Two one-dimensional rods of different materials joined at x = x0 are said to be in perfect thermal contact if the temperature is continuous at x = x0:
u(x0−, t) = u(x0+, t)
and no heat energy is lost at x = x0 (i.e., the heat energy flowing out of one flows into the other). What mathematical equation represents the latter condition at x = x0? Under what special condition is ∂u/∂x continuous at x = x0?
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