Question

what does dt/dx=0 mean in a heat conduction problem?

Answer 1

the rate of change of temperature (the rate of thermal conduction) with respect to (whatever x may be, say time) = 0
ie, the rate of thermal conduction is constant

Answer 2

thanx

Answer 3

In general, d[variable]/d[another variable] is the rate of change of [variable] wrt [another variable]. If that derivative is 0, then [variable] is not changing.