Three cases are studied as variations in the geometry and the thermal boundary conditions pertinent to the classical flash temperature theory. First, the case of multiple surface heat sources is considered. It is shown that the relative location of the sources is the critical factor in predicting the local temperatures at each contact. Second, the case of a short cylinder (or a disk) is analyzed. In addition to the lateral surface boundary conditions, convective cooling from the side faces is considered. It is shown that a considerable reduction in bulk temperature can be achieved by effective cooling from the side faces. Third, the case of a hollow cylinder is studied where, in addition to the outer boundary conditions, uniform internal heating (or cooling) is considered. It is demonstrated that the bulk temperature can be varied significantly by changing the magnitude (and direction) of the internal heat flux. In both the second and the third cases, over a wide range of the pertinent parameters, it is shown that the local temperature rise remains virtually unchanged.

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