Thermal analysis characterisation of solar powered ship using Oldroyd hybrid nano ﬂ uids in parabolic trough solar collector: An optimal thermal application

: The mathematical modeling of hybrid nano ﬂ uid ﬂ ow and heat transfer with entropy generation toward parabolic trough surface collector ( PTSC ) inside the solar - powered ship ( SPS ) is performed. The mathe matical model used non - Newtonian Oldroyd - B model amidst a constant inclined magnetic ﬁ eld in ﬂ uence is being considered. The mathematical model is then reduced by adopting appropriate similarity transformation into a higher - order nonlinear di ﬀ erential equations system. The reduced model is computed using the well - known tech nique called the Keller Box scheme. Physical parameters e ﬀ ectiveness, for instance, thermal radiation, viscous dissi -pation, hybrid nanoparticles, and Joule heating, is displayed in graphs. The silver - ethylene glycol ( Ag - EG ) characteristic performance outperformed the silver - magnetite - ethylene glycol ( Ag - Fe 3 O 4 /EG ) . The maximum e ﬃ ciency of Ag - EG is about 26.3%, while the minimum is at least 5.6%.


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 MoS 2 -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 Al 2 O 3 / 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][45][46][47][48][49][50][51][52][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 twohybrid 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).
This study examines the heat transfer analysis of the solar water pump using mono/hybrid nanofluids (i.e., Ag-EO and Ag-Fe 3 O 4 /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.

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.

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

Model equations
Constitutive flow equations on viscous Oldroyd-B hybrid nanofluid with common boundary layer estimations under the influence of inclined MHD, viscous dissipation, inclined Joule heating, and radiation heat flux are presented (see, for instance, ref. [75]): (3) Aziz et al. [76] provided boundary conditions: Here, is a vector regarding flow velocity. Θ is the signifying fluid temperature. The penetrability of the expanding plate is signified by V w , slip length, heat transfer coefficient N L , and h f and k 0 represent the porousness of material. Convectional heated surface underwent its thermal loss due to conduction (Newtonian heating), and the flow velocity near the surface is proportional to the shear stress exerts in it (slip condition).

Thermophysical properties regarding Oldroyd-B nanofluid
When nanoparticles are dispersed in ethylene glycol fluid, the thermophysical property is enhanced. A summary about physical parameters for Oldroyd-B nanofluid is provided in Table 1 [77][78][79][80]. ϕ has represented the coefficient of nanoparticle volumetric fraction. μ f , ρ f , ( ) C p f , κ f , and σ f are, respectively, dynamic viscosity, density, effective heat capacity, the thermal conductivity, and electrical conductivity of the base fluid. Other parameters including ρ s , ( ) C p s , κ s , and σ s are, respectively, density, adequate heat capacity, thermal conductivity, and electral conductivity of nanoparticles.

Thermophysical characteristics of the Oldroyd-B hybrid nanofluid
Hybrid nanofluids work when there is a suspension of two different nanoparticle types in the working fluid. Suspension increases the heat transfer ability of ordinary fluids meanwhile proving them better heat boosters than nanofluids. Physical factors of Oldroyd-B hybrid nanofluid are summarised in Table 2 [81][82][83].
In Table 2, μ hnf , ρ hnf , ( ) ρ C p hnf , κ hnf , and σ hnf are dynamics viscosity, density, specific heat capacity, and the thermal and electrical conductivity of hybrid nanofluid, respectively. ϕ and = + ϕ ϕ ϕ hnf R H are coefficients of nanoparticle volume concentration for ordinary nanofluid and hybrid nanofluid, respectively. μ f , ρ f , ( ) C p f , κ f , and σ f are dynamic viscosity, intensity, specific heat capacity, and the thermal and electrical conductivity of working fluid, , and σ p2 are parameters of density, specific heat capacity, thermal conductance, and electrical conductance of nanoparticles.

Nanoparticles and base fluid features
Physical properties of ethylene glycol (working fluid), as well as other used nanoparticles in the current analysis, are described in Table 3 [84-86],

Rosseland approximations
Roseland approximation [87] can be written as follows: where σ ⁎ and k ⁎ are Stefan Boltzmann number and absorption coefficient, respectively.

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].

Nusselt number
The physical entity that glows governing is the local Nusselt number ( ) Nu x , stated as follows: where q w represents the heat flux that is determined with The results of the application of non-dimensional transformations (10) are represented as follows: where Nu x is the reduced Nusselt number.

Entropy generation analysis
Mentioned considerations have the following entropy production equation: Entropy equation has the following dimensionless form: Dimensionless entropy equation obtained from equation (10) is expressed as follows:

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.

Block tridiagonal structure
The block tridiagonal structure obtained from a linearised set of equations is expressed as follows: where where the elements defined in equation (46) are expressed as follows: Now we factorize A as follows:

Code validation
Verification is done via a comparison of currently obtained results with the previous literature [89][90][91][92][93][94]. The summary on consistency comparison in the presented studies is presented in Table 4. The accurate results are obtained in the present study.

Results and discussion
The numerical computation is tabulated and represented graphically for more accessible analysis. The essence of characteristic physical parameters such as Deborah number χ 1 , χ 2 , magnetic M, angle inclination Γ q , nanoparticle volume friction ϕ, velocity slip Λ q , Biot number B γ , radiation N q , viscous dissipation Ec, suction ( > S 0)/injection ( <

Effect of Deborah number ( χ 1 ) and ( χ 2 )
The dimensionless Deborah number quantifies that given enough time, even a solid-like material can flow, or a fluidlike substance can behave like a solid when it is deformed quickly enough. Because they flow freely, materials with short relaxation periods decompose under stress very quickly. Hence, it is very crucial to overview the consequence of Deborah's number on the system. Figure 4 displays the impact of the relaxation time to retardation time ratio χ 1 on the velocity profile. Whenever χ 1 is intensified, the relaxation time is diminished along with the retardation time. As a result, nanofluid particles acquire a lot more time to return to equilibrium after being in a disturbed manner. As illustrated in Figure 4, the velocity drops as Deborah's number increases. The effect of Deborah's number on temperature is depicted in Figure 5. It is notable that increment of χ 1 caused the temperature amplified. This phenomenon occurs as a result of the fluid flow being slowed by the resistance provided to it. The different effects can be seen with varying the value of χ 2 , which has been displayed in Figure 6. It is assumed that χ 2 helps as if there is no resistance being affected by the fluid flow. Nonetheless, a higher value of Deborah corresponds to a longer retardation time because it is dependent on the retardation time of the χ 2   by the discrepancy in Prandtl number, = ϕ 0, Ref. [89] Ref. [90] Ref. [91] Ref. [92] Ref. [93] Ref. [    as exposed in Figure 7. Technically, elasticity is strengthened by an upsurge in the retardation time of χ 2 . Elastic and viscosity effects are observed to be inversely related to one another. Therefore, a diminution in viscosity boosts fluid speed. Thus, the velocity rises as the Deborah number increases. Figures 8 and 9 depict the relationship between χ χ , 1 2 and entropy production in the mono and hybrid nanofluids. It is remarked that χ 2 is highly effective on entropy than χ 1 , and both of them reduce the entropy. The hybrid nanofluid is less entropy than the mono as a general. Also, the increasing behaviour of the rate of heat transfer ( Table 5) will lead to improving the performance and efficiency of the solar-powered ship.
7.2 Effect of magnetic parameter (M) and angle inclination parameter (Γ q ) Figure 10 describes the influence of magnetic parameter on velocity distribution. When the magnetic field gets stronger, it creates more drag, which slows down the fluid. Boundary layer flow can be stabilised with the use of a controlled transverse magnetic field. Delaying transition from laminar to turbulent flow can be achieved using this technique. It can be perceived that hybrid nanofluid is slightly improved compared to nanofluid at the same point due to the hybrid nanoparticle in the base fluid, making the fluid challenging to be influenced by the magnetic field. Despite that, the temperature of the system is augmented since less heat can be transferred to other places with the slower movement of the fluid flow. This occurrence is displayed in Figure 11. The positive value indicates that heat is being transported from surface to fluid. It is meaningful to look into the system's entropy with the impact of the magnetic field in the    system. Figure 12 illustrates the intensified entropy due to the lack of heat transfer in the system. This occurrence is expected due to the diminished velocity, which will retard the heat transportation in the system, hence amplifying the entropy generation in the system.
A similar trend can be found for the influence of angle inclination together with the velocity of the fluid flow demonstrated in Figure 13. The normal force reduces with the increasing inclination angle, which reduces the frictional force. The inclination can be augmented up to the point when the fluid flow begins to slide backward. This action will be the retarded force for the fluid to move forward because of the shift in the normal force. However, the velocity for hybrid nanofluid is slightly better than the conventional nanofluid. The molecule bonding in the base fluid helps the flow to maintain the speed from the retardation force. The temperature system will also intensify due to the slower movement of fluid flow ( Figure 14). This phenomenon occurred due to minor heat relocation from the surface towards the flow. The slower movement of the fluid flow causes the buildup of cumulative heat on the surface. Hence, this results in an increment of entropy of the system ( Figure 15). It is worth mentioning, regardless of the temperature in the system amplified, that the hybrid nanofluid seems slightly manageable to reduce the entropy generation.

Effect of nanoparticle volume fraction parameter (ϕ)
Nanoparticle volumetric fraction parameter ϕ effect towards velocity is shown in Figure 16. As ϕ intensified, the speed of the fluid flow is decreased. This occurrence happens due to the increase of fluid viscosity with growing nanofluid concentration and friction escalations. The hybrid nanofluid has a higher velocity than the conventional nanofluid as ϕ augmented. It is found that the temperature of the system    amplified along with ϕ in Figure 16. It is worth mentioning that fluid velocity is critical for heat transmission. The movement of the particles in the fluid decreased, which will cause the heat to accumulate in the system. Hence, the temperature of the system doubles up. It is also expected that the system's entropy will amplify due to heat accumulation-this evidence is illustrated in Figure 17. The analytical results shown in Figure 18 demonstrate that the nanoparticle volume fraction substantially influences the produced entropy. Conversely, hybrid nanofluid generates less entropy than nanofluid, as shown in Figure 18. This finding implies that hybrid nanofluids can better control the entropy system than nanofluids.

Effect of velocity slip parameter (Λ q )
Disparity in velocity between the conveying air and the delivered particles is known as the velocity slip parameter.
Along walls, the velocity slip condition is measured. The velocity slip parameter caused the flow velocity to decelerate, as shown in Figure 19. It happens when the slip increases the friction force between the flow and the surface. It is worth pointing out that the velocity of hybrid nanofluid is still higher than nanofluid because the base fluid contains metal particles that have a strong bond that is hard to be affected. Since the velocity is reduced, the temperature of the flow is distending as the velocity slip heightens. This aspect is observable in Figure 20 and obviously happens due to less heat being transported from one point to another. However, it is eye catching that the system's entropy is reduced regardless of the velocity slip intensification, as shown in Figure 21. This phenomenon is because silver and iron have higher positive enthalpies, which have been stated by Hsu et al. [95], the bonding energy and structural atoms that are good to be counterbalanced with the entropy.    The repercussion of the Biot number towards the temperature of the flow is shown in Figure 22. The trend depicted the temperature aggrandize as the Biot number surge. This notable trend showed the thermal resistances inside the flow amplified hence proliferating the temperature of the flow. This peculiarity triggers the entropy of the system enhanced as embellished in Figure 23. It is noteworthy that the increase in the Biot number rises the rate of heat transfer and entropy of the system as well. This increasing behaviour of the rate of heat transfer ( Table 5) will lead to improving the performance and efficiency of the solar-powered ship. Moreover, it has been pointed out that the minimum relative percentage of (B γ ) is reflecting on point 24.15 and maximum on point 24.38. The radiation response resulting from the heat exchange between the flow and surrounding (far field) is displayed in Figure 24. According to this figure, the surrounding temperature affected the flow temperature to be amplified. This experience is due to both the surrounding and the flow trying to achieve thermal equilibrium with each other. The surrounding temperature is hotter than the flow. Hence, the     temperature of the flow is elucidated. This incident shows the increment of entropy in the system as illuminated in Figure 25. It embossed that energy in the system undergoes the irreversible process. Also, the increasing behaviour of the rate of heat transfer in Table 5 will lead to improving the performance and efficiency of the solar-powered ship.
A similar trend is shown in Figure 26 as the viscous dissipation exaggerates and the flow's temperature increases. It is widely known that all the energy lost by the viscous dissipation will be converted into heat in the system. Therefore, the total heat in the system increased, and later, the temperature in the flow broadened.

Effect of suction ( > S 0)/injection ( < S 0) parameter
It is essential to look at the essence of the suction or injection parameter towards the flow. Figure 27 shows that the velocity of the flow is diminished as the suction is enhanced. The suction effect will disturb the speed to flow on the surface smoothly. Hence, it will gradually degenerate the velocity of the flow. Nonetheless, the suction effect is an assertion in reducing the temperature of the flow as illustrated in Figure 28. The speed of the nearest layer to the surface increases due to the porosity of the surface. The porosity will pull the flow into the hole. With this effect, the heat can be transmitted quickly, hence reducing the flow's temperature faster. However, the drawback of this outcome is the entropy of the system amplified. The existence of the porosity on the surface makes the entropy a bit hard to control. Thus, the entropy of the system augments, as shown in Figure 29.
Different purport can be seen for the significance of injection parameter towards the fluid flow. Figure 30 shows the enhancement of velocity of a fluid with an escalation of injection parameter. This outcome happens due of the flow is being injected or boosted up to an inner layer, which causes the whole velocity of the flow to be    augmented. However, the injection parameter side effect adds more friction on the surface, which will cause the temperature of the flow to intensify. This result is apparent in Figure 31. This figure shows that the injection parameter amplified the temperature of the flow. Despite this increment, the entropy of the system is depreciating due to there is no porosity on the surface, which is easier for the system to control the energy in the flow. This circumstance is shown in Figure 32.

Impact of Reynolds number (Re) and
Brinkman number (B r ) on entropy generation Figure 33 shows that the system's entropy amplifies with the Reynold number because the inertial forces augment the systems. The particles in the hybrid nanofluid have tremendous kinetic energy, which causes them to move faster and have the disorder at a high Reynold number.
The analysis of the effect of the Brinkman number is eye catching in that it shows the ratio between heat produced by viscous dissipation and heat transmission by molecular conduction. Figure 34 indicates that the Brinkman number expend entropy generation of the system. It is specified that heat produced is more caused by viscous dissipation.
7.8 Impact of (ϕ),(M),(N q ) and (Ec) on heat transfer rate (Nu Re It is worth seeing the influence of several factors of the physical parameter that can give impact towards the physical quantity, as such the local Nusselt number. The nanoparticle volume fraction parameter decreases a little heat transfer rate due to the small-sized molecules allowing for free movement and hence micro convection, which can slightly affect the heat transfer. Based on Figure 35, the    hybrid nanofluid has at least 5.6% better heat dispersion rather than the nanofluid. This occurrence is due to the hybrid nanofluid advanced properties of thermodynamics. When nanoparticle volume fraction increases, the heat transfer rate for nanofluid decreases significantly compared to hybrid nanofluid. This phenomenon indicates that hybrid nanofluid can maintain heat transfer rates as the volume of nanoparticles augment. The demeanour of the heat transfer rate with magnetic parameter effect is depicted in Figure 36. The magnetic field acting on the system amplifies as the heat transfer rate reduces in the flow. The flowing current seems like a retarded force in transferring the heat from the surface to the flow. Heat transfer for hybrid nanofluid is more remarkable, at least at 24% than nanofluid. It is due to the base fluid having more metal particles that can uphold the thermal conductivity of the flow. Figure 37 illustrates that the radiation parameter aggrandizes the heat transfer rate. It is well known that radiation is the quickest medium in heat transfer because they emit from a body to the receiver flow in electromagnetic waves. With the bits of help of the magnetic parameter, the radiation further heightens the heat transfer rate in the system. It is observable that hybrid nanofluid     possesses better heat transfer, at least about 24% from nanofluid. The physical reason for this phenomenon is that the metal particle in the hybrid nanofluid is more than nanofluid, which can enhance further the heat transfer rate in the system. The decreasing trend can be observed in Figure 38, which illustrates the depreciation of heat transfer rate with an increment of viscous dissipation. It can be observed that the flow is heating up, but the viscosity of the fluid is low, which is challenging to transform kinetic energy into internal energy of the liquid. However, the hybrid nanofluid has a higher heat transfer rate at about 24% because the viscosity of a fluid is more elevated than the nanofluid. 7.9 Relative heat transfer rate in (Cu-Ag) and (( )

Fe O 3 4 -EO) nanofluid
It is worth mentioning that the relative percentage for the heat transfer rate of hybrid nanofluid for each physical parameter is 24%. This relative percentage is presented in Table 5. It is seen that almost every physical parameter augment produced an increment at most 24%.

Final outcomes
The performance of solar-powered ships using Oldroyd hybrid nanofluids in parabolic trough solar collectors is investigated theoretically. Governing equations involved are altered into ODEs and were further numerically solved using the Keller Box method. All results are analyzed and discussed thoroughly. The results can be summarised as follows: • Only Deborah number χ 2 and injection parameters amplify velocity of the flow, while Deborah number χ 1 , magnetic, angle inclination, nanoparticle volume fraction, velocity slip, and suction parameters diminish the velocity of the flow. • The temperature profile can be augmented with the influence of Deborah number χ 1 , magnetic, angle inclination, nanoparticle volume fraction, velocity slip, radiation, and injection parameter. • The entropy generation can be controlled by Deborah number, velocity slip, and injection parameter. • Heat transmission is reduced with the effect of nanoparticle volume fraction, magnetic and viscous dissipation • Relative percentage of heat transfer rate for hybrid nanofluid is 24% over nanofluid.

Future direction
The future investigation can include other physical parameters such as Joule heating, nanoparticles shape, and others. The analysis of these factors is critical to have a total overview of solar-powered ships.