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The colloidal suspension of nanometer-sized particles of Fe3O4 in traditional base fluids is referred to as Ferro-nanofluids. These fluids have many technological applications such as cell separation, drug delivery, magnetic resonance imaging, heat dissipation, damping, and dynamic sealing. Due to the massive applications of Ferro-nanofluids, the main objective of this study is to consider the MHD flow of water-based Ferro-nanofluid in the presence of thermal radiation, heat generation, and nanoparticle shape effect. The Caputo-Fabrizio time-fractional Brinkman type fluid model is utilized to demonstrate the proposed flow phenomenon with oscillating and ramped heating boundary conditions. The Laplace transform method is used to solve the model for both ramped and isothermal heating for exact solutions. The ramped and isothermal solutions are simultaneously plotted in the various figures to study the influence of pertinent flow parameters. The results revealed that the fractional parameter has a great impact on both temperature and velocity fields. In the case of ramped heating, both temperature and velocity fields decreasing with increasing fractional parameter. However, in the isothermal case, this trend reverses near the plate and gradually, ramped, and isothermal heating became alike away from the plate for the fractional parameter. Finally, the solutions for temperature and velocity fields are reduced to classical form and validated with already published results.

BackgroundNon-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature.MethodsThe governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t ), the Grashof number (Gr), the Prandtl number (), and the phase angle (). Skin friction and the Nusselt number are also evaluated.ResultsThe exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver–Stehfest algorithm.ConclusionThe interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number (), and the phase angle ().

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Abstract. In this paper, the unsteady free convection flow of second grade fluid in a vertical frame with ramped wall temperature is investigated. The governing equations are modeled in a rotating frame where both the fluid and frame rotate in unison with angular velocity. The exact solutions in terms of velocity and temperature are obtained analytically by using Laplace transform method. These solutions are presented graphically and discussed for second grade fluid parameter (α) and rotation parameter (ω).

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Mixed convection of unsteady non-coaxial rotation flow of viscous fluid over an accelerated vertical disk is investigated. The motion in the fluid is induced due to the rotating and buoyancy force effects. The problem is formulated and extended in terms of coupled partial differential equations with some physical boundary and initial conditions. The non-dimensional equations of the problem are obtained by using the suitable non-dimensional variables. The exact solutions of non-coaxial velocity and temperature profiles are obtained by using Laplace transform method which are satisfying all the initial and boundary conditions. The physical significance of the mathematical results is shown in various plots and is discussed for Grashof and Prandtl numbers as well as magnetic, porosity and accelerated parameters. It is found that, the velocity with the effect of acceleration is higher compared to constant velocity. In limiting sense, the present solutions are found identical with published results.