of the wall changes with time. Assuming that the temperature evolves as a sin function around a mean value, demonstrate that a periodic temperature field T(x, t) satisfies the general equation of the conduction. Consider the plane wall of a building made of concrete with thermal diffusivity a 1.03 10- [m2/s] and thermal conductivity k 0.52 [W/mK]. The wall is exposed to the external environment. Assume that the width of the wall is very large so that we can approximate the solid as a semi-infinite medium in the direction normal to the wall. The temperature of the wall is initially a uniform and equal to Ti = 10°C. Due to a snowstorm, the temperature on the external surface of the wall suddenly drops to T 9°C During the day, the temperature on the external surface of the wall changes with time. Assuming that the temperature evolves as a sin function around a mean value, demonstrate that a periodic temperature field T(x, t) satisfies the general equation of the conduction.