Thermal wave effects on heat transfer enhancement in nanofluids suspensions

Vadasz, Johnathan J.; Govender, S.

doi:10.1016/j.ijthermalsci.2009.06.002

Cited by 15 publications

(8 citation statements)

References 38 publications

(81 reference statements)

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“…As a result of the present investigation, a heterogeneous mixture with particles of much larger size is expected to possess memory in the heat conduction even without investigating the molecular dynamics in detail. This is a very important result, because it provides a justification for using fractional hyperbolic heat conduction laws for suspensions of nanoparticles as discussed in Vadasz & Govender (2010).…”

Section: Discussionmentioning

confidence: 81%

Memory effects for the heat conductivity of random suspensions of spheres

Chowdhury

Christov

2010

Proc. R. Soc. A.

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The presence of a particulate phase defines the effective response of a suspension to changes of the average heat flux. Using the random-point approximation we show that within the first order in the concentration, one needs to solve the problem for the temperature field created by a single inclusion in a matrix subject to an unsteady temperature gradient at infinity. We solve this problem by means of Laplace transform and use the solution as the first-order kernel in the functional expansion. From this kernel, we find the statistical average for the heat flux, which turns out to be a memory integral of the spatially averaged time-dependent temperature gradient. Thus, we discover that the constructive relationship between the average flux and averaged temperature gradient is not local in time, but rather involves a convolution integral that represents the memory due to the heterogeneity of the system. This is a novel result, which inter alia gives a rigorous justification to the usage of generalizations of the heat conduction law involving fractional time derivatives. The decay of the kernel is very close to t −1/2 for dimensionless times lesser than one and abruptly changes to t −3/2 for larger times.

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Section: Discussionmentioning

confidence: 81%

Memory effects for the heat conductivity of random suspensions of spheres

Chowdhury

Christov

2010

Proc. R. Soc. A.

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“…These models are being increasingly used in a variety of technical applications, as in ultrafast laser processing of thin-film structures, heat transfer in nanofluids, or in laser irradiation of biological tissues (see, e.g. [14,15,24,26,30,33,34]). …”

Section: Introductionmentioning

confidence: 99%

Difference schemes for time-dependent heat conduction models with delay

Castro¹,

Rodríguez²,

Cabrera³

et al. 2013

International Journal of Computer Mathematics

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Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

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“…Non-Fourier models of heat conduction have increasingly been considered in recent years to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer, where thermal lags and nonclassical phenomena are present (see, e.g., [1] and references therein). The growing area of applications of these models include, among other examples, the processing of thin-film engineering structures with ultrafast lasers [2,3], the transfer of heat in nanofluids [4,5], or the exchange of heat in biological tissues [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

Castro¹,

Rodríguez²,

Escolano³

et al. 2013

Abstract and Applied Analysis

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Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

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Thermal wave effects on heat transfer enhancement in nanofluids suspensions

Cited by 15 publications

References 38 publications

Memory effects for the heat conductivity of random suspensions of spheres

Memory effects for the heat conductivity of random suspensions of spheres

Difference schemes for time-dependent heat conduction models with delay

Exact and Analytic-Numerical Solutions of Lagging Models of Heat Transfer in a Semi-Infinite Medium

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