The question :Two rods L1 and L2 of different materials( hence different thermal conductivities) and different cross-sectional areas,are joined at x=a. The temperature is continuous, i.e
And NO HEAT ENERGY IS LOST AT a, so all heat energy that flows from L1 flows into L2.
? What equation represents the condition that no energy is lost at a ?
My thoughts : Equate the rate at which heat leaves L1 to the rate at which heat enters L2. ???
In the derivation of the heat equation we find the
net rate at which energy flows through a section of the rod. Energy flows in by
and energy flows out by
Where A(x) is the area of a cross section of the rod,
is the thermal conductivity, a and b points on the rod with b>a.
If all heat leaving L1 goes to L2,then across the join
?? (not sure here) and
??
which gives me
and so
??