A novel fuzzy carbon fiber heat exchanger (FFHE) is proposed in this study. The novel constructional feature of the FFHE is that the sinusoidally wavy carbon nanotubes (CNTs) are radially grown on the outer circumferential surface of the hollow cylindrical carbon fiber (HCF) heat exchanger. The effective thermal conductivities of the FFHE have been estimated by employing the method of cells (MOC) approach and the effective medium (EM) approach. The present study reveals that if the amplitudes of the radially grown sinusoidally wavy CNTs are parallel to the axis of the HCF then the effective axial thermal conductivity of the FFHE is significantly improved over that of the bare HCF heat exchanger (i.e., without CNTs). On the other hand, if the amplitudes of the radially grown wavy CNTs are transverse to the axis of the HCF, the effective transverse thermal conductivity of the FFHE is significantly improved over that of the bare HCF heat exchanger. It is also found that the CNT/polymer matrix interfacial thermal resistance does not affect the effective thermal conductivities of the FFHE. The present investigation suggests that exploiting the waviness of radially grown CNTs on the HCF a truly multifunctional and promising heat exchanger can be developed for advanced technological applications. (c) 2014 Elsevier Ltd. All rights reserved.