Modelling heat transfer from Power LED to metal bar
If my understanding is correct, you want to estimate the thermal resistance of a heatsink or a slab of thermally conductive material to ambient, without any airflow (= natural convection).

There is a nice online calculator for finned rectangular heatsinks that implements the natural convection model for heatsinks (a more academic, detailed explanation of the model is here).

Here's an example relevant to your design problem (55x55x55mm outer dimensions, 10x1mm fins, baseplate thickness 10mm and a rather conservative 2,000 W/m2ºC contact conductance):



The resulting source temperature for 25ºC ambient temperature and 26.35 W of heat flowing into the heatsink is aprox 110ºC, which means that heatsink would have a 3.23 ºC/W thermal resistance in natural convection conditions.

Experiment with the calculator in order to find the outer dimensions that suits best your design.