The influence of simultaneously applied ramped boundary conditions on unsteady magnetohydrodynamic natural convective motion of a secondgrade fluid is investigated and analyzed in this study.

This article provides a comprehensive analysis regarding effects of ramped wall temperature and ramped wall velocity on incompressible time-dependent magnetohydrodynamic flow of Maxwell fluid. The flow is due to free convection and bounded to an infinite vertical plate embedded in porous medium. Solutions of mass, shear stress, and energy fields are computed symmetrically by introducing some suitable non-dimensional parameters along with the Laplace transformation technique. The expression for the Nusselt number is also calculated. A comparison between solutions incorporating isothermal temperature and ramped wall temperature conditions is also executed to examine the profile differences. A graphical study is performed to highlight the influence of parameters on mass flow and energy transfer.

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Unsteady, incompressible flow of Casson fluid between two infinitely long upward heated walls nested in a porous medium is analyzed in this work. The mass diffusion and heat transfer phenomena are also studied in the presence of thermal radiation, magnetic field, and heat source/sink. The generalized boundary conditions in terms of continuous time-dependent functions are considered for mass, energy, and momentum fields. Fick’s law, Fourier’s law, and momentum conservation principle are adopted to formulate the mathematical equations. Analytic solution for the concentration equation is established first by adding certain unit-less quantities and then by using the Laplace method of transformation. Semi-analytic solutions are calculated by means of Stehfest’s numerical Laplace inversion algorithm for energy and velocity equations. To demonstrate the verification of those solutions, a tabular comparison is drawn. Graphical illustrations along with physical descriptions are provided to discuss the essential contribution of thermo-physical parameters in heat and mass transfer and flow of the Casson fluid. The numerical computations of Sherwood number, Nusselt number, and skin friction for various inputs of related parameters are organized in tables to investigate mass transfer rate, heat transfer rate, and shear stress respectively. It is observed that porosity of the medium and buoyancy force tend to accelerate the flow. The heat and mass transfer rates are appreciated by Prandtl and Schmidt numbers respectively. Furthermore, radiation parameter and Grashof number significantly minimize the shear stress.

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.

The core purpose of this study is the formulation of a fractional model to anticipate the improvement in heat transfer potential of a particular diathermal oil i.e. engine oil under thermal radiative flux. The magnetohydrodynamic (MHD) freely convectional transport of two different types of engine oil based nanofluids comprised of Titanium (Ti 6 Al 4 V) and Aluminum (AA7075) alloy nanoparticles is considered in a vertical channel frame. In addition, the channel is assumed to be embedded in a permeable media and slip effects are observed at both ends. The transmutation of the governed model from classical to fractional environment is achieved by operating the Atangana-Baleanu derivative. To procure solutions of the proposed fractional model, Laplace transform is employed with an adequate choice of some unit-free quantities. Numerical simulations are performed and outcomes are conveyed through graphical illustrations to discuss the contribution of considered alloy nanoparticles in flow mechanism and thermal behavior of engine oil. It is reported that Ti 6 Al 4 V is more effective to enhance the thermal efficiency of engine oil as compared to AA7075. It is claimed that there is an augmentation of 32.50% in the heat transfer rate of engine oil due to Ti 6 Al 4 V, which is almost twice the improvement in heat transfer rate provided by AA7075. Furthermore, the slip parameters lead to expedite the channel flow of engine oil. This study culminates that Ti 6 Al 4 V and AA7075 significantly improve the lubrication and cooling characteristics of engine oil.