Constructal optimization of longitudinal and latitudinal rectangular fins used for cooling a plate under free convection by the intersection of asymptotes method

This paper is a first of a series aiming at revisiting technical aspects of the volume averaging theory. Here, we discuss the choice of the spatial averaging operator for periodic and quasiperiodic structures. We show that spatial averaging must be defined in terms of a convolution and analyze the properties of a variety of kernels, with a particular focus on the smoothness of average fields, the ability to attenuate geometrical fluctuations, Taylor series expansions, averaging of periodic fields and resilience to perturbations of periodicity. We conclude with a set of recommendations regarding kernels to use in the volume averaging theory.

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Technical Notes on Volume Averaging in Porous Media I: How to Choose a Spatial Averaging Operator for Periodic and Quasiperiodic Structures

Homogenization of the Navier-Stokes equations by means of the Multi-scale Virtual Power Principle

Performance enhancement of cabinet cooling system by utilizing cross-flow plate heat exchanger

Effective NTU of a counterflow heat exchanger with unbalanced flow and longitudinal heat conduction through fluid separating and outer walls

Multi-scale modelling of flow in periodic solid structures through spatial averaging

Thermal design and optimization of small-scale high effectiveness cross-flow heat exchangers

This paper presents spatially averaged temperature equations for modelling macro-scale heat transfer in periodic solid structures such as fin and tube arrays. The governing equations for the periodically developed heat transfer regime in isothermal solids are derived. It is shown that the appropriate macro-scale temperature in the periodically developed heat transfer regime is obtained by averaging the temperature with a specific weighting function which is adapted to the temperature decay rate. This matched weighting function allows the representation of the macro-scale interfacial heat transfer and thermal dispersion source by means of a spatially constant interfacial heat transfer coefficient and thermal dispersion vector, which both can be calculated from the periodic rescaled temperature on a unit cell of the solid structures. Moreover, it is proved that for small temperature decay rates, the matched weighting function yields the same macro-scale description as repeated volume averaging. The theoretical framework of this paper is applied to a case study, describing the heat transfer between a fluid and an array of solid cylinders at constant temperature.

Macro-scale heat transfer in periodically developed flow through isothermal solids

In this work, the friction factor for steady periodically developed flow through micro- and mini-channels with periodic arrays of offset strip fins is analyzed. The friction factor is studied numerically on a unit cell of the array for Reynolds numbers ranging from 1 to 600, and fin height-to-length ratios below 1. It is shown that the friction factor correlations from the literature, which primarily focus on larger conventional offset strip fin geometries in the transitional flow regime, do not predict the correct trends for laminar flow in micro- and mini-channels. Therefore, a new friction factor correlation for micro- and mini-channels with offset strip fin arrays is constructed from an extensive set of numerical simulations through a least squares fitting procedure. The suitability of this new correlation is further supported by means of the Bayesian approach for parameter estimation and model validation. The correlation predicts an inversely linear relationship between the friction factor and the Reynolds number, in accordance with our observation that a strong inertia regime prevails over nearly the entire range of investigated Reynolds numbers. Yet, through a more detailed analysis, also the presence of a weak inertia regime and a transitional regime is identified, and the transitions from the strong inertia regime are quantified by means of two critical Reynolds numbers. Finally, the new correlation also incorporates the asymptotic trends that are observed for each geometrical parameter of the offset strip fin array, and whose origins are discussed from a physical perspective.

Friction factor for steady periodically developed flow in micro- and mini-channels with arrays of offset strip fins

In this work, the friction factor for steady periodically developed flow through micro-and mini-channels with periodic arrays of offset strip fins is analyzed. The friction factor is studied numerically on a unit cell of the array for Reynolds numbers ranging from 1 to 600, and fin height-to-length ratios below 1. It is shown that the friction factor correlations from the literature, which primarily focus on larger conventional offset strip fin geometries in the transitional flow regime, do not predict the correct trends for laminar flow in micro-and mini-channels. Therefore, a new friction factor correlation for micro-and mini-channels with offset strip fin arrays is constructed from an extensive set of numerical simulations through a least-squares fitting procedure. The suitability of this new correlation is further supported by means of the Bayesian approach for parameter estimation and model validation. The correlation predicts an inversely linear relationship between the friction factor and the Reynolds number, in accordance with our observation that a strong inertia regime prevails over nearly the entire range of investigated Reynolds numbers. Yet, through a more detailed analysis, also the presence of a weak inertia regime and a transitional regime is identified, and the transitions from the strong inertia regime are quantified by means of two critical Reynolds numbers. Finally, the new correlation also incorporates the asymptotic trends that are observed for each geometrical parameter of the offset strip fin array, and whose origins are discussed from a physical perspective.

Geert Buckinx

Papers

Multi-scale modelling of flow in periodic solid structures through spatial averaging

Thermal design and optimization of small-scale high effectiveness cross-flow heat exchangers

Macro-scale heat transfer in periodically developed flow through isothermal solids

Friction factor for steady periodically developed flow in micro- and mini-channels with arrays of offset strip fins

Friction factor for steady periodically developed flow in micro-and mini-channels with arrays of offset strip fins