Department of Mechanical Engineering, National Institute of Technology Raipur, Raipur-492 010, Chhattisgarh, India Department of Mechanical Engineering, Indian Institute of Technology Indore, Indore-453 552, Madhya Pradesh, India E-mail: rskumar.me@nitrr.ac.in Manuscript received online 28 March 2020, accepted 15 June 2020 Effect of straight radially grown carbon nanotubes (CNTs) on the periphery of a hollow cylindrical fiber (HCF) has been considered for the thermal conductivity estimation the proposed fiber. Such a hollow fiber with the presence of CNTs on the periphery is termed as fuzzy fiber heat exchanger (FFHE). Two micromechanics approaches namely method of cells (MOC) and the effective medium (EM) have been employed in thermal conductivity estimation of the carbon FFHE. The presence of CNTs radially on the outer periphery of the hollow base fiber tend to significantly improve the transverse thermal conductivities (outof-plane) of carbon FFHE in comparison with hollow carbon fiber (i.e, without CNTs). Approximately an improvement in transverse thermal conductivities of over 400% is seen in FFHE in the presence of only few percentages of radially grown CNTs. Also, it is observed that thermal interfacial resistance between CNT/polymer matrix has negligible or zero effect affect in the estimated thermal properties of FFHE.