4.12. The measured temperature distribution in a solar energy heating system may be represented by the equation T(x)=15.5+68.2\left[1-\frac{\exp (-x / 2.7)}{\left(1+x^{2}\right)}\right] where x is the distance away from the surface being heated and T is the temperature. Compute the temperature gradient dT/dx and the second derivative d²T/dx² at x = 0. The heat transfer rate is proportional to the temperature gradient at x=0. The second derivative is related to energy lost or gained by radiative transport. Employ forward differences to O[(Ax)²] and reduce Ax to obtain numerical results that are largely independent of the value of Ax chosen.

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