Experimental study on the thermal control of a roof-top collective building antenna using a porous matrix filled with Water-Copper nanofluid

Case Studies in Thermal Engineering 32 (2022) 101869 Available online 15 February 2022 2214-157X/© 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Experimental study on the thermal control of a roof-top collective building antenna using a porous matrix filled with Water-Copper nanofluid F. Sastre a , A. Martin-Garin b , E. Martin c , * , A. Velazquez a , A. Baïri d a Universidad Polit´ ecnica de Madrid, Fluid Mechanics and Aerospace Propulsion Department., Plaza del Cardenal Cisneros 3, 28040, Madrid, Spain b Universidad del País Vasco, UPV/EHU, ENEDI Research Group, Department of Thermal Engineering, Plaza Europa 1, 20018, Donostia-San Sebasti´ an, Spain c Universidade de Vigo, Departamento de Ingeniería Mec´ anica, M´ aquinas y Motores T´ ermicos y Fluidos, Escuela de Ingeniería Industrial, Campus Marcosende, 36310, Vigo, Spain d Universit´ e de Paris, Laboratoire Thermique Interfaces Environnement (LTIE), EA 4415, 50 rue de S` evres, F-92410, Paris, France HIGHLIGHTS •Thermal control of a collective building finned cylindrical antenna. •Nanofluid combined with porous media. •Antenna temperature correlation for a range of governing parameters. •Application case to a smart building collective antenna. ARTICLE INFO Keywords: Smart building Thermal regulation Electronics engineering Collective automation antenna Nanofluid Porous media ABSTRACT This experimental work addressed the thermal control a roof-top collective building antenna meant to control home equipment in smart buildings. The antenna was placed inside a concentric quasi-cylindrical cavity maintained at low temperature. Cooling was provided by a Water-Copper nanofluid saturated porous matrix placed between the antenna and the enclosure. The ratio of the thermal conductivity of the porous material to that of the water varied from 4 up to 41.2. The nanoparticles volume fraction varied between 0% and 5%. The main result was a new semiempirical correlation that allows for the determination of the antenna’s average surface temperature as a function of the governing parameters: ratios of nanofluid to water and porous media to water thermal conductivities, nanoparticles volume fraction, and Rayleigh number. The applicability of the correlation was illustrated for a practical application case. It was found that, for some cases, the proposed thermal control system improves power dissipation by a factor of 33% as compared with the case of pure water (2 kW versus 1.5 kW). * Corresponding author. E-mail address: [email protected] (E. Martin). Contents lists available at ScienceDirect Case Studies in Thermal Engineering journal homepage: www.elsevier.com/locate/csite https://doi.org/10.1016/j.csite.2022.101869 Received 10 December 2021; Received in revised form 9 February 2022; Accepted 12 February 2022 Case Studies in Thermal Engineering 32 (2022) 101869 2 1. Introduction The use of home automation, that applies to both individual apartments and groups of buildings, is becoming the tendency in the field of modern housing development. When conjoint installations are planned, often preferred because they reduce operating and maintenance costs, a collective antenna is normally used. Its purpose is to manage equipment in real and delayed time, both on site and remotely, and to serve for big data transmission in connection to building maintenance and safety as described by Martin-Garin et al. [1]. From a thermal viewpoint, these antennae are characterized by the strong heat flux generated by their internal electronic assembly that may lead to temperatures so high that they could even cause malfunctions and shut down. Therefore, their thermoregulation is critical for a reliable system operation. Normally, air natural convection is preferred in these types of thermal control systems given its well-known advantages; among Nomenclature a thermal diffusivity (m 2 s −1 ) C specific heat at constant pressure (J.kg −1 K −1 ) g gravity acceleration (m.s −2 ) H height of the cylinder (m) I current intensity (A) k(φ)function in eq. (11.a), defined in eq. (11.b) L distance L=Re−Ri (m) m(λ*)function in eq. (11.a), defined in eq. (11.c) P power (W) q generated heat flux (Wm −2 ) Q measured global heat flux (Wm −2 ) Re radius of the cavity (m) Ri radius of the active cylinder (m) RaL Rayleigh number (−) S Contact surface with nanofluid saturated porous medium (m 2 ) Si surface of the ith element (m 2 ) Sh lateral surface of the antenna (m 2 ) T temperature (K) Tc average temperature of the cavity (K) Th average temperature of the antenna (K) Ti temperature of the ith element (K) U voltage (V) Greek symbols β volumetric expansion coefficient (K −1 ) δ difference δ=ΔTc−ΔTm (K) ΔY absolute uncertainty for a given parameter Y (unit of Y) ΔY/Y relative uncertainty for a given parameter Y (%) ΔT difference temperature ΔT=Th-Tc (K) ε porosity φ Nanoparticles volume fraction (%) in nanofluid λ thermal conductivity (Wm −1 K −1 ) λ* dimensionless thermal conductivity (−) μ dynamic viscosity (Pa.s) ρ density (kg.m −3 ) Subscripts Cu solid Copper nanoparticles ca calculated m measured nf nanofluid sp solid matrix of the porous medium spm saturated porous medium w base fluid (pure water) F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 3 others: simplicity of design and robustness of operation. This was the case in the study by Kim et al. [2] where the convective heat transfer coefficient was determined for a vertical surface equipped with micro-fin arrays. However, air thermophysical properties, notwithstanding their well proven applicability in engineering applications, are sometimes insufficient when a large volumetric heat flux is generated, as in the case discussed here. In this situation, other working fluids could be used such as water, oils, or alcohols with different compositions and thermophysical properties (Bharti et al. [3], Baïri [4]). In this context, nanofluids have recently proven to be highly effective in enhancing heat transfer, as shown, for instance, in the experimental work of Xu et al. [5] dealing with optoelectronic devices. Furthermore, the improvement of nanofluid’s manufacturing techniques, their ease of use, and the reduction in their cost price makes them more and more attractive (Ali [6] and Sabour et al. [7]). Also, their association with porous materials leads to further enhanced heat transfer as highlighted in several works dealing with components and cavities of different shapes and various nanofluids: Abu-Nada and Oztop [8], Sheikholeslami et al. [9], Baïri and Laraqi [10], Sheremet et al. [11], Alilat [12], Pourfazad et al. [13], Hajipour et al. [14], Sharaf et al. [15], Alilat et al. [16], Salehi et al. [17], Gholinia et al. [18], El-Shorbagi et al. [19] and Li et al. [20]. The thermophysical characteristics of the nanofluid play an important role in the heat exchange phenomena, as shown in Toghraie et al. [21], Soltani et al. [22], Baïri [23] and in the recent critical review published by Zahmatkesh et al. [24]. This review describes, among others, the effect of nanoparticle shape, volume fraction, and temperature on the constitutive characteristics of the nanofluid, whose effective thermal conductivity and dynamic viscosity are the key thermophysical properties for any modelling approach. In this context, several global models have been described in the specialized literature, but it should be noted that they show a large dispersion. Accordingly, research is intensifying to classify those that present the best results validated by measurements, and to associate them with precise operating conditions. Basic models tend to follow, as a reference, the formulation proposed by Maxwell [25] and Brinkman [26] (spherical nanoparticles), and Hamilton and Crosser [27] (non-spherical), to determine the effective thermal conductivity and dynamic viscosity of the nanofluid. A practical implementation of the Hamilton–Crosser model [27] could be found in the work by Abu-Nada et al. [28]. Another relevant model is the one proposed by Koo and Kleinstreuer [29] that decomposes the effective thermal conductivity into a static part (Maxwell) and another part taking accounting for the contribution of Brownian motion. Recent applications of this model could be found in the works of Sharafeldin et al. [30], and Babajani et al. [31]. An interesting conclusion of another model, this time proposed by Timofeeva et al. [32], was that the Brownian motion has less influence on the effective viscosity than on the effective thermal conductivity. A relevant study, that complements those reviewed so far, is the one published by Corcione [33] in which the proposed constitutive correlations are of an empirical nature. The study showed that the actual nanofluid effective thermal conductivity tends to be either under or over-estimated by Maxwell’s model [25], and the effective viscosity to be under-estimated by the Brinkman model [26]. The present work deals with the thermal control of a cylindrical antenna placed vertically. The envisaged application is for its use in collective integrated home automation. The antenna is contained in a concentric quasi-cylindrical isothermal enclosure. Cooling is provided by a porous matrix saturated with H 2 O–Cu nanofluid whose nanoparticles volume fraction varies in the range from 0 (pure water) to 5%. The ratio between thermal conductivity of the porous matrix to that of water spans from 4 to 41.2. A new correlation is developed that allows for determination of the mean temperature of the antenna as a function of the governing parameters. The results obtained could be used to optimize the global design of the antenna to favor its actual implementation. 2. Description of the problem The problem consisted of the determination of the average temperature, Th , of a cylindrical, vertical, finned antenna during steady state operation. A constant heat flux q was generated on the inside of the antenna whose lateral wall contained eight rectangular fins Fig. 1(a). 3D sketch of the considered configuration. F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 4 arranged in the vertical direction. This setup was enclosed in a quasi-cylindrical cavity filled with a porous matrix saturated with a Water-Copper based nanofluid. The enclosing cavity had a double outer wall that was kept isothermal at temperature Tc by means of a water-glycol dilution forced to flow in between the double wall. Two sketches (3D and 2D) of the considered configuration are presented in Fig. 1(a) and Fig. 1(b), respectively. Ri, Re, H, and Sh denote inner and external radius of the system, height, and lateral surface area respectively. The difference (Re−Ri) was denoted as L. The horizontal base of the enclosure (cavity plus antenna) was insulated and could be considered nearly adiabatic. The nanoparticles volume fraction in the Water-Copper nanofluid was varied between 0 (pure water) up to 5%. The properties (thermal conductivity, λ, density, ρ , specific heat, C, thermal expansion coefficient, β, and dynamic viscosity, μ ) of both water and copper nanoparticles (when applicable) are detailed in Table 1, see Abu-Nada et al. [28] and Rashidi et al. [34]. The ratio between the thermal conductivity of the porous matrix (porosity ε =0.97) and the water was varied in the range from 4.0 up to 41.2. 2.1. Nanofluid properties The Water-Copper nanofluid used in the experiments was regularly replaced to avoid problems like agglomeration and sedimentation. Regarding the determination of its thermophysical properties, the Maxwell [25] and Brinkman [26] models were used. The experimental applicability of these models has been tested by Baïri [35] and Baïri et al. [36]. The effective thermal conductivity, λnf , dynamic viscosity, μ nf , density, ρ nf , thermal expansion coefficient, βnf , and specific heat, Cnf , of the nanofluid (subscript nf) were defined as follows: Fig. 1(b). 2D views of the considered configuration. Table 1 Thermophysical characteristics of pure water and Copper nanoparticles. Pure water (w) Copper nanoparticles (Cu) λ (W m −1 K −1 ) 0.613 401 ρ (kg m −3 ) 997 8933 C (J kg −1 K −1 ) 4180 395 β (K −1 ) 2.1 ×10 −4 1.67 ×10 −5 μ (Pa s) 8.91 ×10 −4 F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 5 λnf =(λCu +2λw−2φ(λw−λCu) λCu +2λw+φ(λw−λCu))λw(1) μ nf = μ w (1−φ)2.5(2) ρ nf = (1−φ) ρ w+φ ρ Cu (3) βnf =(1−φ)( ρ β)w+φ( ρ β)Cu ρ nf (4) Cnf =(1−φ)( ρ C)w+φ( ρ C)Cu ρ nf (5) where φ is the volume fraction of the nanofluid. Properties of the nanofluid saturated porous media (subscript spm) were calculated using the porosity ε . λspm = ε λnf + (1− ε )λsp (6) ( ρ C)spm = ε ( ρ C)nf + (1− ε )( ρ C)sp (7) The ratio between thermal conductivity of the porous media’s solid matrix (subscript sp) and that of water, λ∗, was a governing parameter too. λ∗=λsp λw (8) 2.2. Description of the experimental setup The main subsystems (see the sketch presented in Fig. 2(a)) of the experimental rig were: •The thermoregulated bath that generated a glycol-water flow at the desired temperature, Tc, in the range between 278 and 300 K (±0.1 K). •The calibrating thermometer needed to calibrate all the thermocouples of the assembly. •The data acquisition unit that collected the thermal and electrical data of the tested assembly. •The stabilized power supply enabling the antenna to be powered on. Current intensity I and voltage U were measured with integrated high precision multimeters (2 ×10 7 points, 6 digits). Their absolute uncertainties were ΔI= ±0.1mA and ΔU= ± 0.01 V. Relative uncertainty of the resulting global power P=UI was determined by means of the well-known partial derivative method as ΔP/P=ΔU/U+ΔI/I. The uncertainty of the corresponding global measured heat flux Q=P/Sh was, then, calculated by means of the same derivative method ΔQ/Q=ΔP/P+ΔSh/Sh. After accounting for the measurement uncertainties of the antenna’s dimensions, calculations lead to ΔQ/Q varying in the span from 0.8 to 1.7%. •The computer needed to collect and process the measured physical parameters. Fig. 2(a). Sketch of the experimental rig. F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 6 Regarding the tested assembly, see Fig. 2(b) and Fig. 2(c), the antenna was installed on a circular base of insulating material (number 1 in Fig. 2(b)) placed on top of a thick extruded polyurethane foam plate (number 2 in Fig. 2(b)). The average thermal conductivity of this insulating material in the operating temperature range (5–70 ◦C) was 0.036 ±0.002 Wm −1 K −1 measured by using the Transient Plane Source (TPS) method [37,38]. The thermal conductivity of the porous material, λsp, was also measured by means of the same TPS method. Two materials were tested in the experimental campaign with λ∗=λsp/λw=4.8 and 38.4 (±0.3) respectively. In addition, the case without porous material (λ∗=0)was also tested. The porous medium consisted of shavings of these materials made with a lathe. Their high porosity ε =0.97 ±0.02 was measured by using the Mercury Intrusion Porosimetry Method (IPM) [39]. The Water-Copper nanofluid was introduced into the cavity by means of two pipes (number 3 of Fig. 2(b) and (c)). The purpose of these inlet/outlet pipes was just to fill and empty the cavity before and after the experiments respectively but were closed during the experimental campaigns. Two different concentrations of Copper nanoparticles were considered in the tests. The corresponding volume fractions were φ=1.33 % and 4.81 % (±0.02). In addition, tests were also performed with pure water (φ=0%). Thermal conductivity of these three fluids (two Water-Copper nanofluids plus pure water) was measured with the TPS method. The water-glycol mixture generated by the thermostatic bath flowed into the double thickness outer wall of the cavity through the tubes indicated with number 4 in Fig. 2(b) and (c). This flow kept the enclosure’s wall at Fig. 2(b). Photograph of the tested assembly. Fig. 2(c). Sketch of the tested assembly. F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 7 the desired cold temperature Tc within ±0.1 K. The antenna was powered by the wiring (5) connected to the stabilized power supply. Thermocouple cables (number 6) were connected to the data acquisition unit. Thermal conditions of the system were measured by means of 0.05 mm diameter K-type thermocouples calibrated at ±0.1 K by means of the calibrating thermometer. Measurements were performed at intervals of 0.05 s until the steady state was reached. This steady state was assumed to be hold when the temperature variation was less than 0.5%. The cold temperature Tc was measured at both the inlet and outlet lines of the refrigerant fluid, as well as at another station on the internal surface of the cavity. Their values differed by less than 0.2 K when the fluid flow was adjusted correctly. The surface temperature of the antenna was measured at twelve points evenly distributed on the cylinder’s lateral area. The temperature Th considered in this experimental approach was the arithmetic average of the measured surface temperatures. The temperature of the cavity’s base was measured at 4 points distributed uniformly on the internal surface of the base and at other 4 points located on its opposite surface (the external face). This allowed for the determination (using the linearized Fourier law) of the Fig. 3. Evolution of ΔT=Th-Tc versus RaL for some (λ∗,φ)combinations. F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 8 conduction heat transfer passing through the insulating plate. Tests based on the most unfavourable configuration (the one with the highest measured heat flux Q) showed that the conductive losses associated to the insulating plate were very low, of about 0.02Q. Since the radiative heat flux is zero in this experimental setup, the heat flux generated by the antenna q was considered to be 0.98Q, measured with a relative uncertainty of Δq/q=2.5%. The Rayleigh number was defined as: RaL=(β ρ μ λa)w gL4q(9) where a is the thermal diffusivity. With this definition, the relative uncertainty of the Rayleigh number was determined using a maximum relative uncertainty of 0.5% for all thermophysical characteristics of the base fluid (water) and for the distance L . The Fig. 4. Evolution of the difference δ= ΔTca −ΔTm versus RaL for some (λ∗,φ)combinations. F. Sastre et al. Case Studies in Thermal Engineering 32 (2022) 101869 9 maximum value that was obtained was ΔRa/Ra ∼7%. Several values of the Rayleigh number were tested in the range from 3.43x105 up to 5.08x107 (covering about two orders of magnitude). 3. Numerical approach The numerical approach of the considered problem is based on the governing equations presented in several documents such as the work by Patankar [40] and Bejan [41]. The computation procedure adopted here is the same as that of the recent study by Martin et al. [42] dealing with the numerical simulation of a similar problem, where the reader could consult the details of the algorithm. Then, to lighten this manuscript, only the elements necessary for its understanding are presented here. The computational domain was discretized with 553,523 elements of various shapes with a refinement on the lateral surface of the antenna. This operation allowed for the precise determination of the thermal gradients field at the interface of the antenna, and the corresponding local temperatures. Solution of the governing system was obtained by means of a home-made software based on the control volume method associated with the SIMPLE algorithm. The entire computational domain, including the antenna, was initially assumed to be at the lower Tc temperature. During the numerical convergence process, the thermal gradient was set to zero at the horizontal base of the configuration, while the external cavity was maintained at isothermal temperature Tc. A constant heat flux q was generated by the antenna, and the no-slip condition was imposed on the external face of the antenna and internal face of the enclosure. The average temperature of the antenna Th was obtained by weighting the local elements temperatures Ti with the corresponding surfaces Si: Th=1 Sh∮TidSi(10) These calculations were carried out with the nanofluid properties obtained after the Maxwell and Brinkman models, Eq. (1)–(5). 4. Experimental results and comparison between the two approaches: experimental and numerical Results of the ΔT=Th−Tc measurements versus RaL accompanied by their uncertainty are presented in Fig. 3 for some representative (λ∗,φ)combinations. The RaL uncertainties are, intentionally, not represented given the chosen logarithmic scale. The next step was, first, to compute a number of cases in the space of parameters, and, second, to compare the results obtained to those obtained experimentally. This comparison was performed in terms of the parameter δ=ΔTca −ΔTm , where ΔTca is the calculated ΔT, and ΔTm is the measured ΔT. The results obtained are presented in Fig. 4. In the case of cooling with pure water and without porous material (λ∗=0,φ=0), the measured values ΔTm are almost systematically greater than the calculated ones ΔTca, with a difference varying between 0.5 and 3.5 K. However, the measurements are lower for all the configurations affected by the nanofluid (φ∕= 0). The measurement-calculation deviations vary between 1 and 5.5 K. The highest are observed for the highest concentrations of nanoparticles (φ=4.81%), for all the values of the λ∗ratio. These results are acceptable and provide and additional validation of the numerical model. The practical outcome of all these results is the generation of a correlation for ΔT as function of the four governing parameters of the problem; namely: λw/λnf , φ, λ*, and RaL. The correlation is as follows: ΔT =3.532x10−4(λw λnf )[k(φ)m(λ*)]−1Ra0.683 L(11.a) where: k(φ) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1for φ =0(pure water) 1.45φ0.03Ra−0.012 Lfor 1% ≤φ≤5% (11.b) m(λ*) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ 1for λ*=0 10.3(λ*)−0.31Ra−1+0.86(λ*)0.03 Lfor 4≤λ*≤41.2 (11.c) λw λnf =λCu +2λw+φ(λw−λCu) λCu +2λw−2φ(λw−λCu)(11.d) Correlation (11.a) for ΔT exhibits dependence on four parameters: λw/λnf , φ, λ*, andRaL. The first two parameters, λw/λnf and φ, are linked via relations (11.b) and (11.d). Assuming that the term Ra−0.012 L adds up to the Ra0.683 L term in correlation (11.a), changing φ from 0 to 0.01 and to 0.05 decreases ΔT by a factor of 23% and 35% respectively. On the other hand, modifying λ* from 0 to 4 and to 41.2 decreases ΔT by a factor of 20% and 40% respectively (for a typical RaL of 10 7 ). This suggests that, from the physics point of view, the influence of the base fluid (nanofluid or not), and the presence (or not) of the porous matrix have a similar influence on the efficiency of the proposed thermal control system. In a sense, this could be expected because the presence of both effects has the practical outcome F. Sastre et al.