ANEJO Nº13: Instalaciones
4. Electricidad y alumbrado 1 Normativa
Cfiapter 4: f£>(perimenta{ (])ata Correction
4 . 1 Introduction
4.1.1 Objectives
The aim of the experiments described in this chapter was to produce thermal conductivity data that could be used to evaluate effective thermal conductivity models. The experiments also examined the influences of porosity, mean pore size, and component thermal conductivities on effective thermal conductivity.
4.1.2 Experimental Strategy
Of the studies on the thermal conductivities of porous foods undertaken previously (see Section 2.4.2 of Chapter 2), the work of Sakiyama & Yano (1 990) stood out because their approach allowed a systematic investigation of the effects of individual variables (moisture content and porosity) on the thermal conductivity. A similar approach was adopted in this study to examine the relative influences of certain porosity-related variables. Since the emphasis of these experiments was on the effect of porosity on the thermal conductivity (as distinct from other food components), it was convenient for the experimental samples to be considered as two-component materials comprised of a gasous phase and a condensed phase.
4.1.3 Experimental Materials
Real foods are not well suited to the manipulations of structure and composition that were desirable for the type of experiments being performed in this study. Because of the versatility they offer, food analogues, which are materials having similar properties to those of real foods, have often been used in heat transfer experiments (including Sakiyama & Yano, 1 990). Due to the importance of the component thermal conductivity
Cliapter 4: �erimenta[ ([)ata Co[fection and 2.4. 1 of Chapter 2, a food analogue for these experiments required component thermal conductivities as close as possible to the real food components being considered.
The porous foods that were the focus of this study were modelled by suspensions of expanded polystyrene (EPS) beads in gels made from guar gum. The use of EPS beads made it possible to vary the volume fraction of the 'gasous' phase and also allowed the mean 'pore' size to be varied in a controlled manner. Guar gum is a polysaccharide which is extracted from the guar plant. It is used extensively in the food industry as a thickener or emulsifier in a wide range of products including ice-cream, frozen desserts, salad dressings, sauces and pet foods (Kirk-Othmer, 1 994). It was chosen as a gelling agent because it formed a very firm gel with the addition of trace amounts of borax, and could be prepared at room temperature, unlike many other gelling agents such as agar. The guar gels had similar properties to water (see Table 4.1), which has the highest thermal conductivity of the major food components. This mi.'{ture had the highest component thermal conductivity ratio that would be encountered with non-frozen foods, and hence represented a worst case scenario, in the sense that the thermal conductivity bounds described in Section 2.3.9 of Chapter 2 were furthest apart, and hence the uncertainty involved in the thermal conductivity predictions is greatest.
Experiments were also performed on samples containing squat aluminium cylinders suspended in guar gel. While this mixture was not analogous to any food product, it provided a contrast to the EPS/ guar-gel samples in that the thermal conductivity of the dispersed phase was higher than the conductivity of the continuous phase. These experiments were performed in order to examine the relative contributions of the continuous and dispersed phases to the overall thermal conductivity of a material.
Chapter 4: f£:{perimenta[ (/)ata Co[fection
4 . 2 Thermal Conductivity Measurement
4.2.1 Measurement Techniques
The thermal conductivity of a material may be measured by a number of methods that can be divided into two categories: steady state methods, and transient methods. The measurements may be comparative (i.e. relative to a material of known conductivity) or absolute. The choice of measurement technique is often determined by the material for which measurements are required. Thermal conductivity measurement methods that have been used for food materials have been reviewed by Nesvadba (1982), Murakami & Okos (1989) and Rahman (1995) . Selected commonly used methods are discussed briefly below.
4.2. 1. 1 Steacfy State MethodJ
Steady state methods use apparatus that are constructed in such a way that measurements are made according to a direct application of Eq. (2.2), i.e. a constant heat flow between two constant temperatures is imposed over a known heat transfer area across a sample of known thickness. This method allows for the most direct thermal conductivity measurements since only the fundamental quantities from Eq. (2.2) are involved, and hence these methods have the potential for high accuracy. However, steady-state apparatus require lengthy equilibration periods (several hours) and the thickness of the measurement samples must be very small by comparison with the dimensions of the area of heat flow (in order to minimise edge effects), which is often highly impractical with food products. As a result, steady state techniques are not usually the preferred measurement choice for food products (Rahman, 1 995), although devices such as the
guarded hot-plate have been used (e.g., Pham & Willix, 1 989).
4.2. 1.2 TranJient MethodJ
A method developed by Fitch (cited In Nesvadba, 1 982), has been used to measure thermal conductivities, often of low conductivity materials. A material sample is sandwiched between a heat source and a heat sink, one side of which is kept at constant
Chapter 4: iExperimentar (])ata Correction
temperature while the time-temperature history of the other side is recorded. The method
is sometimes referred to as quasi-steady state because it is assumed that a steady temperature profile has been developed in the sample, which is unlikely in reality. The original Fitch apparatus has been modified and developed several times, and has been used for a number of different foods (Rahman, 1 995) . However, the shape of the samples
for the Fitch-type apparatus is constrained, being required either to fill a cavity or fit
between two plates, depending on the exact design of the apparatus. This constraint limits the suitability of the Fitch apparatus for some applications.
Another commonly used transient method is the line heat-source method, also known as the thermal conductivity probe (Murakami & Okos, 1 989). In this method a heat source (i.e. the probe) is introduced into a sample which is a much larger body (assumed to be infinite). The temperature change of the probe that results from a constant rate of heating is recorded. The rate of temperature change is proportional to the thermal conductivity of the sample. The fact that the conductivity probe does not have to surround the test material makes it attractive for irregularly shaped objects. Rahman (1995) states that the line-source method is the most commonly used device for measuring the thermal conductivity of biological materials, including foods. However, the conductivity probe makes local measurements rather than overall measurements, and hence the measurements may be sensitive to the position of the probe within a non-homogeneous sample.
4.2.2 Method of Measurement Employed in this Study
By comparison with most thermal conductivity measurement samples, the food analogue samples that were used for these experiments were necessarily large in order to ensure that the distribution of the EPS beads, which were dispersed randomly in the guar-gel, would be uniform. The size of the samples precluded the use of steady state methods or the Fitch apparatus. The conductivity probe was not suitable because the likelihood that local measurements might differ significantly from overall measurements.
Chapter 4: r£x:penmenta[ !Data Correction
Instead a comparative method was used that involved the cooling of two spheres side by side in a well-stirred ice/water bath (see Fig. 4.2 for a diagram of the set-up). One sphere contained the test material (suspension of EPS beads in guar-gel) and the other contained a reference material of known thermal conductivity (guar-gel). The thermal conductivities of the samples were back-calculated from the temperature-time data of the cooling spheres. The use of spherical sample containers avoided the undesirable edge effects that are associated with other geometries, and allowed for uni-dimensional heat
calculations.
A disadvantage of using a non-steady state method was that the temperature dependence of the thermal conductivities of the materials involved was not determined, and instead temperature-averaged conductivity values were measured. The temperature dependencies of the components of the material investigated in this study were linear in the range investigated, increasing as the temperature was increased (see Appendix C). Since the temperature dependencies of the conductivities of the components were increasing in the same direction and the measurement technique was comparative, the effect of this linear dependence was minimised, and hence no corrections for the temperature variations were made in the calculations. The samples were cooled from approximately 200e to approximately
l°e
and so, due to the linear temperature dependence of the materials, the midpoint value (i.e. 1 00C) was a representative temperature and all physical property data required in the calculations were taken at this temperature (see Table 4. 1).4.2.2. 1 Theoretical Basis of the Measurement Technique
The method was based on the analytical solution for the centre temperature of a sphere being cooled with convection boundary conditions as described by Eq. (4. 1):
T -Too