With time dilation.. time should move more slowly at the equator then.at the poles of the earth... and given that there is that differential between the equator and the poles there should be an energy flow between poles and the equator...
If you mean because someone at the equator is traveling faster than one at either pole, because their path/distance over a 24-hr time period is longer, that is correct, but hardly noticeable. In order for time dilation/length contraction/and mass increase effects to be important, speeds must be a significant fraction of light speed.
However, there is another means for time dilation, length contraction, and mass increase effects to occur: Gravity.
In short, the stronger the gravitational field, the greater the effects. GPS uses BOTH effects in its calculations in order to achieve such high degrees of accuracy. Interestingly, the greater of the effects is actually gravity, which of course is strongest nearer the surface than at high altitudes, as opposed to the high rate of speed of the GPS satellites, which has lesser time dilation, length contraction, and mass increase effects.
So, someone at the equator, due to the *outward* push of centrifugal force due to the rotation of the Earth, weighs LESS than someone of the same mass NOT on the equator. And so therefore has LESS time dilation, length contraction, and mass increase effects on them there than somewhere off the equator.