read the below article which you can find out something

https://www.sciencedirect.com/topics/engineering/hydraulic-diameter

Could you please describe in a better way your heat exchanger concept.

Nick Hamburger , Suppose a stacked wire mesh is used as a regenerator where it absorbs and releases heat. Wouldn't the arrangement of the stack aka. the overall shape (cylindrical, annular ring etc) affect the hydraulic diameter of the said heat exchanger?

A relation Dh= dwire x por/(1-por) was given in multiple books and research papers. I was wondering if this can be applied even if the stack isn't cylindrical.

Heat transfer occurs at the surface and the flow depends on the fluid flow conditions. If we consider the macro-geometry as for instance a pipe in which you place the bundle of wires the conditions at the wire surface on which depends the convection are function of the micro-geometry i.e. the free spaces BETWEEN the wires since the fluid contact is WITH the wires.

It is a question of definition , for different reasons this formula was the choice. It has a logical basis since in the definition of the hydraulic diameter for a section of a not circular geometry dh=4*A/P , the free area for the fluid flow is proportional to "porosity" and the wet perimeter is proportional to the rest of the area thus the higher the porosity the higher the free area and lower the wet perimeter and the higher the hydraulic equivalent diameter.

You can of course use general equations and consider how the wires do touch.

When you apply a formula you should be careful that you have same conditions if not it will loose its validity.