6. El trigo y sus insectos
6.2. Insectos benéficos (Entomófagos) en trigo
A theoretical model was created using the values calculated in the geometrical model in chapter 3 (section 3.4) to study the heat flow through the micro-pod and yarn filaments, and the effect it has on the response and recovery time of the thermistor. It was built in COMSOL Multiphysics® (version 3.4, COMSOL, Stockholm, Sweden) which is a cross-platform finite element analysis, solver and Multiphysics software. This software was used because it contains a heat transfer module which comprises of simulation tools which can be used to study the mechanisms of heat transfer, such as conduction, convection and radiation (COMSOL, 2012).
The heat flow through the micro-pod and the yarn filaments was modelled using the software, this was used to simulate response and recovery times, which was then used to calculate the thermal time constant. However the thermal time constant of the thermistor cannot be integrated into the simulations and the exact construction of the thermistor is not known. Therefore for the simulations a copper block of similar dimensions was used in place of the thermistor and the average temperature measurements at the surface of the copper block was recorded for the simulation data.
It was assumed that the heat would be transferred through thermal conduction inside the micro- pod. Conduction is the transfer of heat from a body at higher temperature to a body of lower temperature or the transfer of heat from one part of a body at higher temperature to another part which is at lower temperature (Rohsenow et al., 1985). The relationship between flow of heat and the temperature field is defined using Fourier’s law (Hahn and Özişik, 2012). For an isotropic and homogenous solid Fourier’s law defining the conductive heat flux is given in equation 4.1.
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𝑞 = −𝑘∇𝑇 (4.1) (Hahn and Özişik, 2012), (COMSOL, 2012)
The micro-pod with the thermistor chip and PE yarn was considered to be an immobile solid, therefore the heat transfer in solids with respect to time was obtained using the equation 4.2 given below
𝜌𝐶𝑝( 𝜕𝑇
𝜕𝑡) = ∇(𝑘∇𝑇) + 𝑄 (4.2) (COMSOL, 2012)
Where:
T is the temperature in kelvin, t is the time taken from the start of the simulation, is the density of the polymer resin/polyester fibres in the encapsulation, Cp is the heat capacity , k is the thermal
conductivity and Q is the Heat source (surface being measured). The properties of the resins and polyester filaments are in table 4.2.
Table 4:2: Thermal Properties of material
Property Multi-Cure® 9- 20801 resin 9001-E-v3.1 Multi-Cure® Polyester Thermal Conductivity 0.9 Wm-1K-1 0.2 Wm-1K-1 1.009 Wm-1K-1 (Kawabata and Rengasamy, 2002) Density 2000 kgm-3 1060 kgm-3 1390kgm-3
(Behera and Hari, 2010)
Specific Heat Capacity
1000 JKg-1K-1 1470 JKg-1K-1 1300JKg-1K-1
In these simulations the heat flow through the polyester fibres surrounding the micro-pod (packing fibres and the knit braided fibre sheath shown in figure 3.1 in section 3.2) was modelled as heat flow through a porous medium. Textile yarns are porous, containing cylindrical fibres and air (Veit, 2012). However there are no simulations done to study the heat flow through a single textile yarn. Most of the work that is in the literature (Haghi, 2011), (Yuchai Sun et al., 2010) is on textile fabrics which are made using several textile yarns. Textile fabrics have also been considered as porous media (Das et al., 2011), (Haghi, 2011), and heat transfer through a textile fabric is a complex process defined by solid conduction through fibres; conduction by intervening air; natural convection in the space between fibres; free convection due to wind flow and buoyancy flow in the surrounding environment; and radiation (Das et al., 2011), (Haghi, 2011), (Yuchai Sun et al., 2010).
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However, the heat flow through a fabric has been simplified and previously modelled, by only using conduction through solid fibres and conduction through the air filling the spaces between fibres (Min et al., 2007). Hence for the simulations documented in the thesis heat flow through the packing fibres and the knit braided fibre sheath was modelled only using heat conduction through a porous medium. This was done to simplify the model and also due to the limitation in the computational power, including convection and radiation in the model caused the COMSOL model to crash. Therefore in the theoretical model the effects of convection and radiation have been ignored.
The relative humidity of the air in-between the fibres was set to 75 % (which was the average humidity during the week). Convective heat transfer does not take place if the fluid is kept stationary (Haghi, 2011). Therefore for the simulation, the air in-between the fibres in the yarn was treated as trapped dead air hence the natural convection in the spaces between fibres have been ignored. It was also assumed that there would be no forced wind flow in the environment and the buoyancy flow was negligible, hence the effects of free convection as a result of wind flow and buoyancy flow have been ignored. The effects of radiation have also been neglected since the research done on non-woven fabrics by Zhu et al has shown that the radiative heat transfer increases with pore size (Zhu et al., 2015). Therefore for these simulations, it was assumed that the packing fibres and fibres in the knit braided fibre sheath were densely packed and the pore size was small enough to not allow radiation.
The conductive heat flow through a porous medium, which was used in the simulations was defined using equation 4.3.
(ρCp)eq (∂T/∂t) = ∇(keq∇T) + Q (4.3) (COMSOL, 2012)
Where (ρCp)eq is given using equation 4.4,
(ρCp)eq = θpρpCp,p+ (1-θp)ρCp (4.4)
And keq is given using equation 4.5,
keq = θpkp + (1-θp)k (4.5)
Where Cp is the Specific heat capacity of air, ρ is the density of air and k is the thermal conductivity
of air. Kp is the thermal conductivity of polyester, Cp,p is the Specific heat capacity of polyester, ρp
is the density of polyester and the Volume fraction is θp. The volume fraction of a braided structure
has been estimated to be 0.5 (Shishoo, 2008).
The images of the simulations done for the samples stated in section 4.2.1 are given in Appendix 10.
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