In this work a mathematical model to study the performance of an irreversible refrigerator has been presented with the consideration of heat exchange by combined convection and radiation. The external irreversibility effects due to finite rate heat transfer as well as the effects of internal dissipations have been considered in the analysis. The relation between the cooling load and the coefficient of performance of the refrigerator has been derived. Furthermore an expression for the maximum cooling rate has been derived. The parameters that affect the cooling load have been investigated. The cooling load has been discussed and the effect of internal irreversibility has been investigated.