Inhomogeneously-doped nanostructure materials are used to construct a conceptual model of the thermoelectric refrigerator. The energy balance equation and Domenicali's equation are combined to compute the heat flow and temperature distributions along the device legs. Effects of the current density, lattice thermal conductivity, and width of the energy selective electron channel on the coefficient of performance are discussed. By comparing with the thermoelectric refrigerator with bulk semiconductors, it is expounded that quantum effects such as confinement and tunneling are capable of significantly reducing the irreversible energy losses due to the electron transport, which has a great potential to improve the cooling efficiency. The results obtained can provide some theoretical guidance for the optimal design of practical thermoelectric refrigerators. (C) 2017 Elsevier Ltd. All rights reserved.