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This article disputes the study of convective flow for improved nanofluid along with an erect heated plate via Prabhakar‐like energy transport. The governing equations for this mathematical model are obtained by Prabhakar fractional derivative. To attain the generalized results for dimensionless velocity profile and temperature profile, a scheme of Laplace transform is applied. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non‐uniform accelerated solution of the model. Prabhakar fractional derivative for improved nanofluid based on generalized Fourier's thermal flux is determined for heat transfer. Different structures of graphs are performed for ordinary fractional parameters. As a result, it is found that temperature of Ag − H2O is higher than Cu − H2O and TiO2 − H2O nanoparticles and the reverse trend can be found for velocity. Furthermore, temperature and velocity can be enhanced by increasing the values of fractional parameters. [ABSTRACT FROM AUTHOR]

The unsteady flow of Williamson fluid with the effect of bioconvection in the heat and mass transfer occurring over a stretching sheet is investigated. A uniform magnetic field, thermal radiation, thermal dissipation, and chemical reactions are taken into account as additional effects. The physical problem is formulated in the form of a system of partial differential equations and solved numerically. For this purpose, similarity functions are involved to transmute these equations into corresponding ordinary differential equations. After that, the Runge-Kutta method with shooting technique is employed to evaluate the desired findings with the utilization of a MATLAB script. As a result, the effects of various physical parameters on the velocity, temperature, and nanoparticle concentration profiles as well as on the skin friction coefficient and rate of heat transfer are discussed with the aid of graphs and tables. The parameters of Brownian motion and thermophoresis are responsible for the rise in temperature and bioconvection Rayleigh number diminishes the velocity field. This study on nanofluid bioconvection has been directly applied in the pharmaceutical industry, microfluidic technology, microbial improved oil recovery, modelling oil and gas-bearing sedimentary basins, and many other fields. Further, to check the accuracy and validation of the present results, satisfactory concurrence is observed with the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, it has been discussed the fractional model of Brinkman type fluid (BTF) holding hybrid nanoparticles. Titanium dioxide (T i O 2) and silver (Ag) nanoparticles were liquefied in water (H 2 O) (base fluid) to make a hybrid nanofluid. The magnetohydrodynamic (MHD) free convection flow of the nanofluid (Ag - T i O 2 - H 2 O) was measured in a bounded microchannel. The BTF model was generalized using constant proportional Caputo fractional operator (CPC) with effective thermophysical properties. By introducing dimensionless variables, the governing equations of the model were solved by Laplace transform method. The testified outcomes are stated as M-function. The impact of associated parameters were measured graphically using Mathcad and offered a comparison with the existing results from the literature. The effect of related parameters was physically discussed. It was concluded that constant proportional Caputo fractional operator (CPC) showed better memory effect than Caputo-Fabrizio fractional operator (CF) (Saqib et al., 2020). [ABSTRACT FROM AUTHOR]

In this paper, it has been discussed a nonlocal fractional model of viscous nanofluid holding a hybrid nanostructure. Hybridized copper (Cu) and aluminium oxide (Al 2 O 3) nanoparticles were liquefied in base fluid water (H 2 O) to form a hybrid nanofluid. The MHD free convection flow of the nanofluid (Cu - Al 2 O 3 - H 2 O) was considered in a microchannel. The viscous nanofluid model was comprehended by a nonlocal constant proportional Caputo (CPC) fractional operator with actual thermophysical properties. The governing equations of the model were exposed to physical initial and boundary conditions. The analytical solutions were gained by the fractional Laplace transform technique. To see the physical significance of parameters, graphs were made by Mathcad software. It was invented that the consequences were universal, consistent and realistic. An outstanding covenant between the theoretic and experiments results could be found by arranging the fractional parameter. In the end, a comparison of CPC with the recent literature and significant findings are obtained. Further, temperature can be enhanced for larger values of heat generation and volume fraction parameters, respectively. [ABSTRACT FROM AUTHOR]

In this work, analytical solution of hybrid Maxwell nanofluid of the vertical channel due to pressure gradient is discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions is converted into dimensionless form. Fractional model for Maxwell fluid is developed by Caputo time fractional differential operator by using the constitutive relation. The dimensionless expression for temperature and velocity are found using Laplace transform. Draw graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters. As a result, we have found by increasing the volumetric fraction of copper and alumina temperature increases and velocity decreases. Also, fluid flow properties showed dual behavior for small and large time, respectively, by increasing fractional parameters values. [ABSTRACT FROM AUTHOR]

The present study is aimed to analyze the unsteady micropolar nanofluid flow passing over an oscillating infinite vertical plate. The flow is affected by thermal radiation and Newtonian heating. Single‐walled carbon nanotubes (SWCNTs) are added to enrich the thermal properties of the micropolar fluid. Kerosene is taken as the base liquid to enhance heat transfer. By using dimensional analysis, the governing equations for temperature, velocity, and microrotation are reduced to dimensionless form and after that, these equations have been solved by applying Laplace transform method to get the exact solutions. Finally, we have presented the effects of material and flow parameters and illustrated graphically by the Mathcad software. We found that microrotation, temperature, and velocity are decreasing functions of Prandtl number but have shown increasing behavior for Grashof number. Furthermore, we found that SWCNTs‐water‐based nanofluid has a comparatively higher heat transfer rate than SWCNTs‐kerosene and SWCNTs‐engine oil‐based nanofluids. [ABSTRACT FROM AUTHOR]

In this article, micropolar nanofluid boundary layer flow over a slanted stretching surface with Soret and Dufour effect is studied. The inclined stretching surface in this study is considered permeable and linear. In this problem, the Buongiorno model is considered for thermal efficiencies of fluid flow in the existence of Brownian movement and thermophoresis properties. The nonlinear problem for Micropolar Nanofluid flow over the slanted channel is developed to think about the heat and mass exchange phenomenon by incorporating portent flow factors to strengthened boundary layers. In this study, nonlinear partial differential equations are converted to nonlinear ordinary differential equations by utilizing appropriate similarity transformations then elucidated the numerical outcomes by the Keller-Box technique. An examination of the set-up results is performed with accessible outcomes and perceived in a good settlement without involved impacts. Numerical and graphical outcomes are additionally displayed in tables and charts. [ABSTRACT FROM AUTHOR]

The present investigation deals with the application of novel way of modeling of heat and mass transfer flow of hybrid nanofluid (Aluminum and Copper) for different base fluid water and engine oil. The governing equations for energy and momentum equations are developed with Caputo fractional power law derivative through constitutive relations. The flow of nanofluids confined between the two parallel plates with distance d apart. This model can be solved by means of the Laplace transform technique. Statically analysis for Nusselt number and Sherwood number is also discussed. To see the impact of fractional parameters α , β and γ on the temperature, concentration and fluid velocity, we have plotted some graphs through MathCad software and presented in the graphical section. As a result, for small value of time, we found that temperature, concentration and velocity are minimum near the plate and for large time they are maximum away from the plate for different fractional parameters α , β and γ. That is, solutions show dual behavior and can be controlled by variation values of fractional parameters α , β and γ and decay for larger values of α and β , respectively. Further, we concluded that water base hybrid nanofluids have higher temperature and velocity than engine oil based hybrid nanofluids. Also, we compared the present results with the recently published results and in limiting case they are in good agreement. [ABSTRACT FROM AUTHOR]

In this work, influence of hybrid nanofluids (Cu and Al 2 O 3 ) on MHD Maxwell fluid due to pressure gradient are discussed. By introducing dimensionless variables the governing equations with all levied initial and boundary conditions are converted into dimensionless form. Fractional model for Maxwell fluid is established by Caputo time fractional differential operator. The dimensionless expression for concentration, temperature and velocity are found using Laplace transform. As a result, it is found that fluid properties show dual behavior for small and large time and by increasing volumetric fraction temperature increases and velocity decreases respectively. Further, we compared the Maxwell, Casson and Newtonian fluids and found that Newtonian fluid has greater velocity due to less viscosity. Draw the graphs of temperature and velocity by Mathcad software and discuss the behavior of flow parameters and the effect of fractional parameters. [ABSTRACT FROM AUTHOR]