At the university where I studied there was a Sterling engine somewhat larger than a typical automotive engine. I could bring it up to full speed, grab the rotating 20 kg flywheel with my bare hands and stop it. Next to this sat a steam engine of similar size and weight. An elephant couldn't have stopped the steam engine. What does this mean? The Sterling cycle sounds good and has a high thermodynamic efficiency, but doesn't produce enough power to do anything useful. Why? Because you can't transfer the heat fast enough into and out of the working fluid in order to drive the piston and ultimately the crankshaft and flywheel. Entropy generation (local or global) is only a very small part of what makes a design effective. If a design is not practical, it doesn't matter if it's efficient or not. dS>=dQ/T While we strive to achieve higher efficiencies and produce less entropy, you need to approach this challenge from a different direction. For example, what processes produce the most entropy? 1) uncontrolled expansion, 2) mixing of two streams (different temperature, concentration, chemical species, etc.), 3) rapid compression, etc. Design a device that avoids these highly irreversible processes.

The lower value is preferable. Higher value decrease your second law efficiency

The question is what you want to optimize.

If you are in a regime where Fourier's Law holds (heat flow proportional to temperature gradient), the temperature profile within a given device and for given temperature levels will assume a shape that minimizes the total entropy production.

If you want to maximize the heat flow (for fixed temperature levels), the entropy production is q1/T1 – q0/T0 = q (1/T1 – 1/T0) ~ q,

i.e., a larger heat flow (better heat conductivity) goes along with a large entropy production.