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In this work, impacts of dispersing nonspherical shaped cobalt nanoparticles in the blood are analyzed for magnetohydrodynamic radiative transport of blood inside a vertical porous channel. An Oldroyd‐B model is used to feature flow characteristics of blood along with Fourier's principle of heat transmission for the mathematical modeling of the problem. A fractional system is constructed by employing the idea of the Caputo–Fabrizio derivative on subsequent differential equations. The Laplace transform method is adopted to solve the fractional flow and energy equations subject to generalized boundary conditions, which involve time‐dependent functions h(τ) $h(\tau)$ and g(τ) $g(\tau)$, respectively. Instead of promoting the analytic velocity and energy expressions, Zakian's numerical algorithm is operated to achieve the reverse transformation purpose of Laplace domain functions. To certify the obtained solutions, two additional numerical algorithms named Stehfest's algorithm and Durbin's algorithm are inculcated in this study, and comparative illustrations are drawn. For the extensive investigation of shear stress and heat transfer phenomenon, numerical simulations for the coefficient of skin friction and Nusselt number are performed, and outcomes are communicated through various tables. The impacts of shape‐dependent viscosity and other significant parameters on flow patterns are investigated through graphs for multiple motion types of the left channel wall. Meanwhile, the thermal performance of nanofluid is examined for platelet, brick, cylinder, and blade shape nanoparticles, along with other thermal parameters. In addition, some recently reported results and flow profiles for Maxwell, second‐grade, and viscous fluids are deduced graphically as special cases of the current study. [ABSTRACT FROM AUTHOR]

The nonlinearity in many problems occurs because of the complexity of the given physical phenomena. The present paper investigates the non-linear fractional partial differential equations’ solutions using the Caputo operator with Laplace residual power series method. It is found that the present technique has a direct and simple implementation to solve the targeted problems. The comparison of the obtained solutions has been done with actual solutions to the problems. The fractional-order solutions are presented and considered to be the focal point of this research article. The results of the proposed technique are highly accurate and provide useful information about the actual dynamics of each problem. Because of the simple implementation, the present technique can be extended to solve other important fractional order problems. [ABSTRACT FROM AUTHOR]

This article critically examines the influences of Newtonian heating and slip effects on unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid near an infinitely long plate. The nonlinear thermal radiation influence is considered in normal direction to the vertical plate. A modern definition of Caputo-Fabrizio fractional derivative is applied to generalize the constitutive mass and energy equations. The Laplace transformation technique and Durbin's numerical algorithm are served to develop the solutions of proposed problem. The solutions are determined for both fractional and ordinary cases and Stehfest's and Zakian's numerical algorithms are employed to secure the authenticity of these solutions. The relations for Nusselt number and skin friction coefficient are efficiently computed to precisely estimate the shear stress and rate of heat transfer at boundary. The respective numerical computations are accessible through tables. To comprehensively analyze the dynamics of the proposed problem, physical influence of various parameters is studied and repercussions are graphically highlighted and discussed. Furthermore, two limiting models named as second grade model and Maxwell model are deduced to compare the pertinent flow characteristics. A comparative analysis between fractional and classical models depicts that the Caputo-Fabrizio fractional model explains the memory effects more adequately. [ABSTRACT FROM AUTHOR]

In the current century, hybrid nanofluids are considered one of the modified forms of heat transferring fluids because of their advanced thermal characteristics. The main motive of this article is the formulation of two different fractional models to explain flow patterns and thermal behavior of sodium alginate (NaAlg/SA) based hybrid nanofluid. The improvement in the thermal performance of NaAlg due to the addition of molybdenum-disulfide ( MoS 2 ) and cobalt (Co) nanoparticles is also analyzed. The ramped motion of an unbounded inclined plate leads to execute the flow of hybrid nanofluid through a porous material. The considered hybrid nanofluid also encounters magnetic effects. The heat transfer process starts due to the application of the ramped heating condition at the inclined boundary and thermal radiation, shape factor of nanoparticles, and heat injection/suction also affect this process. The mathematical modeling of the considered problem is carried out and two different fractional models are developed through Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) fractional derivatives. Using the powerful Laplace transform technique, double mathematical and fractional analysis is performed to establish the analytic solutions. To clearly understand the heat transfer mechanism and behavior of shear stress, numerical simulations are performed for temperature and velocity gradients at the boundary. For a comprehensive physical investigation, several graphs and tables are furnished to evaluate the role of involved thermal and physical parameters in developing the flow patterns and temperature field. This study concludes that even dispersion of Co and MoS 2 nanoparticles in NaAlg enhances the heat transfer rate of host fluid up to 21%. Comparative analysis suggests that AB fractional derivative is more adequate to describe the flow patterns and temperature field. Furthermore, maximum values of Nusselt number are observed when both nanoparticles are considered of blade shape. [ABSTRACT FROM AUTHOR]

• Non-uniform velocity and temperature conditions are imposed for Brinkman-type ferrofluid. • The Caputo-Fabrizio time-derivative is used to construct the fractional model. • Exact solutions are computed to highlight the shape effects of nanoparticles. • Fe 3 O 4 nanoparticles are more effective in water as compared to Kerosene oil. • Blade-shaped Fe 3 O 4 nanoparticles enhance the heat transfer rate up to 13.80%. The prime aim of this article is the construction of a fractional model to enhance the heat transfer rate for magnetohydrodynamic (MHD) convectional transport of ferrofluid by applying the time-fractional concept of Caputo-Fabrizio derivative on Brinkman-type fluid model. Kerosene oil and water are considered to serve as carrier fluids for iron oxide ( Fe 3 O 4 ) nanoparticles of various non-spherical shapes (brick, cylinder, platelet, and blade). The non-uniform time-dependent motion of an unbounded upward plate causes to generate the flow of ferrofluid. The supplementary physical phenomena such as ramped heating, thermal radiation, and heat injection/consumption are also analyzed. In addition, the effectiveness of using differently shaped Fe 3 O 4 nanoparticles for heat transfer and ferrofluid flow is evaluated. The exact solutions for non-integer order modeled differential equations are computed by employing the Laplace transform method. The comparative graphical illustrations for ramped and constant (isothermal) velocity and temperature conditions are prepared to scrutinize the impacts of several associated thermal and physical quantities. Besides, the outcomes of numerical simulations of Nusselt number and shear stress are communicated through multiple tables for an in-depth analysis. It is perceived that blade and platelet shaped Fe 3 O 4 nanoparticles are more effective to enhance the thermal efficiency of Brinkman-type ferrofluid in contrast to cylinder and brick shaped nanoparticles. It is interesting to report that an improvement of 13.80% in Nusselt number is observed for water based ferrofluid that significantly advances its thermal properties. The fractional parameter γ produces inverse variations in momentum boundary layer thickness for isothermal and ramped plate cases. Additionally, velocity and temperature curves for ramped plate case are always lower than those of isothermal plate case. This fact highlights the importance of plate ramping in heat and flow control problems. [ABSTRACT FROM AUTHOR]

In recent times, the study of diathermal oils is an area of interest for multiple researchers because of their numerous pivotal applications in industrial and engineering operations. The core aim of this work is the formulation of a fractional model to anticipate improvement in thermal and flow characteristics of a particular kind of diathermal oils named engine oil due to the dispersion of two different types of nanoparticles. Molybdenum‐disulfide (MoS2) and iron oxide (Fe3O4) nanoparticles are considered to form hybrid nanofluid, and combined impacts of their particular features on the thermal efficiency of engine oil are investigated. The ramped movement of an unbounded vertically inclined wall initiates the flow of hybrid nanofluid and some supplementary physical phenomena such as heat radiation, uniform magnetic field, and ramped heating also influence this flow. Additionally, the significant role of nanoparticles' shape factor in augmenting the heat transfer capacity of engine oil is examined. Initially, the flow of hybrid nanofluid is described through the Brinkman‐type fluid model, which is developed in light of Maxwell equations and Boussinesq approximation. Later, this mathematical model is transmuted to a fractional framework by incorporating the time‐fractional Atangana–Baleanu derivative. Laplace transformation is employed to procure exact solutions of the generalized model. These solutions are portrayed through several graphical illustrations to analyze the influence of various involved physical parameters. Special attention is given to heat transfer rate and shear stress, and a comprehensive tabular study is performed in terms of Nusselt number and skin friction coefficient. It is concluded that the heat‐transferring potential of observed hybrid nanofluid is 17.4% higher than pure engine oil. The combination of fractional model and ramping technique is found to be more effective for increasing the heat transfer rate and reducing the shear stress. [ABSTRACT FROM AUTHOR]