If you increase the flow on the water side, the heat transfer cofficient on that side will increase, of course, increasing the overall heat transfer coefficient. This will increase the delta T on the other side. However, I don't think it will increase the overall heat transfer coefficient enough to result in a higher delta T on the water side.
As IRStuff pointed out, the water side delta T is inversely proportional to the flow rate if the Q is constant. It's a pretty good bet that the effect of the water flow is greater than the effect of the increased heat load.
In our case, the load (Q) is constant. We are only changing flow on a fixed system to determine a possible flow issue. We are seeing a higher than expected delta on the water side and wondered if there my be a flow restriction in the system (as indicated by the increased delta T).
I'm not too clear as to what delta T is being measured. I presumed it was through the plate thickness so an increased htc will produce an increased delta T for an increase in Q through the plate. If you increase the htc then the delta T between the water and plate surface will tend to zero. The delta T measured in the water will also tend to zero for an increasing mass flow rate M, as per ione's equation.
My apologies for the vague reference on delta T. I was in fact looking for temp difference between inlet and outlet of the fluid.
I will endeavour to be more precise with my future postings as it is quite clear that a thread can come unravelled if not properly mended. One could say "a stitch in time saves 9". No more punny references, I promise!!
Given that piece of information, the coolant deltaT would go down with increased flow, since, for a constant heat load, the increased mass transfer requires less of a temperature increase to carry the same heat load.
In the limiting (absurd) case, an infinite coolant flow would result in a zero deltaT across the inlet and outlet, since you would now have an infinite heat sink.
The fluid DT will decrease as the flow increases if the DT is defined as DT=To-Ti, provided the HX areas remains constant and the opposing fluid flowrate remains fixed. Refer to "compact HX theory" ( Kays + London) and the relationship of (Ti-To)min vs the HX effectiveness "e" and the opposing fluid (Ti-To)max
Let's not forget that no matter how much we improve one individual heat transfer coefficient, the overalll heat transfer coefficient would stay at a value smaller than the lowest of both individual values.