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

**??**