I know the heat transfer diferential equation, but I only saw it being used when the temperatures of the extremities of the material are fixed. Is there any phormula that aplies for situations where at least one of the extremities is free to change its temperature? Ex.: the left side of an iron bar with dimentions A,B,C is heated to T1 while the right side starts with T2. Ignoring radiation loss, when the temperature of the right side will be 90% of T1? And if we consider radiation? If it´s too hard to solve, is there any numerical aproximation? Thanks.