Series expansion and asymptotic formulas for heat transfer of an inclined moving heat source

In heat transfer in orthogonal machining or creep-feed grinding we must consider the temperature distribution at the shear plane for an inclined band heat source. From the classical solution given by Hahn in integral form, a series representation of this solution has been calculated whose numerical evaluation is faster than the numerical integration of the integral form. From this series representation simple asymptotic formulas for maximum and average temperatures have been derived, the latter being useful in heat transfer modeling of creep-feed grinding and orthogonal cutting. These asymptotic formulas are quite accurate for typical machining regimes. Further, a closed-form formula for the average temperature in the case of zero shear angle has been obtained.