Thermal analysis characterisation of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: An optimal thermal application

Nomenclature

b

initial stretching rate

B γ

Biot number

B r

Brinkman number

C p

specific heat ( J kg − 1 K − 1 )

E c

Eckert number

E G

dimensional entropy ( J / K )

h f

heat transfer coefficient

κ

thermal conductivity ( Wm − 1 K − 1 )

k ⁎

absorption coefficient

N q

radiation parameter

N G

entropy generation (dimensionless)

Nu x

local Nusselt number

Pr

Prandtl number ( ν / α )

q r

radiative heat flux

q w

wall heat flux

R e

Reynolds number

S

suction/injection parameter

u 1 , u 2

velocity component ( m s − 1 )

U w

velocity of the stretching sheet

V w

vertical velocity

x , y

dimensional space coordinates ( m )

1 Introduction

Solar radiation can accomplish heat by chemical processes or generate electricity, which is known as solar energy. The huge amount of solar energy that strikes earth satisfies the world’s current and proposed energy needs by an extensive limit. This highly assigned source can fulfill all future energy demands if perfectly exploited. Solar energy is well known as a refined form of substitute energy. Increased energy has demand on the one side and the negative environmental encounter of fossil fuels on another side. Different countries deal with alternative energy origins to be a desired and practical choice for industrial and domestic use. The devaluation of organic contaminants in air and water streams regarded as one of the so-called advanced oxidation processes is one of the most important uses of this technology. To achieve the regulated absorption, reflection, or transmission of the appropriate wavelength of the solar spectrum, natural species have created intricate photonic nanostructures on numerous scales and dimensions in a hierarchical, structured manner. A bio-inspired strategy for solar energy manipulation is a powerful and promising method [1,2,3]. Energy is the most expensive component in the manufacturing of agricultural greenhouse crops in thermal climates. In addition, the upfront costs of fossil fuels and ordinary energy are rapidly rising. Solar energy has generated global interest because of the increasing consumption of finite fossil fuel supply as well as their impact on the environment. Many people at all levels of the society are unaware of the importance of solar energy [4,5]. An upgraded approximation of the interplanetary solar spectrum from 0 to 1,000 μm is recommended depending on the solar constant value. It is made by the division of the spectrum into nine bands and choosing typical (and latest) spectra for each band, as well as scaling coefficients that are appropriate [6].

Solar-powered ships are the energy generators that use the cleanest and renewable energy from the sun and convert it into thermal or electrical energy sources. There are many ways to capture solar energy. Usually, to transform solar power for domestic use, solar panel of photovoltaic systems is used. Raphael Domjan is the first person to initiate and complete the round-the-world trip with the help of solar energy within the duration of 2010–2012. He made polar solar navigation first in the Arctic Ocean in 2015. Solar Stratos was the first project created by him in the stratosphere. He has also made solar-free fall and jumped off from a solar plane first time in 2020. The planet Solar MS TURANOR was the first to use solar energy to go around the world on May 4, 2012, from Monaco in the West direction. Its engines can be charged with solar energy, and it can move non-stop for up to 72 h. Ahmed et al. [7] used nanofluids to study the cooling processes of photovoltaic thermal along with the concentrated photovoltaic thermal and other systems utilising solar energy. Khanafer and Vafai [8] presented an analysis on current advancements in nanofluids in the field of solar stills and collectors, along with storage systems of photovoltaic and thermal energy. By using different concentrations of the nanofluids, Lee et al. [9] studied working fluid to improve its capability in solar thermal systems. They analyzed the characteristics of nanofluids like heat transfer, electronic conductivity, and absorbance of UV rays. Olia et al. [10] used nanofluids as working fluids to check the impacts of various factors, including nanoparticles size and volumetric fraction along with working fluid type, on the behaviour of parabolic trough collectors. Vijayan and Rajasekaran [11] used a generation tank of hot water to examine the performance of nanofluids consisting of deionised water and aluminum oxide in the PTSC system used as thermal transfer fluids. Wole-Osho et al. [12] investigated the effect of various nanoparticles to determine the efficiency of solar collectors. Jamshed et al. [13] investigated the entropy production of non-Newtonian Maxwell single-walled and multi-walled carbon nanotube-engine oil nanofluids flowing in PTSC as an operating fluid inside SPS in the existence of Darcy–Forchheimer and Cattaneo–Christov models. They reached to multi-walled carbon nanotubes more efficacy of thermal exchange than single-walled carbon nanotubes. Bayones et al. [14] analyzed the solution by applying the finite element method on MoS₂-Cu/sodium alginate hybrid nanofluid flowing in PTSC at SPS implementation with the suction (injection) and slippery velocity. They concluded that the permeability reduces the heat transfer and boosts the frictional force.

Hybrid nanofluid is a type of nanofluid that is a good conductor of heat transfer compared to conventional fluids [15]. The composition of hybrid nanoparticles is useful for preparing these fluids. Due to enhanced thermal characteristics, these fluids are generally used in solar energy, ventilation, heat pipes, manufacturing, electronic cooling, automotive industry, and air conditioning applications [16]. Time-independent flow and thermal conductivity of the hybrid nanofluid passing through a stretchable have been studied by ref. [17]. To determine the boundary value, a problem solver (bvp4c) with Matlab software has been employed. Huang et al. [18] experimentally analyzed various impacts of a hybrid nanofluid mixture, including thermal conductivity and fall in pressure consisting of alumina nanoparticles and multiwalled carbon nanotubes (MWCNTs) in a chevron corrugated plate heat exchanger. It has been found in this study that the fall of temperature is less than Al₂O₃/water nanofluid and greater than water.

Acharya [19] proposed flow models with heat transfer features for hybrid nanofluids having an impact on nonlinear solar radiation for special solar thermal equipment. The hybrid solution reveals magnificent augmentation in heat transport for suction. The effects are being reduced by imposing the injections; a reduction in the spoil rate is observed for hybrid nanocomposite. Kumar et al. [20] proposed an analysis that involves the stability of heat transfer increment because of the impact of variation in valuable characteristics of fluids with thermal radiation ability along with the suspended hybrid nanofluids. The transfer of heat and properties of hybrid nanofluids in three dimensions under the constraint of turbulent through a parabolic trough solar collector (PTC) receiver was proposed [21]. The study of hybrid nanofluid used in solar energy absorption and tries to stoke the thermal energy was presented by ref. [22]. Recent additions considering fluids flow with heat and mass transfer in various physical situations are given by refs. [23,24,25,26,27,28,29,30,31,32,33,34,35].

Oldroyd-B fluid is a particular non-Newtonian fluid whose transfer behaviour could not be accurately described as the general relationship between share rate and shear pressure in the actual shear flow. Recently, numerous researchers have considered the various issues related to this fluid. The stable 3-D Oldroyd-B nanofluid flow on a two-way stretch surface evaluated the effects of heat production. Applicable similarity conversions are utilised for the minimisation of governing fractional differential equations by combining nonlinear general differential equations [36]. Properties of an Oldroyd-B nanofluid due to axis uniform rotating disk are examined by using the characteristics of the vertically appropriate magnetic field. The movement of fluid on the disk’s surface is caused by turning along with the radically stretching of the disk [37,38]. The unsteady boundary surface flow and heat transfer of the incompressible Oldroyd-B nanofluid thin layer have been analyzed through the stretching sheet. The temperature and the velocity of the stretching sheet vary with sheet and time [39]. The association instability onset in a compact medium layer that is saturated with Oldroyd-B viscoelastic nanofluid has been examined by integrating the results of Brownian dispersion and thermophoresis. As a result, the eigenvalue problems are determined numerically with the help of the Galerkin method [40].

Many utilisations of non-Newtonian nanofluids in solar energy, industry, and engineering have led us to develop a complete model for the unstable 3D flow of the Oldroyd-B nanoparticles [41]. Three distinct partial models of the Oldroyd-B fluid are examined. The triple fractional analysis is presented to evaluate the resultant three models established by three partial operators [42]. Mathematical symmetry between the coaxial cylinders of the 1D partial Oldroyd-B nanofluid flow has been found for heat transfer with no pressure gradient [43].

A modern illustration of the postulate and utilisations of the numerous entropy enhancement fundamentals are specified. These principles involve Jaynes’ maximum entropy principle (MaxEnt), generalised maximum entropy, Kullback’s minimum cross-entropy principle (MinxEnt), minimum cross-entropy principles, minimum interdependence principle, inverse entropy optimisation principles, mini-max entropy principle, and definitely, dual entropy upsurge principles. The relationship between thermodynamic entropy and information-theoretic entropy is uniquely recollected in the background of more ordinary relations that managed among what are originated as essential and trivial entropies. References [44–53] have more detailed information.

Hybrid nanofluids show various benefits in contrast with the traditional forms by their reformed effects. A summary of solar energy systems is displayed, and then, the utilisation of hybrid nanofluids in numerous solar technologies, mainly solar thermal, is presented. Relation between nanofluid structure and traditional structure is presented to attain a complete understanding of the improvement of nanofluids. It follows from the previous discussion that the most important way to maximize the utilization of solar energy is to enhance the thermal properties of the convective fluid. Hybrid nanofluids, the expulsion of nanoparticle or nanocomposite brighten compound designs in conventional fluids, direct the investigation of the research in the current years due to the potential interdependent effects between particles. However, there are only few studies on efficient experimental analysis. The significant flaw of typical solar depends on its deficient production. In this study, enhancement of still solar performance using two-hybrid nanofluids is investigated. Using two conventional nanofluids and hot water was also exploited to discuss the development of solar energy. Hybrid nanofluids, conventional nanofluids, or hot water were connected to the solar system with heat conversation fixed at the base of the basin of the solar system [54,55,56,57]. Following that, plenty of other studies appears, each focusing on a different element of the problem [58,59,60,61,62,63,64,65,66,67,68,69,70], to name a few.

To select and evaluate the sufficient formation of solar curves, eight distinct models that are semi-theoretical are applied to the data of the experiment and compared with the help of determination coefficients that were forecasted by non-linear regression analysis by using the statistical computer program [71]. There is a tendency to describe the recent items immediately but not in the detained reconstruction. There is also a tendency to remember the first temporarily isolated objects. There is a priority for the forward recall order along with output order preferences, which minimize the path length during retrieval [72]. As a result of increasing the demand for global energy and increasing the short supply of conventional or produced crude oils by easy way, the most incredible attention is being rewarded to the exploitation of extra-heavy and unconventional heavy oils [73]. The thermophysical characteristics of nanofluids are necessary to forecast the behaviour of heat transfer. Numerical results, which are based on three oxide nanofluids and their hybrids, have been suggested. All the thermophysical effects of nanofluids are increasing with the inclusion of nanoparticles, and these effects also increase the thermal conductivity by more than 12%. By using theoretical results, the variability in viscosity evaluation and significant experimental correlations were found [74]. The advantages of using solar-powered ships/boats are eco-friendly, worth investing in, prevents noise pollution, long-time charging, replaces the dead boat battery, charging your devices, comparatively less environmental effect, extremely reliable, and connected on more than one level (Figure 1).

Figure 1

Parabolic trough solar collector.

This study examines the heat transfer analysis of the solar water pump using mono/hybrid nanofluids (i.e., Ag-EO and Ag-Fe₃O₄/EG) preceding a parabolic trough solar collector (PTSC) positioned innards a solar-powered ship. Considerations have been made on solar radiation as a heat source. Performance of thermal transfer of ship is analyzed for a circumstance of diverse influences such as thermal radiative flowing, viscous dissipation, and heat source. Entropy production scrutiny has been carried out in the case of Oldroyd-B hybrid nanofluid. The modeled equations in terms of momentum and energy have been handled using an entrenched numerical method, namely, the Keller box method (KBM). The effects of various diverse parameters about shear stress, velocity, temperature profiles, and coefficient of surface drag, including Nusselt number, are deliberated briefly as well as displayed in terms of figures and tables.

2 Present theoretical experiment

Efficiency of a solar-powered ship can be enhanced with the help of hybrid nanofluid flow on PTSC, and a theoretical experiment has been proposed. Various parts of SPS contain PTSC on them. The aim of the present analysis is presented in this section. PVC cell surfaces are replaced with PTSC in the presented model. PTSC equipment is cylindrical rather than absolute PVC surfaces. So more solar energy is absorbed on PTSC because of its huge surface area. Solar energy is cost-effective, and hence, solar-powered ships can be manufactured and maintained on a low budget. The continuous increase in oil prices it leads researchers to use solar energy, especially in the sea ship industry. According to the analysis, amplification in heat transfer and energy is obtained when hybrid nano-solid particles are combined into fluid flow on PTSC under the effects of viscous dissipation, thermal radiation, and thermal conduction. No pollution is created in an atmosphere with solar aircraft, as they are environment friendly.

3 Mathematical formulation

A mathematical model represents the moving flat horizontal surface (Figure 1) having a non-uniform stretching velocity:

4 The solution for the problem

Equations of boundary value problem (2)–(5) are converted via similarity technique that changes governing PDEs in ODEs. Stream functions ψ are introduced as follows:

with similarity variables [77].

in governing equations (2)–(5). The following relation is obtained:

with

where ϕ ′ i s with a ≤ i ≤ e in equations (11–12) represent thermophysical properties about Oldroyd-B nanofluid as mentioned earlier:

As equation (2) satisfied identically, the notation (′) is expressing derivatives according to Ψ ⁎ . Here, χ 1 = b ϱ 1 (Deborah number-I), χ 1 = b ϱ 2 (Deborah number-II) defined along with M = σ f B o 2 c ρ f (magnetic field) parameter, Pr = ν f α f (Prandtl number), α f = κ f ( ρ C p ) f (thermal diffusivity), S = − V w 1 ν f b (mass transfer), N q = 16 3 σ ⁎ Θ ∞ 3 κ ⁎ ν f ( ρ C p ) f (thermal radiation), E c = U w 2 ( C p ) f ( Θ w − Θ ∞ ) (Eckert number) Λ q = b ν f N L ( velocity slip ) , and B γ = h f k 0 ν f b (Biot number) parameters.

5 Numerical implementation

Non-linear ordinary differential equations (9)–(11) are tackled along with endpoint condition (2.12) via implementation of Keller box scheme [88] and algebraic software Matlab for all involved parametric values. The Keller box process is presented as a step-by-step in the flow chart in Figure 2.

Figure 2

Flow chart of Keller box scheme.

5.2 Domain discretisation and difference equations

Following grid points are employed for divisions of the domain [0,1] with the help of regular mesh (Figure 3):

ξ 0 ⁎ = 0 , ξ j ⁎ = ξ j − 1 ⁎ + Δ x j , j = 0 , 1 , 2 , 3 … , J , ξ J ⁎ = 1 ,

where, Δ x j is step-size. First-order ODEs (17–24) are further solved with the central difference method at the midpoint ξ j − 1 / 2 ⁎ , and the following equations are obtained:

(32) ( V k 1 ) j − ( V k 1 ) j − 1 = 0.5 Δ x j ( ( V k 2 ) j + ( V k 2 ) j − 1 ) ,

(33) ( V k 2 ) j − ( V k 2 ) j − 1 = 0.5 Δ x j ( ( V k 3 ) j + ( V k 3 ) j − 1 ) ,

(34) ( V k 3 ) j − ( V k 3 ) j − 1 = 0.5 Δ x j ( ( V k 4 ) j + ( V k 4 ) j − 1 ) ,

(35) ( V k 5 ) j − ( V k 5 ) j − 1 = 0.5 Δ x j ( ( V k 6 ) j + ( V k 6 ) j − 1 ) ,

(36) − χ 2 ( ( V k 1 ) j + ( V k 1 ) j − 1 ) 2 ( ( V k 4 ) j − ( V k 4 ) j − 1 ) + Δ x j χ 2 ( ( V k 3 ) j + ( V k 3 ) j − 1 ) 2 4 + Δ x j ϕ a ϕ b ( ( V k 1 ) j + ( V k 1 ) j − 1 ) 2 ( ( V k 3 ) j + ( V k 3 ) j − 1 ) 2 − ϕ a ϕ b ( ( V k 2 ) j + ( V k 2 ) j − 1 ) 2 4 + 2 Δ x j ϕ a ϕ b χ 1 ( ( V k 1 ) j + ( V k 1 ) j − 1 ) 2 ( ( V k 2 ) j + ( V k 2 ) j − 1 ) 2 − Δ x j ϕ a ϕ b χ 1 ( ( V k 1 ) j + ( V k 1 ) j − 1 ) 2 4 × ( ( V k 4 ) j + ( V k 4 ) j − 1 ) 2 − Δ x j ϕ d ϕ b M sin 2 ( Γ q ) ( ( V k 2 ) j + ( V k 2 ) j − 1 ) 2 + Δ x j ( ( V k 4 ) j + ( V k 4 ) j − 1 ) 2 = 0 , ,

(37) ( V k 6 ) j − ( V k 6 ) j − 1 ) + 1 ϕ d Pr N q ( ( V k 6 ) j − ( V k 6 ) j − 1 ) + Δ x j Pr ϕ c ϕ d ( ( V k 1 ) j + ( V k 1 ) j − 1 ) 2 × ( ( V k 6 ) j + ( V k 6 ) j − 1 ) 2 − Δ x j Pr ϕ c ϕ d ( ( V k 2 ) j + ( V k 2 ) j − 1 ) 2 ( ( V k 5 ) j + ( V k 5 ) j − 1 ) 2 + Pr E c ϕ a ϕ e ( ( V k 3 ) j + ( V k 3 ) j − 1 ) 4 2 + Pr ϕ d ϕ e M E c sin 2 ( Γ q ) ( ( V k 2 ) j + ( V k 2 ) j − 1 ) 4 2 = 0 , .

Figure 3

Typical grid structure for difference approximations.