in 2D case, it starts from very large value and decreasing with time. For 3D case, it starts with negative value, increasing for few time and decrease again. i have checked my program. everything is ok.
It seems your problem is completly numerical and linked with the convergence. Nusselt numbers are not negative at all. I just could guess your program is giving a negative initial value for starting, from the initial conditions or the boundary conditions, but intrinsecally related to the physical process.
About the decrease/increase process, I'm confused, because it will depend strongly of your problem, and how the thermal coefficients are programed to vary. Are they function of the turbulence paremeters? How your wall boundary condition are applied?
The Nusselt number is positive by definition. Any negative Nusselt number would be caused by a numerical inconsistency. The development with time, I'd say, depends on your flow model and on the initial conditions.
I think that in the start time of your 3D flow the value of Nusselt number is zero because the convective heat transfer is zero at the starting time. Numerically this value being very very small may be smaller than minimum number of a computer and casually it is known by the computer as a negative value.