1. Increase coefficient of friction

2. Increase thermal conductivity of material

3. Increase convective heat loss by increasing Reynold's and Prandtl's number.

Sagnik, don't you mean increase thermal conductivity of material? You want the heat to become dissipated faster, not slower, if thermal stress is too high. Also, reducing coefficient of friction will result in greater slipping of the clutch plates, so I'm not sure how that solves the problem. I have to believe that all else equal, the same amount of heat will be generated, except that the clutch with lower coefficient of friction will slip longer. Or at worst, that lower coefficient of friction clutch will never stop slipping! Same as happened with worn out clutches. Accelerate hard, and even with foot off the clutch pedal, the clutch will slip.

Take it to the extreme. Extremely high coefficient of friction. You will get a jerky start, but almost not clutch plate heat at all. So I think you want high coefficient of friction in your clutch plate.

If engaging the clutch at lower RPM, with less engine torque being demanded while the clutch is engaging, is not an option, then the usual solution is to install a bigger clutch or a multi-plate design, no? Take a look at the videos of the single and then multi-plate clutches.

https://www.quora.com/What-is-the-concept-behind-single-clutch-plate-and-double-clutch-How-different-are-they

Albert thanks for pointing out the mistakes, I contradicted myself in the answers, I shall edit it.

Thermal conductivity must indeed be increased.

About the coefficient of friction, i acknowledge that friction clutches require sufficient friction to keep the plates engaged with each other. In fact what you said is true, the heat generation due to friction is less when there is less slipping between the plates.

Also yes, heat generation is much more at lower RPMs and high torques. I think maximum clutch damage occurs in the first gear of an automobile itself.

Thanks again.

Maybe you can add on the lubricant if it is a wet cluch. Otherwise on the efficiency of all the components such as bearings etc.

Franco

you need to check for the materials used in the manufacture of the clutch plate, off course I am not sure that you developed the clutch yourself. from the material composition you will be able to know the various parameters and how  to vary them in your heat transfer calculation. try this first to no the material composition of the clutch plate before we can think of application of the thermophysical properties in your work