In order to cut the development costs of liquid rocket engines full-scale hardware tests are supplemented with numerical analyses. For the correct prediction of the engine performance as well as its thermomechanical verification conjugate heat transfer analyses are performed. The present work presents ArianeGroup Ottobrunn\'s novel, fully three-dimensional approach for these investigations and includes first results of such a simulation of a full-scale demonstrator defined in the German national research programme Sonderforschungsbereich Transregio 40.