Effects of Nanoparticle Clustering on the Heat Transport in Nanofluids Through Fractal Theories

2008 ◽  
Vol 59 (2) ◽  
pp. 195-198
Author(s):  
Manuela Girtu ◽  
Agop Maricel ◽  
Constantin Bejinariu ◽  
Anca Harabagiu ◽  
Camelia Popa
Keyword(s):  
Heat Transfer ◽  
Coherent Structures ◽  
Thermal Gradient ◽  
Relativity Theory ◽  
Growth Speed ◽  
Topological Dimension ◽  
One Dimensional ◽  
Oscillation Modes ◽  
Scale Relativity ◽  
The One

Considering that the motion of microphysical object takes place on continuous but non-differentiable curves, i.e. on fractals, effects of nanoparticle clustering on the heat transfer in nanofluids using the scale relativity theory in the topological dimension are analyzed. In the one-dimensional differentiable case, the clustering morphogenesis process is achieved by cnoidal oscillation modes of the speed field and a relation between the radius and growth speed of the cluster is obtained. In the non-differentiable case, the fractal kink spontaneously breaks the vacuum symmetry by tunneling and generates coherent structures. Since all the properties of the speed field are transferred to the thermal one and the fractal potential (fractal soliton) acts as an energy accumulator, for a certain condition of an external load (e.g. for a certain value of thermal gradient) the fractal soliton breaks down (blows up) and releases energy. As result, the thermal conductibility in nanofluids unexpectedly increases.

scholarly journals Small-Scale Spectrum of a Scalar Field in Water: The Batchelor and Kraichnan Models

2011 ◽  
Vol 41 (11) ◽  
pp. 2155-2167 ◽  
Author(s):  
Xavier Sanchez ◽  
Elena Roget ◽  
Jesus Planella ◽  
Francesc Forcat
Keyword(s):  
Scalar Field ◽  
Thermal Gradient ◽  
Theoretical Models ◽  
Measured Data ◽  
Small Scale ◽  
Temperature Profiles ◽  
One Dimensional ◽  
Kraichnan Model ◽  
The One ◽  
Rate Of Dissipation

Abstract The theoretical models of Batchelor and Kraichnan, which account for the smallest scales of a scalar field passively advected by a turbulent fluid (Prandtl > 1), have been validated using shear and temperature profiles measured with a microstructure profiler in a lake. The value of the rate of dissipation of turbulent kinetic energy ɛ has been computed by fitting the shear spectra to the Panchev and Kesich theoretical model and the one-dimensional spectra of the temperature gradient, once ɛ is known, to the Batchelor and Kraichnan models and from it determining the value of the turbulent parameter q. The goodness of the fit between the spectra corresponding to these models and the measured data shows a very clear dependence on the degree of isotropy, which is estimated by the Cox number. The Kraichnan model adjusts better to the measured data than the Batchelor model, and the values of the turbulent parameter that better fit the experimental data are qB = 4.4 ± 0.8 and qK = 7.9 ± 2.5 for Batchelor and Kraichnan, respectively, when Cox ≥ 50. Once the turbulent parameter is fixed, a comparison of the value of ɛ determined from fitting the thermal gradient spectra to the value obtained after fitting the shear spectra shows that the Kraichnan model gives a very good estimate of the dissipation, which the Batchelor model underestimates.

Determination of Optimum Profile of One-Dimensional Cooling Fins

1983 ◽  
Vol 105 (3) ◽  
pp. 317-320 ◽  
Author(s):  
S. K. Hati ◽  
S. S. Rao
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Minimum Principle ◽  
Problem Formulation ◽  
One Dimensional ◽  
A New Technique ◽  
The One ◽  
Optimum Profile

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.

scholarly journals A one-dimensional modeling study on the effect of advanced insulation coatings on internal combustion engine efficiency

2020 ◽  
pp. 146808742092158
Author(s):  
Alberto Broatch ◽  
Pablo Olmeda ◽  
Xandra Margot ◽  
Josep Gomez-Soriano
Keyword(s):  
Heat Transfer ◽  
Combustion Engine ◽  
Heat Transfer Model ◽  
Transfer Model ◽  
Insulation Material ◽  
One Dimensional ◽  
Engine Efficiency ◽  
Dimensional Modeling ◽  
The One ◽  
The Impact

This article presents a study of the impact on engine efficiency of the heat loss reduction due to in-cylinder coating insulation. A numerical methodology based on one-dimensional heat transfer model is developed. Since there is no analytic solution for engines, the one-dimensional model was validated with the results of a simple “equivalent” problem, and then applied to different engine boundary conditions. Later on, the analysis of the effect of different coating properties on the heat transfer using the simplified one-dimensional heat transfer model is performed. After that, the model is coupled with a complete virtual engine that includes both thermodynamic and thermal modeling. Next, the thermal flows across the cylinder parts coated with the insulation material (piston and cylinder head) are predicted and the effect of the coating on engine indicated efficiency is analyzed in detail. The results show the gain limits, in terms of engine efficiency, that may be obtained with advanced coating solutions.

scholarly journals A variational formulation for translation and assimilation of coherent structures

2013 ◽  
Vol 20 (5) ◽  
pp. 793-801
Author(s):  
M. Plu
Keyword(s):  
Dynamical System ◽  
Data Assimilation ◽  
Coherent Structures ◽  
Variational Formulation ◽  
Landau Equation ◽  
Variational Data Assimilation ◽  
Ginzburg Landau ◽  
One Dimensional ◽  
Ginzburg Landau Equation ◽  
The One

Abstract. The assimilation of observations from teledetected images in geophysical models requires one to develop algorithms that would account for the existence of coherent structures. In the context of variational data assimilation, a method is proposed to allow the background to be translated so as to fit structure positions deduced from images. Translation occurs as a first step before assimilating all the observations using a classical assimilation procedure with specific covariances for the translated background. A simple validation is proposed using a dynamical system based on the one-dimensional complex Ginzburg–Landau equation in a regime prone to phase and amplitude errors. Assimilation of observations after background translation leads to better scores and a better representation of extremas than the method without translation.

Heat-Transfer Stability of Porous Fibrous Composition under Different Condition

2014 ◽  
Vol 1004-1005 ◽  
pp. 557-561
Author(s):  
Yu Juan Wang ◽  
Hai Zhen Chen ◽  
Jin Mei Wang ◽  
Mei Zhen Wang
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Thermal Process ◽  
Surface Condition ◽  
Transfer Model ◽  
Unsteady Heat Transfer ◽  
One Dimensional ◽  
The One ◽  
Thermal Difference ◽  
Key Parameter

In this paper, the influences of different conditions on heat-transfer stability of porous fibrous composition were analyzed by the one-dimensional unsteady heat transfer model. It was resulted that the surface condition of composition was key parameter for heat performance during different thermal process. Great humidity and thermal difference caused the heat transfer fluctuating of material covering, and then changed the thermal conductivity. For the insulation materials under low temperature, the heat performance was sharply fluctuated nearby 0°C.

Analytical accuracy of the one dimensional heat transfer in geometry with logarithmic various surfaces

2014 ◽  
Vol 4 (4) ◽  
Author(s):  
A. Vahabzadeh ◽  
M. Fakour ◽  
D. Ganji ◽  
I. Rahimipetroudi
Keyword(s):  
Heat Transfer ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Physical Parameters ◽  
One Dimensional ◽  
Adomian Decomposition ◽  
Analytical Accuracy ◽  
Study Heat Transfer ◽  
The One

AbstractIn this study, heat transfer and temperature distribution equations for logarithmic surface are investigated analytically and numerically. Employing the similarity variables, the governing differential equations have been reduced to ordinary ones and solved via Homotopy perturbation method (HPM), Variational iteration method (VIM), Adomian decomposition method (ADM). The influence of the some physical parameters such as rate of effectiveness of temperature on non-dimensional temperature profiles is considered. Also the fourth-order Runge-Kutta numerical method (NUM) is used for the validity of these analytical methods and excellent agreement are observed between the solutions obtained from HPM, VIM, ADM and numerical results.

Two-Dimensional Analysis of Conduction-Controlled Rewetting With Precursory Cooling

1976 ◽  
Vol 98 (3) ◽  
pp. 407-413 ◽  
Author(s):  
S. S. Dua ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Dimensional Analysis ◽  
Vertical Surface ◽  
Dimensionless Temperature ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
One Dimensional ◽  
The One

This paper presents a two-dimensional analysis of the effect of precursory cooling on conduction-controlled rewetting of a vertical surface, whose initial temperature is higher than the sputtering temperature. Precursory cooling refers to the cooling caused by the droplet-vapor mixture in the region immediately ahead of the wet front, and is described mathematically by two dimensionless constants which characterize its magnitude and the region of influence. The physical model developed to account for precursory cooling consists of an infinitely extended vertical surface with the dry region ahead of the wet front characterized by an exponentially decaying heat flux and the wet region behind the moving film-front associated with a constant heat transfer coefficient. Apart from the two dimensionless constants describing the extent of precursory cooling, the physical problem is characterized by three dimensionless groups: the Peclet number or the dimensionless wetting velocity, the Biot number and a dimensionless temperature. Limiting solutions for large and small Peclet numbers have been obtained utilizing the Wiener-Hopf technique coupled with appropriate kernel substitutions. A semiempirical matching relation is then devised for the entire range of Peclet numbers. Existing experimental data with variable flow rates at atmospheric pressure are very closely correlated by the present model. Finally a comparison is drawn between the one-dimensional limit of the present analysis and the corresponding one-dimensional solution obtained by treating the dry region ahead of the wet front characterized by an exponentially decaying heat transfer coefficient.

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