Create a Multi-body part in DM by selecting the four solids and Form New Part.
In Mechanical, define the three rods as Fluid, repair the Named Selections. If you get an automatically generated Contact, delete it.
Use a Sweep Method on the fluids and use Inflation on the circular holes.
In Fluent, for each pipe-wall Boundary Condition, change the Thermal setting to Coupled. (I think this is correct, the CFD experts can correct me if I'm wrong).
The velocity of the water at the outlet is 0.77 m/s on a diameter of 9.525 mm. If you calculate the Reynolds Number, you will find this is Turbulent flow. You have selected Laminar in the Models. Change to Turbulent.
The plate is a six sided box. You have defined a heat flux on one face, but on the other five faces, you have specified a temperature of 310 K. That seems odd. They could be just insulated faces. Why are these five sides maintained at a constant temperature? I changed them to zero heat flux (insulated).
I notice you have three water inlets with three different temperatures: 290, 293 and 296 K. Why do the inlets have different temperatures?
Here are the contours of temperature on a plane at the center of the block.
If you cut the inlet mass flow rate by a factor of 10, then you get an x gradient.