This paper presents an entropy generation analysis for steady conduction in a hollow sphere with temperature dependent internal heat generation and asymmetric convective cooling. An exact analytical solution for the temperature distribution is used to compute dimensionless local and total entropy generation rates in the hollow sphere. The total entropy generation rate depends on reference heat generation rate Q, the heat generation-temperature variation parameter a, the temperature asymmetry parameter λ and Biot numbers Bi1 and Bi2. Graphs illustrating the effect of these parameters on the local and total entropy generation rates are presented. Total entropy generation in the hollow sphere can be minimised with an appropriate choice of cooling parameters.