Three dimensional heat transfer analysis of combined conduction and radiation in honeycomb transparent insulation (original) (raw)

Abstract

In this work a three dimensional heat transfer analysis of honeycomb Transparent Insulation Materials (TIM) destined for improving the efficiency of flat plate solar collectors is performed. The cellular and repetitive nature of the TIM structure has allowed simplify the problem and simulate a single isolated cell with opaque and adiabatic walls. The combined heat transfer by radiation and conduction across the isolated cell is treated by means of the solution of the energy equation in its three dimensional form which is coupled to the Radiative Transfer Equation (RTE). The Finite Volume Method is used for the resolution of the RTE. The numerical results are compared to experimental measurements of the heat transfer coefficient on various honeycomb TIM given by different authors in the literature showing a reasonable agreement. The 3D simulations have allowed to study in detail the thermal behavior of the TIM and to understand the real physics of the problem. Finally, a parametric study is conducted in order to investigate the effect of the variation of the most relevant optical and dimensional parameters of the TIM on the heat transfer.

Figures (15)

Fig. 1. (a) Honeycomb structure (Wacotech Gmb H. & Co., 2013) (b) Sketch of two adjacent cells, ray treatment. 2.1. Boundary conditions reflected the original arising ray (R1). Taking this into account, it is considered a single isolated cell with opaque and adiabatic walls having a fictitious reflectivity equal to the sum of the reflectivity and transmissivity of the wall itself.

Fig. 1. (a) Honeycomb structure (Wacotech Gmb H. & Co., 2013) (b) Sketch of two adjacent cells, ray treatment. 2.1. Boundary conditions reflected the original arising ray (R1). Taking this into account, it is considered a single isolated cell with opaque and adiabatic walls having a fictitious reflectivity equal to the sum of the reflectivity and transmissivity of the wall itself.

Fig. 2. Sketch of the honeycomb cell.

Fig. 2. Sketch of the honeycomb cell.

Fig. 3. Overall heat coefficient, h,, calculated vs measured (Hollands et al., 1984) at the hot plate for different aspect ratios and different hot and cold walls emissivity (W m7? K7'). Although the FVM can lead to some numerical errors. the discrepancy may also be due to the experimental errors in the measurement of the heat transfer coefficients, the material optical properties or the honeycomb dimensions A sensitivity analysis has been done in order to check how dependent is the calculated overall heat coefficient on the variability and uncertainty in the parameters €w, €nl€c, Dry and Lry. This effect has been investigated by computing the overall heat coefficient fixing each

Fig. 3. Overall heat coefficient, h,, calculated vs measured (Hollands et al., 1984) at the hot plate for different aspect ratios and different hot and cold walls emissivity (W m7? K7'). Although the FVM can lead to some numerical errors. the discrepancy may also be due to the experimental errors in the measurement of the heat transfer coefficients, the material optical properties or the honeycomb dimensions A sensitivity analysis has been done in order to check how dependent is the calculated overall heat coefficient on the variability and uncertainty in the parameters €w, €nl€c, Dry and Lry. This effect has been investigated by computing the overall heat coefficient fixing each

Sensitivity analysis for honeycomb with A = 2.4 of Hollands et al. (1984) Bold values refer to the measured values. Table 1

Sensitivity analysis for honeycomb with A = 2.4 of Hollands et al. (1984) Bold values refer to the measured values. Table 1

Fig. 4. Conductive, radiative and total heat losses at the center-line axis of the hot plate for different aspect ratios and different plates emissivities; top A = 2.4, middle: A = 4.75, bottom: A = 9.61; left: BB, center: SB, right: SS. parameter to the two limiting values of the corresponding uncertainty interval given by Hollands et al. (1984) while maintaining the others as the average value. For each varied parameter, the relative discrepancy 6 between the computed heat transfer coefficients is calculated. The results are presented in Table | where it can be seen that the uncertainty in each one of these parameters entails a different error between the calculated values. The uncer- tainty in the walls and the bounding plates emissivities have the most significant effect on the computed values of h,, while the variability in the cell dimensions has less effect. Thus, at least part of the discrepancy between the numeri- cal and experimental results can be due to measurement errors.

Fig. 4. Conductive, radiative and total heat losses at the center-line axis of the hot plate for different aspect ratios and different plates emissivities; top A = 2.4, middle: A = 4.75, bottom: A = 9.61; left: BB, center: SB, right: SS. parameter to the two limiting values of the corresponding uncertainty interval given by Hollands et al. (1984) while maintaining the others as the average value. For each varied parameter, the relative discrepancy 6 between the computed heat transfer coefficients is calculated. The results are presented in Table | where it can be seen that the uncertainty in each one of these parameters entails a different error between the calculated values. The uncer- tainty in the walls and the bounding plates emissivities have the most significant effect on the computed values of h,, while the variability in the cell dimensions has less effect. Thus, at least part of the discrepancy between the numeri- cal and experimental results can be due to measurement errors.

Fig. 5. Isotherms at the three investigated honeycomb cells with different aspect ratios (SB case).

Fig. 5. Isotherms at the three investigated honeycomb cells with different aspect ratios (SB case).

Table 2 5.2. Parametric study In Fig. 6 are presented the temperature profiles at the center-line of the TIM cavity for the three studied TIMs with the different aspect ratios. It can be seen that when a SB combination is used, the temperatures in the cavity are lower than the SS and BB cases. This is due to a ow radiative loss from the hot plate and thus less heat by radiation received by the TIM walls and consequently ess heat transferred from the walls to the air filling. In he BB and the SS cases, the temperature profiles present a symmetry with respect to the center of the cavity. For he BB case, the radiation from both bounding plates is high. This leads to an important heat transfer to the cell walls and thus resulting to a maximum temperature at the bottom half of the cavity and a minimum temperature at he upper half of the cavity. On the contrary, in the SS case the radiation losses are almost negligible and the heat is principally transferred by conduction through the air. This entails lower temperatures at the bottom half and higher temperatures at the upper half than those seen for the BB case.

Table 2 5.2. Parametric study In Fig. 6 are presented the temperature profiles at the center-line of the TIM cavity for the three studied TIMs with the different aspect ratios. It can be seen that when a SB combination is used, the temperatures in the cavity are lower than the SS and BB cases. This is due to a ow radiative loss from the hot plate and thus less heat by radiation received by the TIM walls and consequently ess heat transferred from the walls to the air filling. In he BB and the SS cases, the temperature profiles present a symmetry with respect to the center of the cavity. For he BB case, the radiation from both bounding plates is high. This leads to an important heat transfer to the cell walls and thus resulting to a maximum temperature at the bottom half of the cavity and a minimum temperature at he upper half of the cavity. On the contrary, in the SS case the radiation losses are almost negligible and the heat is principally transferred by conduction through the air. This entails lower temperatures at the bottom half and higher temperatures at the upper half than those seen for the BB case.

Fig. 6. Temperature profiles at the center-line of the honeycomb cavities for different aspect ratios.

Fig. 6. Temperature profiles at the center-line of the honeycomb cavities for different aspect ratios.

Fig. 7. Conductive, radiative and total heat transfer coefficients as a function of the cell aspect ratio (¢, = 0.43, T,,. = 306K, T.. = 298 K. Dny = 10mm and f, = 1).

Fig. 7. Conductive, radiative and total heat transfer coefficients as a function of the cell aspect ratio (¢, = 0.43, T,,. = 306K, T.. = 298 K. Dny = 10mm and f, = 1).

Fig. 8. Conductive, radiative and total heat transfer coefficients as a function of the wall emissivity (A = 8,7. = 306K, T., = 298 K and f, = 1).

Fig. 8. Conductive, radiative and total heat transfer coefficients as a function of the wall emissivity (A = 8,7. = 306K, T., = 298 K and f, = 1).

Fig. 9. Conductive, radiative and total heat transfer coefficients as a function of the temperature difference between the cold and the hot plates (€, = 0.43, A= 8, T.. = 298 K and f, = 1).

Fig. 9. Conductive, radiative and total heat transfer coefficients as a function of the temperature difference between the cold and the hot plates (€, = 0.43, A= 8, T.. = 298 K and f, = 1).

Fig. 11. Conductive, radiative and total heat transfer coefficients as a function of f, (€, = 0.43, Th. = 308K, T., = 298 K and A = § Fig. 10. Conductive, radiative and total heat transfer coefficients as a function of the absorber plate temperature («,, = 0.43, A = 8, AT = 10 and f, = 1).

Fig. 11. Conductive, radiative and total heat transfer coefficients as a function of f, (€, = 0.43, Th. = 308K, T., = 298 K and A = § Fig. 10. Conductive, radiative and total heat transfer coefficients as a function of the absorber plate temperature («,, = 0.43, A = 8, AT = 10 and f, = 1).

Fig. A.1. Schematics of a control volume and control angle.

Fig. A.1. Schematics of a control volume and control angle.

Characteristics of the studied honeycomb TIM (Hollands et al., 1984) Table B.1 References A summary of the characteristics of the hexagonal poly- ester honeycomb of Hollands et al. (1984) is shown in the table below (see Table B.1). Abdullah, A.H., Abou-Ziyan, H.Z., Ghoneim, A.A., 2003. Thermal performance of flat plate solar collector using various arrangements of compound honeycomb. Energy Convers. Manage. 44 (19), 3093-3112.

Characteristics of the studied honeycomb TIM (Hollands et al., 1984) Table B.1 References A summary of the characteristics of the hexagonal poly- ester honeycomb of Hollands et al. (1984) is shown in the table below (see Table B.1). Abdullah, A.H., Abou-Ziyan, H.Z., Ghoneim, A.A., 2003. Thermal performance of flat plate solar collector using various arrangements of compound honeycomb. Energy Convers. Manage. 44 (19), 3093-3112.

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