Suppose that the temperature in a long, thin rod placed along the x-axis is initially C/(2a) if
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Suppose that the temperature in a long, thin rod placed along the x-axis is initially C/(2a) if |x | < a and 0 if |x | > a. It can be shown that if the heat diffusivity of the rod is k, then the temperature of the rod at the point x at time t is
To find the temperature distribution that results from an initial hot spot concentrated at the origin, we need to compute 
Use l’Hospital’s Rule to find this limit.
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Both numerator and denominator approach 0 as a 0 so ...View the full answer
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