This paper reports on measurements of the effective thermal conductivity and thermal diffusivity of various nanofluids using the transient short-hot-wire technique. To remove the influences of the static charge and electrical conductance of the nanoparticles on measurement accuracy, the short-hot-wire probes are carefully coated with a pure Al 2 O 3 thin film and only those probes that are coated well are used for measurements. In the present study, the effective thermal conductivities and thermal diffusivities of Au/toluene, Al 2 O 3 /water, and carbon nanofiber ͑CNF͒/water nanofluids are measured and the effects of the volume fraction and thermal conductivity of the nanoparticles and temperature are clarified. The average diameters of Au and Al 2 O 3 spherical particles are 1.65 and 20 nm, respectively. The average length and diameter of CNFs are 10 m and 150 nm, respectively. The uncertainty of the present measurements is estimated to be within 1% for the thermal conductivity and 5% for the thermal diffusivity. The measured results demonstrate that the effective thermal conductivities of the nanofluids show no anomalous enhancements and can be predicted accurately by the model equation of Hamilton and Crosser ͓Ind. Eng. Chem. Fundam. 1, 187 ͑1962͔͒ for the spherical nanoparticles and by the unit-cell model equation of Yamada and Ota ͓Waerme-Stoffuebertrag. 13, 27 ͑1980͔͒ for carbon nanofibers.
In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal holomorphic bisectional curvature.
This paper reports measurements of the effective thermal conductivity and thermal diffusivity of various nanofluids using the transient short-hot-wire technique. To remove the influences of the static charge and electrical conductance of the nanoparticles on measurement accuracy, the short-hot-wire probes are carefully coated with a pure Al 2 O 3 thin film. Using distilled water and toluene as standard liquids of known thermal conductivity and thermal diffusivity, the length and radius of the hot wire and the thickness of the Al 2 O 3 film are calibrated before and after application of the coating. The electrical leakage of the short-hot-wire probes is frequently checked, and only those probes that are coated well are used for measurements. In the present study, the effective thermal conductivities and thermal diffusivities of Al 2 O 3 /water, ZrO 2 /water, TiO 2 /water, and CuO/water nanofluids are measured and the effects of the volume fractions and thermal conductivities of nanoparticles and temperature are clarified. The average diameters of Al 2 O 3 , ZrO 2 , TiO 2 , and CuO particles are 20, 20, 40, and 33 nm, respectively. The uncertainty of the present measurements is estimated to be within 1% for the thermal conductivity and 5% for the thermal diffusivity. The measured results demonstrate that the effective thermal conductivities of the nanofluids show no anomalous enhancement and can be predicted accurately by the model equation of Hamilton and Crosser, when the spherical nanoparticles are dispersed into fluids.
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