Traditional incandescent, fluorescent or halogen lamps are currently being replaced by LEDs due to their energy saving, relatively low price, high operational reliability with a long lifetime of 50,000 h or more vs. 10,000 h for incandescent lamps and a wide range of color temperatures 4500-12,000 K [2]. It is estimated that energy savings resulting from the replacement of traditional lighting with efficient LED on a global scale within 1 year may amount to 1000 TWh, which is equivalent to a reduction of greenhouse gas emissions by about 200 million tons [3]. For this reason, LEDs are eagerly used to illuminate streets, squares, stadiums or parks, in households as cheap indoor lighting, in horticulture to stimulate plant growth and influence their desired characteristics through the selection of light color and duration, in the automotive industry, aerospace, military and many other applications. However, it should be noted that only 20-30% of the total LED energy is total radiant energy, and the rest is converted into heat in nonradiative Shockley-Read-Hall or Auger recombination process between energy carriers occurring in active region of a diode as a result of transfer their excess energy to the semiconductor lattice leading to self-heating of the junction [4]. In the absence of a tailored cooling system, the temperature of the p-n junction can rise above 120 $℃$, damaging the LED [5]. It is well known that an increase in the junction temperature Tj of the LED directly reduces its lifetime (the time after which the light output or the lamp lumen maintenance factor reaches 70% of that initial output), lighting power and photometric flux, with Sökmen et al. [6] found that the percentage decrease in LED photometry in the junction temperature range (25-150) $℃$ is 10% for every 25$℃$ increase in Tj. The decrease in luminous flux and associated luminous efficacy with increasing temperature Tj of the LED is due to a decrease in the probability of carrier recombination in the active region and, in proportion to the increase in Tj, an increase in the rate of non-radiative recombination [7]. Narendran and Gu [8] investigated several white LEDs from the same manufacturer which were subjected to life tests at different ambient temperatures. Taking into account exponentially decays of device lifetime with the temperature increases they estimated the lifetime decrease from about 50,000 h to 9000 h when the device temperature at T-point (cathode side) increased from 38 $℃$ to 58 $℃.$ It follows from the above considerations that, in order to maintain the performance of LEDs over the long term, it is necessary to keep the junction temperature relatively low. In engineering practice, two types of cooling systems for electronic components are used: passive or active cooling. Each of these methods has its own advantages and drawbacks. It should be noted, however, that although active cooling systems are more efficient than passive systems, they require an external energy source to operate, which makes them more unreliable. Unlike active cooling systems for thermal energy management, passive technology based on latent heat thermal energy storage (LHTES) during the reversible melting/crystallization processes occurring in phase change materials (PCM) is more reliable and cheaper. Thermal energy (TE) can be stored effectively at high volumetric density in the form of latent heat unlike other forms of storage such as sensible heat (TE is stored by changing the temperature of the medium) or thermochemical heat (TE is absorbed or released by breaking and reforming molecular bonds in a completely reversible reaction) [9]. Commercial paraffin waxes which are cheaper than pure paraffins, have a great potential to become a good PCM candidate for LHTES due to their high volumetric thermal energy storage density, non-toxicity, good thermal and chemical stability, little or no supercooling, lack of phase separation, good self-nucleating properties on freezing and reasonable price. Paraffin waxes which are mixture (more than 75%) of heavy saturated hydrocarbons ($C_n{H}_{2n+2},20\le n\le 40)$ with mostly iso-alkanes, cyclo-alkanes and alkyl benzene [10] have a moderate latent heat of fusion (ΔH about 200 J⋅g^-1), useful melting temperature range from sub-zero to above 100 $℃$ [11] but their main drawback is low thermal conductivity (k about 0.2 Wm^-1 K^-1) [12] which influences the extension of the charging / discharging time of the heat storage systems in the processes of melting / solidification waxes. Low thermal conductivity of paraffin waxes can be enhanced using different techniques such as addition of nanoparticles, nanopowders or nanowires (carbon nanotubes, metals, oxide or carbide ceramics), by addition of expanded graphite, high thermal conductivity metallic foams (Cu, Ni, Al) or by encapsulation with extended pins or fins of different shapes to increase surface of heat transfer [13]. The research on the influence of various additives on the improvement of thermal conductivity of composites containing paraffin as PCM material was carried out both experimentally and numerically. Zhang et al. used non-equilibrium molecular dynamics simulations of paraffin/EVA/graphene nanocomposites as phase change materials [14] and revealed that the nanocomposite with the addition of 0.7 wt% graphene had the highest value of effective thermal conductivity equals 0.4331 Wm^-1K^-1 at 313 K when changing of graphene content from 0 to 7.0 wt%. Additives used to increase the effective thermal conductivity k of paraffin include, for example: Multi-Walled Carbon Nanotubes (MWCNT) and activated carbon by a dispersion technique (experimentally confirmed by Sahan et al. [15] increase in k-value by 34% -39%), expanded graphite (EG) and nano-metals particles (Cu, Al, Ni, Fe) giving the best result for paraffin-EG(11%)- Cu(1.9%) composite (experimentally confirmed by Ma et al. [16] increase in k-value from 0.216 Wm^-1K^-1 for pure paraffin to 3.825 Wm^-1K^-1 for the composite at 30 $℃$). It should be added, however, that obtaining such a large improvement in thermal conductivity of the composite is associated only with very little decreases of phase change enthalpy and phase change temperature. Khan Z. and Khan Z.A. [17] used 3D computational models to optimize LHS system including paraffin, graphene nano-platelets (GNP) and longitudinal, circular and wire-wound fins as extended surfaces in vertical shell-and-tube configurations. They found that melt front movement of PCM, natural convection and heat transfer performance significantly depend on geometrical orientation of extended surfaces and volume concentration of GNP. The results of numerical simulations showed a 23-fold reduction in the melting time of 1% GNP doped paraffin (optimal amount of GNP in the range of 1 - 5%) for wire-wound fins configurations. Hosseinizadeh et al. [18] studied both experimentally and numerically effects of power levels, fin geometry (height, thickness) and number of fins on thermal performance of PCM-based heat sink. The authors concluded that by reducing the distance between the fins and increasing their height the melting period is reduced and the melting onset time of PCM is delayed while an increase in fin thickness had a slight contribution in enhancement of thermal performance. When approaching the development of a PCM-based heat sink with fins, it is useful to keep in mind several guidelines given by Hua et al. [19] gathered from literature reports. These observations relate to the shape of the fins, their thickness, the way they are arranged, the volume fractions of the fins and the PCM relative to the total volume of the heat sink. It follows that a fin volume fraction of 9% best improves heat transfer between the heat sink and the surroundings, which was confirmed experimentally by Baby and Balaji [20]. In case of PCM volume fraction, 90%, is usually chosen. The fin arrangement (alternating or linear) should be chosen depending on whether the heat sink contains PCM or not. For a heat sink without PCM, a staggered arrangement is preferred regardless of fin shape [21]. However, there is little work in the available literature on the effect of silver nanoparticles on the effective heat transfer enhancement of paraffin waxes. Kalidasan et al. [22] studied the effect of addition of graphene-silver (Gr:Ag) nanopowder for enhancement thermal energy storage of organic paraffin RT50 for effective utilization of solar energy. It was found that the addition of 1.0 wt.% Gr:Ag increased the effective thermal conductivity by 53.77% (from 0.212 to 0.326 Wm^-1K^-1) and only slightly reduced the latent heat of fusion of RT50 from 157.5 (pure RT50) to 157.3 J⋅g^-1. It is also difficult to find papers in which the authors have investigated the effect of nano-additives with a weight percentage greater than 1% on the enhancement of heat transfer of paraffin waxes. The present work fits into this niche and, in addition, the effect of MWCNTs and silver nanowires on the thermal properties of commercially available and relatively cheap LTP ST paraffin was assessed.

The paraffin waxes LTP 56/20, LUXOLINA, LUXOLINA-ST and LTP ST were supplied by the national company POLWAX S.A., based in 38-200 Jasło, Poland. The materials were derived from crude oil processing (LTP 56/20, stearin 0.5%), contact refining of slack waxes (LUXOLINA, stearin 2.5%), composition of refined paraffin hydrocarbons with stearic acid (LUXOLINA-ST, oil<4.0%, stearin 10%), composition of paraffins with stearic acid(LTP ST, oil < 0.75%, stearin 30%). The density of the tested paraffins at 20.0 $℃$, determined by the double weighing method (in air and in water) using a RADWAG X/60/220 analytical balance (RADWAG, 26-600 Radom, Poland) with a readability of 0.01 / 0.1 mg, were: 890, 830, 870 and 930 kg⋅m^-3, respectively [1]. Multi-walled carbon nanotubes (MWCNT) with an outer diameter of 5÷20 nm, length 1÷25 μm and wall number 2÷15 [23] were purchased from SMART NANOTECHNOLOGIES (32-566 Alwernia, Poland). The second nanomaterial was silver nanowires (SNW) with an average diameter of 50 nm and a length 5÷50 μm [24], purchased from the 3D NANO company (30-702 Kraków, Poland). Literature reports indicate that the density, specific heat and thermal conductivity of MWNCTs at RT are ρ=2100 kg⋅m^-3, C_p=550 J⋅kg^-1K^-1 and k=2000 Wm^-1K^-1, respectively [25].

Based on the previously performed TG/DTG/DTA thermogravimetric and DSC microcalorimetric studies of the above-mentioned paraffins, the results of which are presented in [Table 1, Table 2 and Table 3], LTP ST paraffin was selected for further research as a phase transformation material for the construction of a passive cooling system for LED panels due to its (melting range (44.5 - 55.4) ℃, high latent heat of fusion ΔH = 218.8 J⋅g^-1, high specific heat Cp = 2.11 J⋅kg^-1K^-1 and thermal conductivity k = 0.233 Wm^-1K^-1 at 0 ℃).

In order to carry out heat transfer studies of the passive cooling system and to benchmark the temperature characteristics obtained, three different versions of the heat sinks shown in Figure 1 were designed:

(a) heat sink without PCM filling - no chamber - configuration A;

(b) heat sink with PCM chamber without intra-chamber fins - configuration B;

(c) heat sink with PCM chamber with intracellular fins - configuration C

with the LED panel shown in Figure 2 under test.

The individual components of the heat sinks were made by machining on a HAAS TM-1P CNC milling machine, ensuring a high accuracy of the design geometry. The material used was PA6 aluminum alloy (PN/EN: 2017A; ISO: AlCu4MgSi(A)) with well-known thermo-physical properties [30]. Each of the designed heat sinks was tested for the cooling efficiency of the LED panel shown in Figure 2 and fixed as shown in Figure 3.

The paper presents the results of experimental studies of the thermophysical parameters of POLWAX’s commercially available LTP ST paraffin doped with multi-walled carbon nanotubes or silver nanowires with relatively high mass fraction. The results of temperature measurements at selected points of the developed versions of the LED panel cooling systems in configurations A, B and C are also presented. Based on the results obtained, it was concluded that:

The experimental results of thermophysical parameters of pure LTP ST paraffin and doped with MWCNT or SNW presented in this work can be used in the process of numerical modelling of heat transfer with phase transitions of the first kind. The numerical simulations results obtained in this way can be validated against the temperature measurements presented in this paper using the developed heat sinks versions.