This paper describes some R&D activities conducted in support of the design and safe operation of a high-power liquid Pb-Bi target within the LIEBE (Liquid Eutectic Lead Bismuth Loop Target for EURISOL) project. The target material is lead bismuth eutectic (LBE) which also acts as a primary coolant. As a consequence of interaction of the highly pulsed 1.4-GeV protons at ISOLDE with the target, heat powers of the order of 2GW would be instantaneously deposited in the target during a bunch. Considerable R&D effort is thus required to demonstrate its continued coolability and structural integrity. This paper mainly reports on the conjugate flow (CFD) and heat deposition (Monte Carlo) calculations, not accounting for Fluid–Structure Interactions.