A theoretical study on the performance of a solar collector using CeO2 and Al2O3 water based nanofluids with inclined plate: Atangana–Baleanu fractional model

Sheikh, Nadeem Ahmad; Ali, Farhad; Khan, Ilyas; Gohar, Madeha

doi:10.1016/j.chaos.2018.08.020

Cited by 30 publications

(16 citation statements)

References 42 publications

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“…Different applications of this phenomenon can be seen in modern technologies and industries such as food processing, solar collectors, cooling processes, different lubricants such as engine oil etc. [57][58][59]. Reddy and Firdows [60] investigated the heat and mass transfer phenomena of micropolar dusty fluid across a paraboloid revolution.…”

Section: Introductionmentioning

confidence: 99%

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

et al. 2020

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The aim of this study is to obtain the closed form solutions for the laminar and unsteady couple stress fluid flow. The fluid is allowed to flow between two infinite parallel plates separated by distance. Moreover, we have considered that the lower plate is moving with uniform velocity 0 U and upper plate is stationary. For this purpose, engine oil is taken as a base fluid and to enhance the efficiency of lubricating oil, Molybdenum disulphide nanoparticles are dispersed uniformly in the engine oil. The flow is formulated mathematically in terms of partial differential equations of order four. Furthermore, the derived system of partial differential equations are fractionalized by using the mostly used definition of Caputo-Fabrizio time fractional derivative. The more general exact solutions for velocity, temperature and concentration distributions are obtained by using the joint applications of Fourier and the Laplace transforms. The effect of different parameters of interest of the obtained general solutions are discussed by sketching graphs. Furthermore, substituting favorable limits of different parameters, four different limiting cases are recovered from our obtained general solutions i.e. (a) Couette flow (b) Classical couple stress fluid (c) Newtonian viscous fluid and (d) in the absence of thermal and concentration. Moreover, the effect of different physical parameters on the velocity, temperature and concentration distributions are discussed graphically. It is worth noting that couple stress parameter corresponds to a decrease in the velocity profile. In order to observe the differences clearly, all the figures are compared for integer order and fractional order which provide a more realistic approach as compared to the classical model. Additionally, skin friction is calculated at lower as well as upper plate. Nusselt number and Sherwood number are also tabulated. It is noticed that the rate of heat transfer of engine oil can be enhanced up to 12.38% and decrease in mass transfer up to 2.14% by adding Molybdenum disulphide nanoparticles in regular engine oil. INDEX TERMS Couple stress nanofluid (CSNF); Caputo-Fabrizo (CF); Fourier transform (FT); Generalized Couette flow; Laplace transform (LT); Molybdenum disulphide (MoS2).

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Section: Introductionmentioning

confidence: 99%

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

et al. 2020

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“…The solutions are presented in terms of special functions. The obtained solutions (8) and (9) are plotted in various graphs and also presented in tables. Moreover, the statistical analysis is presented in this paper in terms of linear dependency of current on embedded variables.…”

Section: Resultsmentioning

confidence: 99%

“…As we can see clearly from Eqs. (8) and (9), that the obtained solutions are in series form, and hence for numerical compautation, the first 100 terms are considered. In order to show the impact fractional derivative on current profile in the circuit, Fig.…”

Section: Resultsmentioning

confidence: 99%

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Mathematical and Statistical Analysis of Rl and Rc Fractional-Order Circuits

et al. 2020

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The RL and RC circuits are analyzed in this research paper. The classical model of these circuits is generalized using the modern concept of fractional derivative with Mittag-Leffler function in its kernel. The fractional differential equations are solved for exact solutions using the Laplace transform technique and the inverse transformation. The obtained solutions are plotted and presented in tables to show the effect of resistance, inductance and fractional parameter on current and voltage. Furthermore, the statistical analysis is presented to predict the seasonal of time and other parameters on the current flowing in the circuit. The statistical analysis shows that the variation in current is insignificant with respect to time and is more significant with respect to other parameters.

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“…The logarithmic-KdV equation with the AB fractional operator and Mittag-Leffler type kernel was investigated by Mustafa et al [32] using the numerical iterative method. Some plenteous literature regarding ABFD, their analytical solution, and applications can be found in [33][34][35][36] and the references therein. A few previous studies with ABFD are referenced in [34,35,37,38], but mostly they are focused on non-Newtonian fluids, nanofluids, or some are formulated with constant wall velocity.…”

Section: Introductionmentioning

confidence: 99%

Natural convection flow of a fluid using Atangana and Baleanu fractional model

2020

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A modified fractional model for the magnetohydrodynamic (MHD) flow of a fluid is developed utilizing Atangana-Baleanu fractional derivative (ABFD). Natural convection and wall oscillation instigate the flow over a vertical plate positioned in a porous medium. The partial differential equations (PDEs) are transmuted to ordinary differential equations (ODEs). The Laplace transform method with its inversion is employed to accomplish the exact solutions of momentum and heat equations. The final solution is expressed in terms of gamma function, modified Bessel function, and Mittag-Leffler function. The previous definitions Caputo fractional and Riemann-Liouville are rarely used by the researchers now due to their limitations. The newly introduced ABFD has got significance nowadays due to its nonlocal and nonsingular kernel. This work focuses on the oscillating boundary conditions for the viscous model in terms of ABFD. The influence of involved parameters is interpreted through plots. The velocity profile is an increasing function of fractional parameter and jumps for a higher Grashof number due to buoyancy push. Furthermore, the Atangana-Baleanu (AB) model is compared with the ordinary derivative model for limiting case and analyzed in detail. It is noted that the ordinary fluid flows faster compared to the fractional fluid.

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A theoretical study on the performance of a solar collector using CeO2 and Al2O3 water based nanofluids with inclined plate: Atangana–Baleanu fractional model

Cited by 30 publications

References 42 publications

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

A Time Fractional Model of Generalized Couette Flow of Couple Stress Nanofluid With Heat and Mass Transfer: Applications in Engine Oil

Mathematical and Statistical Analysis of Rl and Rc Fractional-Order Circuits

Natural convection flow of a fluid using Atangana and Baleanu fractional model

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