The relation between heating load and coefficient of performance (COP) of an endoreversible Carnot heat-pump is derived based on a new generalized convective heat-transfer law and generalized radiative heat-transfer law, q alpha (Delta T-n)(m). Our results include those obtained in many literature studies and can provide some theoretical guidance for the designs of real heat pumps. (c) 2007 Elsevier Ltd. All rights reserved.