Topic

# Volume fraction

About: Volume fraction is a(n) research topic. Over the lifetime, 16312 publication(s) have been published within this topic receiving 374181 citation(s).

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TL;DR: In this paper, the authors used the finite volume technique to solve the governing equations of heat transfer and fluid flow due to buoyancy forces in a partially heated enclosure using nanofluids.

Abstract: Heat transfer and fluid flow due to buoyancy forces in a partially heated enclosure using nanofluids is carried out using different types of nanoparticles. The flush mounted heater is located to the left vertical wall with a finite length. The temperature of the right vertical wall is lower than that of heater while other walls are insulated. The finite volume technique is used to solve the governing equations. Calculations were performed for Rayleigh number (103 ⩽ Ra ⩽ 5 × 105), height of heater (0.1 ⩽ h ⩽ 0.75), location of heater (0.25 ⩽ yp ⩽ 0.75), aspect ratio (0.5 ⩽ A ⩽ 2) and volume fraction of nanoparticles (0 ⩽ φ ⩽ 0.2). Different types of nanoparticles were tested. An increase in mean Nusselt number was found with the volume fraction of nanoparticles for the whole range of Rayleigh number. Heat transfer also increases with increasing of height of heater. It was found that the heater location affects the flow and temperature fields when using nanofluids. It was found that the heat transfer enhancement, using nanofluids, is more pronounced at low aspect ratio than at high aspect ratio.

1,538 citations

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TL;DR: In this paper, untreated catalytically-grown carbon nanotubes were dispersed in an epoxy matrix and the electrical properties of the composite were measured in order to relate the filler volume fraction to the electrical conductivity.

Abstract: To avoid electrostatic charging of an insulating matrix an electrical conductivity above σ=10−6 Sm−1 is needed. At present, the most common practice to achieve this conductivity is to use a conductive filler such as carbon black. In this work, untreated catalytically-grown carbon nanotubes were dispersed in an epoxy matrix. After curing the epoxy, the electrical properties of the composite were measured in order to relate the filler volume fraction to the electrical conductivity. The intense stirring process used to disperse the carbon nanotubes has made it possible to achieve a matrix conductivity around σ=10−2 Sm−1 with filler volume fractions as low as 0.1 vol.%. These figures represent an advance on best conductivity values previously obtained with carbon black in the same epoxy matrix. These low filler fractions ensure that the mechanical properties of the matrix are not compromised.

1,395 citations

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DuPont

^{1}TL;DR: In this paper, the effects of rubber particle size and rubber-matrix adhesion on notched impact toughness of nylon-rubber blends are analyzed. And the general condition for toughening is that the interparticle distance must be smaller than the critical value.

Abstract: The effects of rubber particle size and rubber-matrix adhesion on notched impact toughness of nylon-rubber blends are analysed. A sharp tough-brittle transition is found to occur at a critical particle size, when the rubber volume fraction and rubber-matrix adhesion are held constant. The critical particle size increases with increasing rubber volume fraction, given by d c = T c {( π 6Φ r ) 1 3 − 1} −1 , dc is the critical particle diameter, Tc the critical interparticle distance, and or the rubber volume fraction. The critical interparticle distance is a material property of the matrix, independent of rubber volume fraction and particle size. Thus, the general condition for toughening is that the interparticle distance must be smaller than the critical value. Van der Waals attraction gives sufficient adhesion for toughening. Interfacial chemical bonding is not necessary. Even if there is interfacial chemical bonding, a polymer-rubber blend will still be brittle, if the interparticle distance is greater than the critical value. The minimum adhesion required is about 1000 J m−2, typical for van der Waals adhesion. In contrast, chemical adhesion is typically 8000 J m−2. The present criterion for toughening is proposed to be valid for all polymer—rubber blends which dissipate the impact energy mainly by increased matrix yielding.

1,191 citations

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TL;DR: Ding et al. as discussed by the authors used a transient hot-wire apparatus with an integrated correlation model to measure the thermal conductivities of these nanofluids more conveniently, and they also characterized the pH value and viscosity of the nanoparticles.

Abstract: Nanofluids are prepared by dispersing TiO2 nanoparticles in rod-shapes of ∅10nm×40nm (diameter by length) and in spherical shapes of ∅15 nm in deionized water. A transient hot-wire apparatus with an integrated correlation model is used to measure the thermal conductivities of these nanofluids more conveniently. The pH value and viscosity of the nanofluids are also characterized. The experimental results show that the thermal conductivity increases with an increase of particle volume fraction. The particle size and shape also have effects on this enhancement of thermal conductivity. For TiO2 particles of ∅10nm×40nm and ∅15 nm dimensions with maximum 5% volume fraction, the enhancement is observed to be nearly 33% and close to 30%, respectively over the base fluid. For 5% volumetric loading of rod-shape TiO2 nanoparticles of ∅10nm×40nm in deionized water, this enhancement is found to be 12% higher than that predicted by the Hamilton–Crosser model [I & EC Fundamentals 1 (1962) 187]. However, with the same volumetric loading, the maximum enhancement is determined to be about 16% higher than that predicted by the Bruggeman model [Y. Ding, D. Wen, R.A. Williams, in: Proceedings of 6th International Symposium on Heat Transfer, Beijing, 2004, pp. 66–76] for TiO2 nanoparticles of ∅15 nm in the same base fluid of deionized water. The measurement error is estimated to be within 2%.

1,098 citations

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TL;DR: In this article, a critical analysis of the extensive experimental data on the relative viscosity of suspensions of uniform spherical particles was made, and the coefficients of different power series relating relative visco-solutions and volume fraction solids were determined using a nonlinear least squares procedure.

Abstract: A critical analysis was made of the extensive experimental data on the relative viscosity of suspensions of uniform spherical particles. By appropriate extrapolation techniques, non-Newtonian, inertial, and nonhomogeneous suspension effects were minimized. As a result, the scatter of the data was reduced from ±75% to ±13% at a volume fraction solids of 0.50. The coefficients of different power series relating relative viscosity and volume fraction solids were determined using a nonlinear least squares procedure. It was shown that a new expression containing three terms of a power series with coefficients determined from previous theoretical analyses and an exponential term with two adjustable constants fit the data as well as a power series with six terms, either three or four of which were adjustable constants with the remaining coefficients being theoretical values.

965 citations