Heat Transfer Analysis For Oscillating Flow of Magnetized Fluid By Using The Modified Prabhakar-Like Fractional Derivatives

In this analysis, an unsteady and incompressible flow of magnetized fluid in presence of heat transfer has been presented with fractional simulations. The oscillating plate with periodically variation has induced the flow. The model is formulated in terms of partial differential equations (PDE’s). The traditional PDEs cannot analyze and examine the physical behavior of flow parameters with memory effects. On this end, the solution approach is followed with the efficient mathematical fractional technique namely Prabhakar fractional derivative. The non-dimensional leading equations are transformed into the fractional model and then solved with the help of the Laplace transformation scheme. The effects and behavior of significant physical and fractional parameters are analyzed graphically and numerically. As a result, we have concluded that the temperature and velocity profiles decrease with the enhancement of fractional parameters. Furthermore, with time both (temperature and velocity fields)decreasing away from the plate and asymptotically increases along y-direction, which also satisfies the corresponding conditions.

Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo–Fabrizio Derivative

This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.

Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions

A number of mathematical methods have been developed to determine the complex rheological behavior of fluid’s models. Such mathematical models are investigated using statistical, empirical, analytical, and iterative (numerical) methods. Due to this fact, this manuscript proposes an analytical analysis and comparison between Sumudu and Laplace transforms for the prediction of unsteady convective flow of magnetized second grade fluid. The mathematical model, say, unsteady convective flow of magnetized second grade fluid, is based on nonfractional approach consisting of ramped conditions. In order to investigate the heat transfer and velocity field profile, we invoked Sumudu and Laplace transforms for finding the hidden aspects of unsteady convective flow of magnetized second grade fluid. For the sake of the comparative analysis, the graphical illustration is depicted that reflects effective results for the first time in the open literature. In short, the obtained profiles of temperature and velocity fields with Laplace and Sumudu transforms are in good agreement on the basis of numerical simulations.

Advancement of Non-Newtonian Fluid with Hybrid Nanoparticles in a Convective Channel and Prabhakar’s Fractional Derivative—Analytical Solution

The present paper deals with the advancement of non-Newtonian fluid containing some nanoparticles between two parallel plates. A novel fractional operator is used to model memory effects, and analytical solutions are obtained for temperature and velocity fields by the method of Laplace transform. Moreover, a parametric study is elaborated to show the impact of flow parameters and presented in graphical form. As a result, dual solutions are predicted for increasing values of fractional parameters for short and long times. Furthermore, by increasing nanoparticle concentration, the temperature can be raised along with decreasing velocity. A fractional approach can provide new insight for the analytical solutions which makes the interpretation of the results easier and enable the way of testing possible approximate solutions.

Heat Transfer Analysis for Viscous Fluid Flow with the Newtonian Heating and Effect of Magnetic Force in a Rotating Regime

In this article, an unsteady free convection flow of MHD viscous fluid over a vertical rotating plate with Newtonian heating and heat generation is analyzed. The dimensionless governing equations for temperature and velocity fields are solved using the Laplace transform technique. Analytical solutions are obtained for the temperature and components of velocity fields. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are presented graphically.

MHD flow of a Newtonian fluid in symmetric channel with ABC fractional model containing hybrid nanoparticles

Introduction: The nanofluid is novelty of nanotechnology to overcome the difficulties of heat transfer in several manufacturing and engineering areas. Fractional calculus has many applications in nearly all fields of science and engineering which comprises electrochemistry, dispersion and viscoelasticity. Objectives: This paper focused on the heat transfer of hybrid nanofluid in two vertical parallel plates and presented a comparison between fractional operators. Methods: The fractional viscous fluid model is considered with physical initial and boundary conditions for the movement occurrences. The analytical solutions were obtained via Laplace transform method for the concentration, temperature and velocity fields. After that we presented a comparison between Atangana-Baleanu (ABC), Caputo (C) and Caputo-Fabrizio (CF) fractional operators. Results: The comparison of different base fluids (Water, kerosene, Engine Oil) is discussed graphically for temperature and velocity. It is resulted that due to high thermal conductivity in water, temperature and velocity are high. While engine oil has maximum viscosity than water and kerosene, so temperature and velocity are very low. Due to the thermal conductivity improving with the enrichment of hybrid nanoparticles, so the Temperature is increased and since viscosity increased, so the velocity is reduced. Conclusion: Atangana-Baleanu (ABC) fractional operator gives better memory effect of concentration, temperature and velocity fields than Caputo (C) and Caputo-Fabrizio (CF). Temperature and velocity of water with hybridized nanoparticles is high in comparison with kerosene and engine oil.

Long-time experimental investigation of turbulent superstructures in Rayleigh–Bénard convection by noninvasive simultaneous measurements of temperature and velocity fields

Large-scale mean patterns in Rayleigh–Bénard convection, also referred to as turbulent superstructures, have mainly been studied by means of numerical simulations so far, but experimental investigations are still rare. However, the analysis of turbulent superstructures, which are of great importance due to their effect on the local transport of heat and momentum, require both numerical and experimental data. Therefore, within the scope of this study measurements were performed in the horizontal mid plane and in a horizontal plane closer to the top of a Rayleigh–Bénard cell with an aspect ratio of $$\varGamma =l/h=25$$ Γ = l / h = 25 , thereby showing the initial formation of turbulent superstructures and their long-time rearrangement. The turbulent superstructures are investigated experimentally by noninvasive simultaneous measurements of temperature and velocity fields, using the color signal of thermochromic liquid crystals (TLCs) for the evaluation of the temperature and their temporal displacement for the determination of all three velocity components in the measurement planes via stereoscopic particle image velocimetry (stereo-PIV). Applying this measuring technique it is demonstrated that the time-averaging of instantaneous temperature and velocity fields uncovers the turbulent superstructures in both fields. Furthermore, the combination of the temperature and velocity data is used to characterize the local heat flux quantified by the local Nusselt number, which confirms that the turbulent superstructures strongly enhance the heat transfer in Rayleigh–Bénard convection. Graphic abstract

Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating

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.

Dynamic mode decomposition of numerical data in natural circulation

Dynamic mode decomposition (DMD) has been used for experimental and numerical data analysis in fluid dynamics. Despite of its advantages, the application of the DMD methodology to investigate the natural circulation in nuclear reactors are very scarce in literature. In this paper it is applied the traditional DMD and its variation, the sparsity-promoting dynamic mode decomposition (SPDMD), for analysis of temperature and velocity fields data, generated by computational simulation of an experimental setup in reduced scale, similar to a heat removal system by natural circulation of a pool-type research reactor. Firstly the numerical data is partitioned, using a space-time correlation approach, in order to identify fundamental sequences to compute the dynamic modes. Next, the DMD and SPDMD methodologies are applied over each subsequence to obtain the dynamic modes of the temperature and velocity fields. Finally the flow fields are reconstructed and compared with the original numerical data. The conclusion is that the SPDMD performs better than DMD to represent both the temperature and velocity data.