Non-dimensional Partial Differential Equations Research Articles

Thermal characterization of Sutterby nanofluid flow under Riga plate: Tiwari and Das model

This investigation uses the Tiwari and Das nanofluid model to enhance the heat transfer rate in Sutterby nanofluid over a Riga plate. The effects of heat source/sink, viscosity dispersion, and mass flow for water-based fluids are also considered in this work. Sutterby fluid has been utilized to investigate the rheological features of nanofluids. The transverse Lorentz force produced by the Riga plate assists in the flow down the plate by producing an electromagnetic field. The main aim of this investigation is to evaluate the presence of two different types of nanoparticles in water, specifically silicon carbide [Formula: see text] and copper [Formula: see text]. Dimensionless variables are first used to convert the mathematical model into a non-dimensional form. The similarity approach is then used to further rewrite the non-dimensional partial differential equations into a set of similarity equations. The bvp4c function in MATLAB software provides a numerical solution to these equations. The effects on temperature and velocity profiles of many physical factors, including the Reynold number, heat source/sink, and Deborah number, have been analyzed and presented. Furthermore, using tables, a detailed analysis of the skin friction coefficient and local Nusselt numbers is conducted. The results show that convective flow is suppressed when solid nanoparticles are added to the base fluid. The velocity distribution improves as Deborah and Reynold’s numbers get a higher value. Also, the temperature field improves by incrementing exponential and thermal heat source/sink parameters.

Entropy analysis of Hall effect with variable viscosity and slip conditions on rotating hybrid nanofluid flow over nonlinear radiative surface

PurposeWith possible uses in engineering and industrial processes, this work aims to further our knowledge of fluid dynamics and heat transfer in complicated flow configurations. This study looks at how Al2O3−Cu/H2O hybrid nanofluids move across a nonlinear radiative 3D unsteady surface. It tries to figure out what happens when the Hall current, variable viscosity, viscous dissipation, velocity and thermal slip conditions work together. The goal of this analysis is to provide insight into the system's thermodynamic behavior and the ways in which these elements affect the flow's entropy generation. MethodologyThe controlling system is converted into nonlinear nondimensional partial differential equations (PDEs) by applying suitable non-similar transformations. In this work, the governing equations are simulated using the local non-similarity (LNS) approach up to the second truncation level using the numerical technique bvp4c in MATLAB. FindingsThe temperature, velocity, entropy production, skin friction in both directions, and Nusselt number profiles of the nanofluid and hybrid nanofluid are detailed in many figures. The tabular form contains the results of computing the local Nusselt number for linear, nonlinear, and radiation-free scenarios. The velocity profiles in both directions and the temperature profile grow as the rotation parameter and nanoparticle volume fraction parameter increase. Conversely, the velocity profiles drop when the variable viscosity parameter falls, while the temperature profile increases. When the unsteadiness parameter A is set to 0.5 and the nanoparticle volume fraction is 1%, hybrid nanofluid has 4.26% lower x-direction skin friction than nanofluid and 3.62% greater y-direction friction. When the unsteadiness parameter A = 0.5 and the nanoparticle volume percentage is 1%, a hybrid nanofluid has a 2.77% higher Nusselt number than a nanofluid. The generation of entropy was also enhanced by an increase in the volume fraction of nanoparticles, radiation, temperature ratio, and Brinkman number. We evaluate and contrast the results of this study with those of earlier research.

Investigation of convective peristaltic flow of non-Newtonian fluids through a non-uniform tapered porous conduit with Ohmic heating and viscous dissipation

ABSTRACT The study of convective magnetohydrodynamic (MHD) biofluid transport through a non-uniform duct is of interest due to its applications to biomedical devices and equipment. Because of this, a comparative study of free convective peristaltic flow of non-Newtonian (Casson and Jeffrey) fluids in a tapered porous symmetric duct with Hall current and viscous dissipation effects is carried out. The proposed dimensional governing equations are converted into a system of non-dimensional partial differential equations by invoking adequate non-dimensional parameters. Furthermore, a long-wavelength approximation is used to reduce the complexity of the system. Then the reduced system of partial differential equations is solved analytically using the regular perturbation method. The fascinating features of the influential parameters on the flow characteristics are demonstrated and analyzed in depth through graphs and tables. The results demonstrate that the velocity and temperature in the Jeffrey fluid flow are larger compared to those in the Casson fluid flow. The thermal Grashof number and the Hall current parameter enhanced the pressure rise profile. This research has significant implications in biomedical devices (MRI, vitamins A and D injections, heart-lung machines, etc.) and pharmaceutical fluid preparation in biomedical sciences.

Non-similar analysis of micropolar magnetized nanofluid flow over a stretched surface

The study of micropolar nanofluids unveils intriguing applications, propelled by their exceptional heat transfer capabilities in comparison to conventional fluids. This investigation focuses on analyzing the behavior of magnetized micropolar nanofluid flow over a stretched surface, taking into account crucial factors such as viscous dissipation and heat source. The chosen base fluid is blood, with Copper [Formula: see text] nanoparticles serving as the selected material. Incorporating the single-phase (Tiwari-Das) model with boundary layer assumptions for micropolar nanofluid flow, we introduce the volume fraction of nanoparticles to assess heat transport. The governing system undergoes transformation into a set of dimensionless non-linear coupled differential equations through appropriate transformations. This transformation involves the utilization of a combination of the local non-similarity technique and bvp4c (MATLAB tool) to derive the system of nondimensional partial differential equations (PDEs) for micropolar nanofluid. Our systematic exploration delves into the consequences of nondimensional parameters on velocity, microrotation, and temperature profiles within the boundary layer, including the Eckert number, micropolar parameter, magnetic field parameter, heat source, Prandtl number, and microorganism parameter. Graphical representations vividly demonstrate that the velocity and temperature of micropolar nanofluid increase with the rise in material parameter values, while the microrotation profile decreases. Increasing the magnetic field parameter leads to a reduction in the velocity profile. Moreover, the micropolar temperature profile shows an increase with the rising Eckert number. Crucially, the research emphasizes that factors like the heat source and Eckert number play a role in decreasing the local Nusselt number. In contrast, an increase in the local Nusselt number is observed for material parameters. Furthermore, the skin friction coefficient decreases as micropolar parameter values increase, whereas an increase in the skin friction coefficient is noted for the magnetic field. The primary focus of this research lies in the development of suitable non-similar transformations for the investigated problem, aiming to yield authentic and efficient results. These results hold substantial promise to make meaningful contributions to future research on nanofluid flows.

Nonsimilar analysis of ternary hybrid Eyring–Powell nanofluid flow over a linearly stretching surface

Purpose This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.Design/methodology/approach The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.Findings The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.Originality/value The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.

Nonsimilar mixed convection analysis of ternary hybrid nanofluid flow near stagnation point over vertical Riga plate

PurposeThis work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al2O3), silicon dioxide (SiO2) and titanium dioxide (TiO2) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.Design/methodology/approachThrough the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.FindingsNumerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.Originality/valueThe fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

Unsteady magneto bioconvective Sutterby nanofluid flow: Influence of g-Jitter effect

This study is driven by the potential applications of a microgravity environment in various sectors and fields of engineering, especially in the manufacturing of semiconductors. An electrically conducting bioconvective Sutterby nanofluid flow was considered around an exponentially stretching surface through g-Jitter and nonlinear thermal radiation effects. The dimensional partial differential equations (PDEs) that govern the fluid flow system are changed into nondimensional PDEs through nonsimilar transformations. Once these PDEs have been linearized using Quasilinearization, the implicit finite difference scheme is used to solve them numerically. A MATLAB code was constructed for the numerical calculations and for analysing the results via graphs. These findings indicate that the greater values of amplitude ε1 result in a steep rise in the velocity and surface drag near the sheet's wall for assisting buoyancy. An enhancement of approximately 108 % in the drag coefficient is observed when ε1(the amplitude in g-Jitter) jumps to 1 from 0. The percentile increments in heat transport strength due to the rise of radiation Rd from 1 to 2 is 80 %, and due to the intensification of the temperature difference ratio φw from 1.5 to 2 is about 167 %. Elevating Peclet number Pe led to the depletion of the microbial boundary layer thickness. Oxytactic microbes' presence impacts the enhanced mass transport strength of nanoparticles. The current findings have been validated by comparing them to previously published results, and they have been shown to be in perfect agreement with those results.

Finite element analysis of MHD naturally convective flow past an exponentially accelerated plate with viscous dissipation

The MHD finite element analysis naturally convective flow across an exponentially accelerating plate with viscous dissipation is investigated numerically. In this process dimensional partial differential equations are changed to dimensional less form. The Galerkin finite element method is emerged to solve non-dimensional partial differential equations. Obtained results are effectively depicted through the utilization of graphs, allowing for a comprehensive understanding of the impact that different physical parameters on primary velocity, transverse velocity, temperature, and concentration profiles. The study effectively differentiated between the present and prior findings, ultimately demonstrating a strong consensus of excellent agreement between the results. The key findings of this study are: The primary velocity increases on growing the values of Thermal Grashof number, Solutal Grashof number, Eckert number, and Dufour number and decreases on climb up the values of Magnetic parameter, Prandtl number, Schmidt number, and Hall parameter. The secondary velocity increases on raising the values of Thermal Grashof number and Solutal Grashof number and diminishes on enhancing the value of Hall parameter. The temperature increases on increasing the values Eckert number and Dufour number and decreases on improving the value of Prandtl number. The concentration decreases on increasing the value of Schmidt number.

Numerical Computation of Williamson Hybrid Nanofluid Flow Over the Curved Surfaces With Effects of Thermal Radiation

Abstract The current investigation is based on Williamson's features of a hybrid nanofluid flow over a curved surface made mixture of silver (Ag) and titanium dioxide (TiO2) with engine oil. Under the presumption of a low magnetic Reynolds number, a constant homogenous magnetic field is applied. Consideration is given to the ramping temperature and the time-varying surface concentration. Thermal absorption and first-order consistent chemical reaction are also taken into account. To create a hybrid nanofluid, silver (Ag), and titanium nanoparticles are dispersed in a base fluid made of water and engine oil. Quasi-linearization technique and Finite difference scheme are employed on the nondimensional partial differential equations. All physical parameters of practical importance, such as velocity, temperature, and concentration profile are analyzed and provided in tables and graphs along with the impact of physical parameters. As the Williamson parameter (W) increases, the surface velocity of the steep plate decreases. Also, as the parameter temperature ratio of Nt and Rd increases, the forces opposing the flow field reduce the friction force, and the thermal field increases with temperature effects.

Analysis of mixed convective-radiative heat transfer in a porous square cavity filled with various nanofluids

The present study examines the numerical simulation of mixed convective fluid movement and heat transference within the square cavity with various nanofluids. In this work, the nanofluids are prepared by suspending zinc oxide (ZnO)/silicon dioxide nanoparticles into water /kerosene /ethylene glycol base liquids. Features of various nanofluids flow inside cavity are investigated and this kind of studies may be useful in automobile applications and electrical gadgets. The vertical walls of the cavity are hot, the bottom wall is partially cooled, and the top wall is considered to be adiabatic. The Marker-And-Cell (MAC) method is utilized to solve the governing non-dimensional partial differential equations. The impact of heat generation/absorption (Q), nanoparticle volume fraction Darcy number (Da), Richardson number (Ri), Reynolds number (Re), and the thermal radiation parameter (Rd) are scrutinized. The outcomes are displayed informs of streamlines, isotherms, and local and average Nusselt numbers. The comparative study is performed and it finds a good accordance with the literature. As fluid flow and heat transfer are concerned, ZnO-Ethylene Glycol(EG) nanofluid explores the optimum features among the considered nanofluids. When 5% ZnO/SiO 2 nanoparticles are suspended into water, compared to SiO 2-water nanofluid, ZnO-water nanofluid has more than 10.81% mean rate of heat transmission. Suspension of 5% ZnO in water/kerosene/EG has the tendency to enhance the mean heat transfer rates of water/kerosene/EG up to respectively. The highest mean heat transfer rate is attained when the cavity’s aspect ratio is fixed as 1:1.

Effect of thermal radiation on nonDarcy hydromagnetic convective heat and mass transfer flow of a water–SWCNT’s and MWCNT’s nanofluids in a cylindrical annulus with thermo-diffusion and chemical reaction

The examined through analysis of the movement of water-based single wall carbon nanotube (SWCNT) and multiwall carbon nanotube (MWCNT) nanofluids in a coordinate annulated zone under influence of non-uniform heat source/sink. By imposing the appropriate nondimensional variables, the governing partial differential equations are converted into a system of coupled nondimensional partial differential equations. By means of the usage of quadratic polynomials and the Galerkin finite element detail approach, the nonlinear equations have been executed. The expressions representing fluid velocity, temperature and concentration are discussed graphically. While skin friction, heat transfer and mass transfer are revealed in tabular structure. The proposed scheme is shown to have faster convergence than the existing scheme with excellent accuracy. Various parametric values have been analyzed and observed that higher temperatures and concentrations are produced with lower velocities with and bigger velocities with higher radiative heat flux or nanoparticle volume fraction.

A Numerical Assessment of Time-Dependent Magneto-Convective Thermal-Material Transfer over a Vertical Permeable Plate

The objective of this work is to investigate the influences of thermal radiation, heat generation, and buoyancy force on the time-dependent boundary layer (BL) flow across a vertical permeable plate. The fluid is unsteady, incompressible, viscous, and electrically insulating. The heat transfer mechanism happens due to free convection. The nondimensional partial differential equations of continuity, momentum, energy, and concentration are discussed using appropriate transformations. The impressions of thermal radiation and buoyancy forces are exposed in the energy and momentum equation, respectively. For numerical model, a set of nonlinear dimensionless partial differential equations can be solved using an explicit finite difference approach. The stability and convergence analyses are also established to complete the formulation of the model. The thermophysical effects of entering physical parameters on the flow, thermal, and material fields are analyzed. The variations in local and average skin friction, material, and heat transfer rates are also discussed for the physical interest. The analysis of the obtained findings is shown graphically, and relevant parameters pointedly prejudice the flow field. Studio Developer FORTRAN 6.2 and Tecplot 10.0 are applied to simulate the schematic model equations and graphical presentation numerically. The intensifying values of the magnetic field are affected decreasingly in the flow field. The temperature profiles decrease within the BL to increase the value of radiation parameters. The present study is on the consequences for petroleum engineering, agriculture engineering, extraction, purification processes, nuclear power plants, gas turbines, etc. To see the rationality of the present research, we compare these results and the results available in the literature with outstanding compatibility.

Diffusion effects on mixed convective peristaltic flow of a bi-viscous Bingham nanofluid through a porous medium with convective boundary conditions

The study of heat transfer and peristaltic pumping of magnetohydrodynamic biofluids has many physiological applications, such as heart–lung machines during surgeries, dialysis, vitamin injections, and cancer treatment. Also, it has many industrial applications, such as pharmaceutical fluid production, filtration, and dispensing cosmetic/glue emulsions with no contamination. Furthermore, the bi-viscous Bingham nanofluid model is the best for several bio/industrial fluids. Therefore, the impact of Hall current, thermal radiation, and cross-diffusion on the mixed convection peristaltic pumping of a bi-viscous Bingham nanofluid in a porous medium is considered. Also, we focus on the flexibility of the walls along with the convective boundary conditions. We adopted the lubrication strategy to reduce the system’s complexity. The system of non-dimensional partial differential equations along with the pertinent boundary conditions is solved by using a regular perturbation method (RPM) for several sets of values of the dimensionless parameters. The expressions for the temperature, concentration, velocity, and heat transfer coefficient are obtained analytically. The impact of the relevant parameters on the velocity, temperature, coefficient of heat transfer, concentration, skin friction coefficient, Nusselt number, and trapping is discussed in depth with the help of graphical illustrations and tables. The results indicate that the velocity distribution is reduced with growing Darcy parameter and concentration Grashof number. Intensifying the magnetic parameter results in shrinking the trapped bolus. Decay in the heat transfer coefficient is observed for rising values of the radiation parameter. The current findings are compared with the existing studies in the literature and are found to agree very well for special cases. Moreover, the closed form solution (RPM) is compared with the numerical solution (BVC5C, MATLAB) for validation.

Entropy generation on chemically reactive hydromagnetic oscillating flow of third grade nanofluid in a porous channel with Cattaneo-Christov heat flux

The heat and mass transfer characteristics along with Cattaneo-Christov heat flux on oscillating hydromagnetic flow of third grade nanofluid through a permeable channel under entropy generation analysis have been examined in this paper. The impacts of chemical reaction, Brownian motion, thermophoresis, Ohmic heating, and radiative heat have also been taken into consideration. The Buongiorno nanofluid model has been utilized for the present analysis.The investigation related to the present study is helpful in biomedical engineering, manufacturing industries as coolants, energy conservation, cancer treatments (like hyperthermia), dynamics of physiological fluids, biomedicines, and nano-drug suspension in pharmaceuticals. The system of nonlinear ordinary differential equations (ODEs) have been attained and solved by applying the Runge-Kutta 4th order method with the help of shooting process after the execution of the perturbation procedure on nondimensional partial differential equations (PDEs). The results of the present study have been deliberated by plotting graphs for the effects of various non-dimensional parameters on entropy, Bejan number, concentration, velocity, and temperature. The numerical values of heat and mass transfer rates for different physical parameters have been computed.

Note on the Numerical Solutions of Unsteady Flow and Heat Transfer of Jeffrey Fluid Past Stretching Sheet with Soret and Dufour Effects

A numerical investigation of unsteady boundary layer flow with heat and mass transfer of non-Newtonian fluid model, namely, Jeffrey fluid subject, to the significance of Soret and Dufour effects is carried out by using the local nonsimilarity method and homotopy analysis method. An excellent agreement in the numerical results obtained by both methods is observed and we establish a new mathematical approach to obtain the solutions of unsteady-state flow with heat and mass transfer phenomenons. Similarity transformation is applied to governing boundary layer partial differential equations to obtain the set of self-similar, nondimensional partial differential equations. Graphical results for different emerging parameters are discussed. The dimensionless quantities of interest skin friction coefficient, Sherwood number, and Nusselt number are discussed through tabulated results. The main novelty of the current work is that the average residual error of the mth-order approximation of the OHAM scheme for steady-state solution is decreased for higher-order approximation. Further, a rapid development of the boundary layer thickness with the increasing values of dimensionless time τ is observed. It is noted that for large values of τ, the steady state in the flow pattern is gained. It is worth mentioning that the magnitude of Sherwood number is increased with the increasing values of Schmidt number Sc and Dufour number Df. The magnitude of local Nisselt number is increased for the increasing values of Soret number, Sr.

Heat and Mass Transfer Analysis of MHD Jeffrey Fluid over a Vertical Plate with CPC Fractional Derivative

Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter β,γ→1, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.

Radiative Magnetohydrodynamic Flow Over a Vertical Cone Filled With Convective Nanofluid

This article describes the magnetohydrodynamic radiative nano convective flow over a cone. Brownian motion and thermophoresis effects in nanofluid transport R-K method is used to compute the solutions to the governing non-dimensional partial differential conservation equations and free stream boundary conditions. Numerous thermo-physical parameters were presented, There is a detailed explanation of the simulations as well. Magnetic parameter increases, reduce velocity. According to the findings, there are numerous applications for heat exchanger technology, including geothermal energy storage and cooling, solar energy systems, and materials processing.

MHD flow of a nanofluid due to a nonlinear stretching/shrinking sheet with a convective boundary condition: Tiwari–Das nanofluid model

PurposeNanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.Design/methodology/approachThe mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.FindingsFor a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.Originality/valueThe present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.

Double Diffusive Magneto-Free-Convection Flow of Oldroyd-B Fluid over a Vertical Plate with Heat and Mass Flux

The purpose of this research is to analyze the general equations of double diffusive magneto-free convection in an Oldroyd-B fluid flow based on the fundamental symmetry that are presented in non-dimensional form and are applied to a moving heated vertical plate as the boundary layer flow up, with the existence of an external magnetic field that is either moving or fixed consistent with the plate. The thermal transport phenomenon in the presence of constant concentration, coupled with a first order chemical reaction under the exponential heating of the symmetry of fluid flow, is analyzed. The Laplace transform method is applied symmetrically to tackle the non-dimensional partial differential equations for velocity, mass and energy. The contribution of mass, thermal and mechanical components on the dynamics of fluid are presented and discussed independently. An interesting property regarding the behavior of the fluid velocity is found when the movement is observed in the magnetic intensity along with the plate. In that situation, the fluid velocity is not zero when it is far and away from the plate. Moreover, the heat transfer aspects, flow dynamics and their credence on the parameters are drawn out by graphical illustrations. Furthermore, some special cases for the movement of the plate are also studied.

Fractional Modeling of Viscous Fluid over a Moveable Inclined Plate Subject to Exponential Heating with Singular and Non-Singular Kernels

In this paper, a new approach to investigating the unsteady natural convection flow of viscous fluid over a moveable inclined plate with exponential heating is carried out. The mathematical modeling is based on fractional treatment of the governing equation subject to the temperature, velocity and concentration field. Innovative definitions of time fractional operators with singular and non-singular kernels have been working on the developed constitutive mass, energy and momentum equations. The fractionalized analytical solutions based on special functions are obtained by using Laplace transform method to tackle the non-dimensional partial differential equations for velocity, mass and energy. Our results propose that by increasing the value of the Schimdth number and Prandtl number the concentration and temperature profiles decreased, respectively. The presence of a Prandtl number increases the thermal conductivity and reflects the control of thickness of momentum. The experimental results for flow features are shown in graphs over a limited period of time for various parameters. Furthermore, some special cases for the movement of the plate are also studied and results are demonstrated graphically via Mathcad-15 software.