Doped CeO2/water nanofluids analyzed the performance of thermal conductivity and heat transfer: An experimental and theoretical investigations

A combined experimental and theoretical study on thermal conductivity, heat transfer specific heat, and electronic properties has been done for doped CeO2/water nanofluid. First, the sol-gel method was implemented for the synthesis of doped CeO2 nanoparticles and then a mixture of nanoparticles with different concentrations of nanofluid. X-ray diffraction and SEM analysis confirm the structural phase purity and homogeneous mixing of nanofluids. Experimental thermal conductivity and specific heat of pure and 4f-doped CeO2 were estimated and found very close to our theoretical calculations. Experimental investigations have been carried out for the measurement of heat transfer using pure and doped CeO2/water nanofluid as the coolant. The experiments were aimed at determining the heat transfer and other thermal properties with different concentrations and with various fluid with Reynolds number 2500 and 3500. The heat transfer coefficient of nanofluids increases not only with an increase in the volume flow rate of the hot water but also increases with increase in the atomic number of dopant elements in CeO2. Electronic states show variation in band gap with doping which may also play an important role in the improvement of solar collectors. It is clear from experimental and theoretical findings that the thermal and electronic properties depend on number of valance electrons. Hence doping of 4f-element in CeO2 plays a vital role to increase the thermal conductivity and tuning of electronic properties leads to many applications in thermal sensors and solar cell-based industries.


Introduction
4][15][16] Thermal conductivity is a function of the thermodynamic state of a material, and it reflects the processes that occur with the energy carriers in the system, which are mainly electrons and phonons in a polycrystalline system.2][23][24][25] Theoretical calculations, such as Boltzmann transport equation (BTE) calculations, are used by many research groups to determine the thermal conductivity of crystalline solids, where phonons are associated with atomic vibrations.Thermal conductivity is a measure of a material's ability to conduct heat.It is defined as the amount of heat that flows through a unit area of a material per unit time, per unit temperature gradient.When high thermal conductivity nanoparticles are added to a fluid, they can enhance the thermal conductivity of the fluid.This is because the nanoparticles have a higher surface area-to-volume ratio compared to larger particles, which allows for more efficient transfer of thermal energy between the particles and the fluid.This can be particularly useful in various applications such as in cooling systems, heat exchangers, and electronic devices where heat dissipation is critical.These calculations can provide insight into the mechanisms of phonon transport and can help researchers design materials with specific thermal properties.
Oxygen vacancy can have a significant impact on the properties of rare earth doped CeO 2 , and many researchers have investigated the effects of doping and vacancy in semiconducting oxides such as CeO 2 .
Recent studies have suggested that the development of stable defects on the surface of CeO 2 depends on its charge states, and doping in ceria can show different formation energy in different environments.Therefore, a comprehensive understanding of the influence of doping on the resulting CeO 2 materials requires a detailed experimental and theoretical analysis.Experimental techniques, such as X-ray diffraction, scanning electron microscopy, and transmission electron microscopy, can be used to investigate the structural and morphological changes in doped CeO 2 .Kanti et al. 19,26,27 conducted an experimental study to estimate the heat transfer coefficient and friction factor of fly ash (14.5 nm)/water nanofluid with varying concentrations (0.5-2.0 vol%) flowing in a horizontal copper tube subjected to uniform heat flux for a range of Reynolds numbers (7000-45,000).They observed the highest augmentation in Nusselt number and pressure drop to be 67.4% and 11.9%, respectively, for an inlet fluid temperature of 60°C and a nanofluid concentration of 2%.In addition, Kanti et al. 17,28,29 conducted a numerical study to determine the heat transfer coefficient of fly ash and fly ash-Cu hybrid nanofluid flowing in a pipe subjected to constant heat flux under turbulent flow.The study highlights the potential for using fly ash and fly ash-Cu hybrid nanofluids to improve heat transfer in various industrial applications.Overall, Kanti et al.'s studies demonstrate the potential for using fly ash and fly ash-Cu hybrid nanofluids to improve heat transfer in various industrial applications, with implications for improving energy efficiency and reducing costs. 17,27,28n the study by Shanbedi et al., 30,31 they investigated the effect of non-covalently functionalized carbon nanotubes (CNTs)-based water nanofluids on heat transfer coefficient and pressure drop in the laminar flow.The results of the study showed that the addition of non-covalently functionalized CNTsbased water nanofluids improved the heat transfer coefficient compared to pure water.The statement you provided suggests that Heris et al. 15,[30][31][32][33] conducted a study on the heat transfer properties of turbine oil-based nanofluids inside a circular tube.The study likely involved measuring various heat transfer parameters such as heat transfer coefficient, [34][35][36] pressure drop, and thermal conductivity of the nanofluid in the circular tube.The statement you provided suggests that the study conducted by Heris et al. 13,15,30,33 found that the addition of TiO 2 nanoparticles to turbine oil improved its heat transfer properties.Specifically, the study found that the heat transfer coefficient and pressure drop of the turbine oil increased, which indicates that the oil was more efficient at transferring heat.Additionally, the study concluded that the overall quality of the turbine oil improved with the addition of TiO 2 nanoparticles. 33,37][40][41] Cerium (IV) oxide, also known as ceria, is a versatile material with unique properties that make it useful for a variety of applications, such as catalysis, automobile exhaust catalysts, and solid oxide fuel cells.To optimize its performance in these applications, researchers often use doping or manipulate the presence of defects, such as oxygen vacancies and Ce 3 + ions.To understand the electronic properties of ceria and the effects of doping, theoretical approaches are used to calculate the band structure, which describes how electrons move within the material.Many experimental and theoretical studies [42][43][44][45] have been conducted to investigate the influence of doping on the properties of semiconducting oxides, 46,47 including ceria.In the early stages of research, semi-empirical tight-binding approximations were used to calculate thermal conductivity, electronic band structures, charge densities, and the density of states. 48resent study reveals the combined experimental and theoretical study on the thermal conductivity, heat transfer specific heat, and electronic properties of doped CeO 2 /water nanofluid.The study first synthesized doped CeO 2 nanoparticles using the solgel method, followed by mixing them with water to create nanofluid with different concentrations.The experimental thermal conductivity and specific heat of pure and 4f-doped CeO 2 were estimated and found to be close to theoretical calculations.The study then investigated the heat transfer and other thermal properties of the nanofluid at different concentrations and fluid flow rates.The results showed that the heat transfer coefficient of the nanofluids increases with an increase in the volume flow rate of hot water and also with an increase in the atomic number of dopant elements in CeO 2 .The study also found that doping of 4f-element in CeO 2 plays a vital role in increasing the thermal conductivity and tuning of electronic properties, which could lead to various applications in thermal sensors and solar cell-based industries.Overall, the findings suggest that doping with 4f-element in CeO 2 can enhance the thermal and electronic properties, potentially leading to a wide range of industrial applications.

Sample preparation
The Ce 1-x M x O 2 (M = 4f-elements, with x = 0 and 0.06) nanoparticles have been synthesized by sol-gel method.Firstly, cerium nitrate hexahydrate (Ce (NO 3 ) 3 .6H 2 O) dissolved in distilled de-ionized water.Lanthanide carbonates dissolved in dilute HNO 3 by heating at 70°C.Then mix both the solutions and stirred for 2 h.For making chelating agent citric acid and glycerol mixed together.Finally, the solution of precursor gets cooled at room temperature with following reaction: Nanoparticles of pure and doped CeO 2 were dried at 250°C for 10 min and sintered with different temperatures that is, 250°C, 450°C, and 550°C for 1 h each.
Earlier studies shows that pure phase stabilizes at less than 600°C. 6,25,49Schematic of synthesis process of pure and 4f-doped CeO 2 nanofluid are shown in Figure 1.
For structural characterization of Ce 1-x Mn x O 2 (M = lanthanide elements with x = 0 and 0.06) nanoparticles studied by XRD using a Bruker X-ray Diffractometer.Field Emission Scanning Electron Microscope (FESEM, JSM-7600F) have been used for Surface morphology. 50Nanofluid of 4f-doped CeO 2 nanoparticles has been prepared after adding different volume concentration of water.The desired volume concentrations used in this study are 0.5, 1.0, 1.5 vol.%.

Ultra-sonification
Ultrasonic vibrator was used to split the accumulation of the nanoparticles into nanofluid.Ultrasonication, also known as ultrasound-assisted homogenization, is a technique that utilizes high-frequency sound waves above 20 kHz to generate mechanical vibrations in a liquid medium. 51,52These mechanical vibrations create cavitation bubbles, which collapse and generate intense local heating and pressure gradients that cause the breakdown of larger particles into smaller, more uniform-sized particles.Ultrasonication is commonly used in various fields such as nanotechnology, biotechnology, and food processing for particle size reduction, emulsification, dispersion, and extraction. 53It is a powerful and efficient technique that can be used to process a wide range of materials, including solids, liquids, and gases.In the context of nanofluid, ultrasonication is used to disperse and de-agglomerate nanoparticles in the base fluid to improve their stability, enhance their properties, and facilitate their use in various applications such as heat transfer, lubrication, and energy storage.The use of ultrasonication in nanofluid preparation has been shown to improve the dispersion and homogeneity of nanoparticles in the base fluid, resulting in improved performance and properties of the nanofluid.

Thermal conductivity measurement
Thermal conductivity measurement done using most commonly used and most effective method guarded hot plate (GHP). 54Based on the measured power input, the thermal conductivity (k) of the test specimen can be calculated using the following equation: where Q is the measured power input, A is the area of the hot plate, DT is the temperature difference between the hot and cold plates, and Dx is the thickness of the test specimen.This equation is based on Fourier's law of heat conduction, which states that the rate of heat transfer through a material is proportional to the temperature gradient (DT/Dx) and the cross-sectional area (A) of the material.The proportionality constant is the thermal conductivity (k) of the material. 5,13,26By measuring the power input and the temperature difference, the thermal conductivity of the material can be determined.Schematic of experimental setup of Guarded Hot Plate instrument to measures the thermal conductivity are shown in Figure 2.

Specific heat capacity and heat transfer coefficient measurement
The specific heat capacity is measured using differential scanning calorimetry. 55,56Differential Scanning Calorimetry (DSC) is a thermal analysis technique used to study the behavior of materials as a function of temperature or time.It measures the heat flow associated with a sample as it is heated, cooled, or held at a constant temperature.DSC works by measuring the difference in heat flow between a sample and a reference material as they are subjected to a controlled thermal program. 57During a DSC experiment, the sample and reference materials are placed in separate sample and reference pans and then subjected to a controlled temperature program.The temperature program typically involves heating the samples from a low temperature to a high temperature at a controlled rate.As the samples are heated, the DSC instrument measures the heat flow between the sample and reference materials as a function of temperature.DSC can provide information about the thermal properties of materials, including phase transitions, melting points, glass transition temperatures, and reaction kinetics.][57] The rate of heat transfer through convective heat transfer is determined by the properties of the fluid, the velocity of the fluid, and the temperature difference between the two locations.Convective heat transfer is important in many engineering applications, including cooling of electronic devices, air conditioning systems, and heat exchangers. 32,33,58,59The tested heat exchanger is a vertical shell-and-tube model in which the condensing water vapor flows downwards inside vertical tubes and the cooling water flows in a counter current in the outer shell.The shell side has a complex geometry with complicated flow patterns so using the Wilson plot method is suitable for determining the shell-side heat transfer coefficient.Heat transfer coefficient measurement includes two flow loops, for the cold and hot fluids (nanofluid and distilled water flow loops). 33,58,59Hot water loop comprises with an insulated hot water tank of 30 L capacity with four 2.5 kW immersion heaters.Nanofluid of all doped CeO 2 have been stored in 20 L container and recirculated using centrifugal pump.

Methods and computational details
First-principle calculations 38,39,60,61 have been performed with projected-augmented wave (PAW) potentials, 61,62 initiated with Quantum Espresso. 61,63ur present model for pure and metals doped CeO 2 have been taken with 2 3 2 3 1 super cell (48 atoms) of CeO 2 (i.e.Ce 16 O 32 ) with 7 3 7 3 1 k-meshes.Where Ce atom were replaced by a 4f-transition metal atom for cubic CeO 2 (space group Fm3m) with 6.25% of doping of transition metals (i.e.Ce 16- M M 1 O 32 ) For calculations, pure and 4f-doped CeO 2 structures were fully relaxed until the forces per atom declined to less than 0.01 eV/A 8 while energy convergence of 1 3 10 25 eV were achieved and plane wave cutoff energy of 400 eV were used. 40,42,44,45,60Our calculations also have evaluated the impact of the pseudo-potential like Local Density Approximation (LDA), 61 Perdew-Burke-Ernzerhof (PBE), 64 and Heyd-Scuseria-Ernzerhof (HSE) 65 on thermal conductivity prediction.Figure 3 shows flow chart of calculations for thermal conductivity measurement using BTE calculations. 14,66

Result and discussion
Sol-gel method has been used for deposition of nanoparticles of pure and doped CeO 2 nanoparticles and then nanofluid were prepared using different volume concentration of water.Figure 1 shows schematic of pure and 4f-doped CeO 2 nanofluid synthesis process.Lanthanides have 4f electron in its outermost orbital which may contribute to change in mechanical and electronic properties after doping in CeO 2 .SEM analysis 67 shows preparation of nanoparticles (see Figure 4(a)), while for nanofluid CeO 2 -water depicted in Figure 4(b).Uniformity of nanofluid have been checked through elemental mapping shown in Figure 5 it is clear that elemental mixing is uniform.It is clear from SEM images prepared nanoparticles of CeO 2 have been uniform even after doping [68][69][70] of 4f-electronic elements (lanthanides).Nanoparticles have size are around 700-800 nm. 67rom elemental mapping CeO 2 in Figure 5(a) to (c) represent elemental mapping of Ce, O and 4f-electron elements; interestingly shows homogeneous mixing of all nanoparticles.To see the structural stability of prepared pure and doped CeO 2 , we have done Xray diffraction analysis (see Figure 6).X-ray diffraction patterns of the pure CeO 2 with indexing of all the diffraction peaks confirms the phase purity of CeO 2 . 26,27The diffraction pattern of doped CeO 2 also plotted in Figure 5 and a clear shift in peak position  found.According to bragg's law, shift of peak position toward higher theta value concludes decrease in a lattice parameter (lattice contraction).Due to contraction in lattice parameter with doping confirms the presence of compressive strain in prepared samples.
To see the structural stability of prepared pure and doped CeO 2 , we have done X-ray diffraction analysis (see Figure 6).X-ray diffraction patterns of the pure CeO 2 with indexing of all the diffraction peaks confirms the phase purity of CeO 2 . 26,27The diffraction pattern of doped CeO 2 also plotted in Figure 6 and a clear shift in peak position found.According to bragg's law, shift of peak position toward higher theta value concludes decrease in a lattice parameter (lattice contraction).
Zeta potential is a widely used technique for investigating the stability of nanofluids. 16,17It is a measure of the electrostatic potential difference between the surface of the nanoparticle and the surrounding liquid medium.The magnitude of the zeta potential determines the degree of repulsion between particles, which influences their aggregation and sedimentation behavior.In general, a higher absolute value of zeta potential indicates greater repulsion between particles and a more stable nanofluid.A zeta potential value above 30 mV is often recommended as an indication of good stability, although this value can vary depending on the specific system and conditions. 16,17,27The Zetasizer (Malvern Instruments), is a commonly used instrument for measuring zeta potential in nanofluids. 13,16,17,27It uses dynamic light scattering (DLS) to measure the size distribution of particles in a sample, and electrophoretic light scattering (ELS) to measure the zeta potential In the present study, the stability of nanofluids was evaluated by measuring the zeta potential using the Zetasizer Nano.The measurement was repeated three times at each nanofluid concentration to ensure the reliability of the results, and an average value was reported.This is a standard procedure to obtain accurate and reproducible measurements of zeta potential.Table 1 shows the typical zeta potential of doped CeO 2 nanofluids versus 10 days later for the varied concentrations.Table 1 shows that even after 10 days of preparation, nanofluids were stable.Due to contraction in lattice parameter with doping confirms the presence of compressive strain in prepared samples.Guarded hot-plate (GHP) method has been used for the calculations of thermal conductivity of pure and doped CeO 2 .Mostly, the GHP method has been used to investigate the thermal properties of nonmetals like thermal insulated materials, ceramics, and polymers glasses in the various temperature ranges lies from 80 and 800 K. Hence keeping this in view, we have used GHP setup for thermal conductivity measurement on doped CeO 2 ceramic materials.Thermal conductivity of lanthanide doped CeO 2 shown in Figure 7(a).The maximum value of thermal conductivity has been found 3.95 W/m-k for pure CeO 2 near to room temperature and then decreases with increase in temperature.Similarly, value of thermal conductivity increases up to Gd and then decreases for higher dopant elements.
To evaluate the reliability and accuracy of the measurements, experimental system was tested with distilled water before measuring the heat transfer of nanofluids.Figure 8(a) shows variation in heat transfer coefficient with doping of 4f-elements using Reynolds number 2500 for 0.5%, 1%, and 1.5% of volume concentration.Increase in heat transfer coefficient is clearly observed with increase in atomic number of dopant element in CeO 2 nanofluid (see Figure 8(a)).Similarly, we have also performed an experiment for Reynolds number 3500 (see Figure 8(b)) and it is found that heat transfer coefficient has higher value with higher Reynolds number.Specific heat is basically inversely proportional to volume concentration, which is important to increase absorption and  heat transport capacity of CeO 2 nanofluids.Hence, we also have done specific heat measurement of all nanofluids shown in Figure 9 and it is clear that as dopant atomic number increases specific heat decreases.We have also used theoretical approach to estimate specific heat capacity, and tabulated in Table 2.It is clearly observed that value obtained from experimental investigation shows good agreement with theoretical calculations.
To further confirm the experimental values, we have performed theoretical calculations for thermal conductivity using BTE approach for all 4f-doped CeO 2 , and from our calculations it is quite interesting to see the variation of thermal conductivity which is very close to our experimental findings.First, we have taken cubic CeO 2 system with Fm3m space group for our calculations with supercell of 2 3 2 3 1(Ce 16 O 32 ), while for doping we have removed one Ce-atom from supercell and use 4f-elemnets (M = Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm Yb, and Lu).
Interestingly we have found that mechanical properties like thermal conductivity of CeO 2 increases with increase in unpaired electron of 4f orbital with doped lanthanides. 71We have calculated thermal conductivity of CeO 2 with different approximations are 4.90 (PBE), 4.99 (LDA), and 4.98 (HSE).Values obtained from HSE calculations of thermal conductivity matches with various experimental findings.Here, Gd have 7 half-filled electrons in f-orbitals which shows maximum thermal conductivity amongst all doped samples, which means that unpaired electrons are playing major role to increase thermal conductivity against paired electrons.From Table 2 shows calculated values of thermal conductivity of 4f-doped CeO 2 Nano fluid.

Calculation of formation energy of ceria with doping
The formation energies of the doped V a (a = Ce, M (M = lanthanides), and O) were calculated using the super cell approach.Here we use 48 atoms of 2 3 2 3 1 super cell with k-point mesh of 5 3 5 3 5 for doped CeO 2 calculations.The formation energy DH M q ð Þ is expressed for dopant (M) with charge state q is- Here, E tot (M q ) and E tot (bulk) are denoted as total energies of the CeO 2 super cell for with and without doping M, respectively, while, E F is denoted as Fermi energy of a given system measured from the VBM.Additionally, Dn i is the number of atoms i (i = Ce, M, and O) which is removed from the supercell to create defects.Finally, m i is the resultant chemical potential of standard elemental state, that is, m i = m 0 i + Dm i , where the reference potentials m 0 i are those of metallic  Sr, Ti, and O atoms.Since we calculated the neutral defects (q = 0), so equation ( 4) becomes; Hill 72 suggested that actual value of bulk (B) and shear (S) moduli must be a arithmetic averages of the Voigt and Reuss bulk (B V , B R ) and shear (S V , S R ) moduli (i.e.B = (B V + B R )/2 and S = (S V + S R )/2).The Young's modulus (Y) and Poisson's ratio h ð Þ can be calculated - Where

Conclusion
In present study a combined experimental and theoretical investigation has been done for thermal conductivity, heat transfer, specific heat, and electronic properties of doped CeO 2 /water nanofluids.The nanofluids were analyzed using X-ray diffraction and SEM to confirm their structural phase purity and homogeneous mixing.Experimental measurements of thermal conductivity and specific heat of pure and doped CeO 2 were conducted and found to be very close to theoretical calculations.Heat transfer coefficient of the nanofluid increased with an increase in the volume flow rate of hot water and with the atomic number of dopant elements in CeO 2 .Thermal and electronic properties of CeO 2 / water nanofluids depend on the number of valence electrons, and doping with 4f-elements plays a vital role in increasing thermal conductivity and tuning electronic properties, with potential applications in thermal sensors and solar cell-based industries.
Overall, the study highlights the potential for using doped CeO 2 /water nanofluids to improve heat transfer and electronic properties, with important implications for various industries.

Figure 1 .
Figure 1.Schematic of Sol-gel preparation method for synthesis of doped CeO 2 -water nano-fluids.

Figure 2 .
Figure 2. Experimental setup of Guarded Hot Plate instrument to measures the thermal conductivity.

Figure 3 .
Figure 3. Flow chart of calculations for thermal conductivity measurement of semiconducting oxide samples.

Figure 4 .
Figure 4. (a) Shows scanning electron microscopic images of nanoparticles of CeO 2 with 0.5% concentration and (b) nano-fluid of CeO 2 -water.

Figure 6 .
Figure 6.X-ray diffraction of pure and doped CeO 2.

Figure 7 .
Figure 7. Experimental thermal conductivity measurement of pure and doped CeO 2 (a) with the variation of temperature and (b) with the variation of volume concentration.

Figure 8 .
Figure 8. Variation of heat transfer coefficient pure and doped CeO 2 nanofluids at (a) coolant Reynolds number 2500 and (b) Reynolds number 3500.
, S v = Voigt shear modulus, S R = Reuss shear modulus, Y = Young's Modulus, h = Poisson ratio and C 11 , C 12 , C 44 represents elastic constants.Using all above equations and elastic constant 73,74 approximations we have calculated shear modulus, Young's modulus and Poisson ratio of all given samples and tabulated in Table 3. Young's modulus increases with increase 4f-electrons in doping of lanthanides.As shown in Figure 10 in pure phase of cubic CeO 2 have no extra electronic transition (only transition between Ti-3d and O-2p) were found in between maximum of valance band (MVB) and minimum of conduction band (MCB), while in case of doping of 4f-elements in CeO 2 have many possible transitions in between MVB and MCB.The reasons of getting extra possible electronic transitions are due to the presence of dopant atom in Ce 1-x M x O 2 (M = lanthanides).Dopant atoms having different number of electrons in 4f (like Pr has 3-e in 4f orbital) orbital this allows these electrons to have different possible electronic

Figure 10 .
Figure 10.Total electronic density of states of 4f-doped CeO 2 shows an extra state near fermi energy as atomic number increases.

Table 2 .
Calculated thermal conductivity and specific heat capacity of lanthanide doped ceria with 0.5% concentration of nano fluid.

Table 3 .
Formation energy and elastic constant calculations of lanthanide doped CeO 2 .