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Problem ( 1 ) : Consider a rectangular 1 - D bar lying in the domain - x . Initially at t = 0 the
Problem : Consider a rectangular D bar lying in the domain Initially at the first halfpart of the bar lying in the domain is at a temperature of while the other half is at zero temperature. It is apparent that for heat will start conducting from the first halfpart to the other half thereby leading to development of a temperature profile within the bar. Show that the temperature profile in the entire domain is given by
erf;
where is the thermal diffusivity of the bar material. Hint: Use Laplace transform.
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