Please gentlemen need help on this issue. A blacksmith wants to forge a 30 cm Io

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Please gentlemen need help on this issue.

A blacksmith wants to forge a 30 cm Ions metal bar (Figure-1). The initial temperature of the bar is at 1100 degree C. The surrounding air temperature is 23 degree C. He is wondering if he could get prediction on the time required and the region that is ready for hammering. To help the blacksmith, you've been asked to solve the case of 1-D unsteady heat conduction and you end up with the following general solution: T - Ti / T infinity - Ti = 1 - x / L - 2 / pi sin(pi x / L) times e - pi2 FO Where Fourier number FO = alpha .t/L2 t time, in second Ti initial temperature, in degree C T ambient temperature, in degree C x distance, in m L bar length, in m alpha metal diffusivity, in m2 / s A- Draw the followings: The temperature variation along the bar at t = 0. 30 s. 1 min. 10 min. 30 min. and 1 hr The temperature variation at the holding position during 1 hr. B- Determine the following: The time when the temperature at point 4 becomes 400 degree C. The time when the temperature at point 2 becomes 40 degree C.

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