Forced convection heat transfer with slurry of phase change material in circular ducts: A phenomenological approach

doi:10.1016/j.enconman.2007.10.016

Energy Conversion and Management

Volume 49, Issue 5, May 2008, Pages 928-932

https://doi.org/10.1016/j.enconman.2007.10.016 Get rights and content

Abstract

A model describing the thermal behaviour of a slurry of phase change material flow in a circular duct is presented. Reactors connected in series are considered for the representation of the circular duct with constant wall temperature. A phenomenological equation is formulated to take account of the heat generation due to phase change in the particles. Results of the simulation present a plateau of temperature along the longitudinal direction, characteristic of the phase change. The effect of different parameters such as the Reynolds number, the weight fraction and the temperature of the cold spring on the length of the plateau is analysed. A correlation resulting from numerical results is proposed for use in the determination of the characteristics of the exchanger for a phase change material slurry.

Introduction

Recently, a new technology of using phase change material (PCM) in energy storage and transport has been proposed for cooling and air conditioning applications [1]. The method consist of adding to a carrier fluid a large quantity of phase change material particles whose phase transition (melting/freezing) temperature is between the sending and the return temperatures of aconventional district cooling system. The PCM particles consist of water in a polymer network. The size of the particles is millimetric in order to minimize the supercooling phenomenon [2]. This technique offers many advantages such as a high cooling capacity, the possibility of using the same medium for both energy transport and storage (thereby reducing losses during the heat exchange process), a constant temperature during heat exchange, high heat transfer rates to the phase change component due to the large surface area to weight ratio, a lower pumping rate and a higher heat transfer coefficient than a conventional single phase working fluid.

Preliminary investigations [3] on slurries of water stabilized in a polymer network have been made to cheek their suitability for district cooling applications. Good stability under repeated thermal cycling without supercooling confirms the possibility of using such fluid as a reversible cold storage. Volume fractions are limited, in the range 0.15 < ϕ < 0.30, to permit both good efficiency of the cold storage and the transport of the fluid in a unit including pumps [4]. The following step is to study the thermal behaviour of the stock under dynamic conditions. To this end, a suitable model has to be developed for describing the forced convection heat transfer with a PCM suspension in a heat exchanger.

The storage time is clearly one of the most important factors to consider when designing a storage process. The problem, being governed by nonlinear differential equations, has to be solved numerically. Different methods were continuously proposed for a PCM of macroscopic size, Refs. [4], [5], [6] for example. Methods with a moving interface (finite element methods) permit giving the interface velocity of the phase change front [7], [8], [9]. The problem becomes more complex when small PCM particles are dispersed in a carrier liquid, and that is why this heat transfer problem has received only limited attention until now. Several models [10], [11], [12], [13], based on the energy equation, formulated by taking into consideration the heat transfer absorption (or release) due to the phase change process, have been developed for a suspension of microencapsulated PCM particles. For all of them, the simulation results agreed well qualitatively with the experimental results obtained using n-eicosane microcapsules in water for laminar flow in a circular tube with a constant heat flux boundary condition, but the quantitative agreement was not good. This important difference between the experimental data and theoretical simulation (more than 30%) can be involved with the supercooling phenomenon, which appears in particles of small size (ca. under a few μm diameter). Roy and Sengupta’s results [14] clearly confirm a delay of crystallisation in n-eicosane microcapsules in water during the freezing process. So, this supercooling effect introduces an additional difficulty and suggests developing a new approach to take into account the erratic character of this phenomenon (by introducing a probability of nucleation for example).

For the millimetric PCM particle considered, previous experimental results showed the limited effect of the supercooling phenomenon [3]. A phenomenological model [15], based on a global description of the heat transfer between the particles and the suspending fluid, was previously proposed to describe the heat transfer during a storage cycle in an agitated tank. The results of the simulation are very much in accordance with experimental data obtained with this fluid, which justifies use of the method for the PCM’s dispersion of millimetric particles.

The aim of this paper is to propose an extension of the model, based on the preceding approach, for the description of heat transfer of a suspension of millimetric particles of PCM in a circular duct with constant wall temperature. The idea is to postulate a representation of the PCM’s slurry flow consisting of a number of agitated reactors connected in series; each reactor being characterized by constant and uniform parameters (same geometric parameters, limiting conditions). The model gives the opportunity to access the temperature of the suspended liquid for different positions along the axial direction of the circular duct. Several simulations were conducted to investigate the effects of the flow parameter (Reynolds number), slurry parameter (weight fraction) and exchanger parameter (wall temperature).

Section snippets

Description of the proposed model

Consider a slurry of millimetric particles of phase change material where both the liquid and the particles are at its temperature of solidification T_o. All thermophysical properties of the two components (liquid and particles) are assumed constant. In the following, the subscripts p, ℓand w will be referred, respectively, to the particles of the phase change material, the suspended liquid and the wall temperature.

The fluid enters at uniform velocity υ in a tubular heat exchanger of length Λ

Results and discussion

In what follows, the solution procedure outlined in the previous section is illustrated by a practical example. The considered phase change material is a particle containing water confined in a network of polymer. Millimetric particles are dispersed in a carrier liquid (oil) in order to form a slurry. The phase change occurs at 0 °C and the physical constants are very near those of water or ice.

The different parameters investigated for the present study are the mass fraction ϕ_m of particles, the

Concluding remarks

We have developed a simple model to describe the forced convection heat transfer with millimetric phase change material slurry in a circular duct flow. The representation of the phase change material slurry flow consists of a number of agitated reactors connected in series, where heat generation due to phase change in the particles is included in a heat thermal balance based on a phenomenological approach (previously validated). A typical plateau of the temperature characteristics of the phase

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Forced convection heat transfer with slurry of phase change material in circular ducts: A phenomenological approach

Abstract

Introduction

Section snippets

Description of the proposed model

Results and discussion

Concluding remarks

Int Comm Mass Heat Transfer

Int Comm Heat Mass Transfer

Int J Heat Mass Transfer

Int. J. Heat Mass Transfer

Int J Heat Mass Transfer

Int Comm Heat Mass Transfer

Transport of cold thermal energy with a slurry as secondary biphasic refrigerant

Int J Energ Res