Modeling and assessment of the thermo-electrical performance of a photovoltaic-thermal (PVT) system using different nanofluids

Abstract

The proposed study aims to test the thermo-electrical, and exergy efficiency of a hybrid PVT collector cooled by pure water, copper (Cu)/water, and aluminum-oxide (Al₂O₃)/water nanofluids, respectively. A model is mathematically constructed using the energy-balance equation across all the layers of the hybrid PVT collector. For the validation of the proposed mathematical model, the outcomes of the proposed numerical model are compared with the experimental data of the literature. The impact of volume fraction (vol%) and mass flow rate (m) of the nanofluids on the PVT outcomes has been analyzed and demonstrated. The study displays a better PVT performance with Cu/water nanofluid compared to Al₂O₃/water nanofluid and pure water. Merely a 2% volume concentration of Cu nanoparticles results in a 4.98% and 5.23% improvement in the average electrical and thermal efficiencies, respectively. At a mass flow rate of 0.03 kg/s, the thermo-electrical efficiency of the PVT with Cu/water nanofluid improve by 4.45% and 2.9%, respectively, concerning the pure water. Further, the impact of several tubes and their diameter is also investigated on the thermo-electrical efficiencies of the hybrid PVT collector. The tube diameter has not any substantial effect on the performance, whereas the thermo-electrical performance significantly enhanced with the rise in the number of tubes.

Graphic abstract

Appendix

The heat transfer coefficients (HTCs) used in Eqs. (1–3)

$$H_{{{\text{pv}} \cdot {\text{Ab}}}} = \frac{{\lambda_{{{\text{ad}}}} }}{{\delta_{{{\text{ad}}}} }}\left( {1 - \frac{{D_{{{\text{out}}}} }}{W}} \right)$$

$$H_{{{\text{pv}} \cdot {\text{t}}}} = \frac{{\delta_{{{\text{pv}}}} }}{{\frac{{W^{2} }}{{8\lambda_{{{\text{pv}}}} }} + \frac{{\delta_{{{\text{ad}}}} }}{{\lambda_{{{\text{ad}}}} }} \cdot \frac{{\delta_{{{\text{pv}}}} W}}{{D_{{{\text{out}}}} }}}}$$

where δ, λ are the depth of the particular layer and thermal conductivity, respectively. D_out is the outer tube diameter.

The heat transfer coefficients (HTCs) used in Eq. (4)

$$H_{{{\text{Ab}} \cdot {\text{t}}}} = \frac{{8\lambda_{{{\text{Ab}}}} }}{{W - D_{{{\text{out}}}} }} \cdot \frac{{\delta_{{{\text{Ab}}}} }}{W}$$

$$H_{{{\text{Ab}} \cdot {\text{ins}}}} = \frac{1}{{\frac{{\delta_{{{\text{Ab}}}} }}{{\lambda_{{{\text{Ab}}}} }} + \frac{{\delta_{{{\text{ins}}}} }}{{\lambda_{{{\text{ins}}}} }}}}$$

The heat transfer coefficients (HTCs) used in Eq. (5)

$$H_{{{\text{t}} \cdot {\text{ins}}}} = \frac{{2\lambda_{{{\text{ins}}}} }}{{\delta_{{{\text{ins}}}} }}\left( {\frac{\Pi }{2} + 1} \right)\frac{{D_{{{\text{out}}}} }}{W}$$

$$H_{{{\text{t}} \cdot {\text{nf}}}} = \frac{1}{{\frac{W}{{h_{{{\text{nf}}}} \Pi D_{{{\text{in}}}} }} + \frac{W}{{\lambda_{{{\text{ad}}}} }}}}$$

where h_nf is the convective HTC represents the forced flow of nanofluid circulating in the tubes.

$$h_{{{\text{nf}}}} = \frac{{{\text{Nu}}_{{{\text{nf}}}} \lambda_{{{\text{nf}}}} }}{{D_{{{\text{in}}}} }}$$

The heat transfer coefficients (HTCs) used in Eq. (6)

$$H_{{{\text{ins}} \cdot {\text{air}}}} = \frac{1}{{\frac{{\delta_{{{\text{ins}}}} }}{{2\lambda_{{{\text{ins}}}} }} + \frac{1}{{h_{{{\text{g}}\cdot{\text{air}}}} }}}}$$

The constant used in Eq. (8)

$$C = \frac{{H_{{{\text{t}} \cdot {\text{nf}}}} \cdot W_{{\text{d}}} }}{{m_{{{\text{nf}}}} \cdot c_{p} }}$$

The constant A and B used to simply Eq. (10)

$$A = e^{{ - CL_{{\text{c}}} }}$$

$$B = \frac{1 - A}{{C \cdot L_{{\text{c}}} }}$$

The Pe, Re and Pr denotes the Peclet, Reynold and Prandtl numbers

$${\text{Pe}}_{{{\text{nf}}}} = \frac{{\rho_{{{\text{nf}}}} V_{{\text{f}}} d_{{{\text{nf}}}} c_{{{\text{pnf}}}} }}{{\lambda_{{{\text{nf}}}} }}$$

$${\text{Re}}_{{{\text{nf}}}} = \frac{{\rho_{{{\text{nf}}}} VD}}{{\upsilon_{{{\text{nf}}}} }} = \frac{4m}{{\Pi \upsilon_{{{\text{nf}}}} D}}$$

$$\Pr_{{{\text{nf}}}} = \frac{{\upsilon_{{{\text{nf}}}} c_{{p{\text{nf}}}} }}{{\lambda_{{{\text{nf}}}} }}$$

The thermophysical properties of base fluid used in mathematical modeling

$$\rho_{{{\text{water}}}} = - 0.03XT^{2} + 1.505XT + 816.781$$

$$c_{{p,{\text{water}}}} = - 0.0000463XT^{3} + 0.0552XT^{2} - 20.86XT + 6719.637$$

$$\upsilon_{{{\text{water}}}} = 0.00002414X10^{{\frac{247.8}{{T - 140}}}}$$

$$\lambda_{{{\text{water}}}} = - 0.000007843XT^{2} + 0.0062XT - 0.54$$