Magnetohydrodynamic Casson Fluid Research Articles

MHD Casson Fluid Flow over a Stretching Surface with Suction, Double Stratification, and Heat and Mass Transfer Effects

Abstract In this article, we investigated the flow of a magnetohydrodynamic Casson fluid across an extending surface with exponential permeability in a double-stratified medium. Thermal radiation, suction, heat sources, viscous dissipation, and chemical reactions drive the stream field. We converted the flow describing partial differential equations into terms of ordinary differential equations by applying appropriate transformations. Next, we utilised the bvp4c package in Matlab to obtain numerical solutions for these equations. We explored and graphically showed the implications of different non-dimensional governing parameters for temperature, concentration, and velocity profiles. After analysis, we provide a tabular presentation of the friction factor, Nusselt, and Sherwood numbers. The Casson fluid temperature shows a rising trend for the solutal stratification parameter and a decreasing trend for the thermal stratification parameter, while the Casson fluid velocity shows a declining trend towards both of these parameters. The Casson fluid concentration also behaves differently depending on the stratification parameter; for example, it increases for thermal stratification and decreases for solutal stratification. We notice that an increase in the Casson parameter's value suppresses the velocity field. However, as the Casson parameter increases, both the temperature and the concentration improve. Furthermore, comparisons with previously published findings also support the current results. \sethlcolor{yellow}\hl{The study of MHD Casson fluid flow that includes suction, dual stratification, and the effects of heat and mass transfer is very useful in many areas, such as polymer processing, metallurgical engineering, biomedical applications, environmental sciences, and advanced cooling technologies.

Advanced modelling techniques for magnetohydrodynamic Casson fluid squeezing flow via generalized fractional operators with neural network scheme

Abstract This paper aims to simulate and examine the unstable squeezed circulation of fractional-order (FO) magnetohydrodynamic (MHD) Casson fluid via a permeable medium. The Casson fluid system performs an essential role in comprehending the characteristics of non-Newtonian fluids, including toothpaste, condiments, printing substances and plasma circulation. The outcomes of this investigation are significant because previous research has not addressed the unsteady circulation of Casson fluid in a fractional nonsingular kernel and neural network-based stochastic context, considering the indicated consequences. An exceptionally dynamic ordinary differential equation is produced by using fractional calculus in combination with similarity transforms. After that, the predicted problem is addressed employing an amalgam of the Laplace transform in the Caputo-Fabrizio, modified Atangana-Baleanu-Caputo fractional derivatives operators, and the $q$-homotopy analysis transform method, accompanied by no-slip boundary requirements. The responses and oversights at various points in the FOs are scrutinized, along with previous findings, in order to ensure reliability. In terms of precision, $q$-HATM findings outperform other outcomes that are accessible in research. The focus of this research is on the influence of FOs on the velocity distribution, skin friction coefficient (SFC) and practices of relevant fluid factors. To find out how relevant fluid components affect the velocity distribution and SFC, an extensive, qualitative and visual evaluation is carried out. It was discovered through evaluation that the FO shows an analogous impact for both positive and negative squeezing numbers. Additionally, as the FO increases, SFC reduces. Analysis revealed that the FO exhibits a similar effect with regard to positive and negative compression numbers. Furthermore, SFC decreases with increasing FOs. Additionally, a highly effective stochastic method employing artificial neural networks (ANNs) and a back-propagated Levenberg-Marquardt (BPLM) procedure is generated to explore the effect of different parameter modifications on the SFC, velocity distribution, as well as various fluid factors. Multiple effectiveness measures were developed according to mean absolute deviations (MAD), erroneous Nash-Sutcliffe effectiveness (ENSE), and Theil's inequity coefficient (TIC) in order to verify the preciseness, productivity, and computing cost of the ANN-BPLM algorithms. The outlined scheme's analytical findings are verified through comparison using numerical outcomes obtained through the $q$-HATM, artificial intelligence strategies like NARX-LM, and the least squares methodology (LSM). The outcomes indicate the resilience and accuracy of the layout procedure by demonstrating that the average percentage of errors in our proposed outcomes in terms of ENSE, TIC, and MAD is nearly zero.

The comprehensive analysis of magnetohydrodynamic Casson fluid flow with rectangular porous medium through expanding/contracting channel

PurposeThis study examines fluid flow within a rectangular porous medium bounded by walls capable of expansion or contraction. It focuses on a non-Newtonian fluid with Casson characteristics, incompressibility, and electrical conductivity, demonstrating temperature-dependent impacts on viscosity.Design/methodology/approachThe flow is two-dimensional, unsteady, and laminar, influenced by a small electromagnetic force and electrical conductivity. The Hybrid Analytical and Numerical Method (HAN method) resolves the constitutive differential equations.FindingsThe fluid’s velocity is influenced by the Casson parameter, viscosity variation parameter, and resistive force, while the fluid’s temperature is affected by the radiation parameter, Prandtl number, and power-law index. Increasing the Casson parameter from 0.1 to 50 results in a 4.699% increase in maximum fluid velocity and a 0.123% increase in average velocity. Viscosity variation from 0 to 15 decreases average velocity by 1.42%. Wall expansion (a from −4 to 4) increases maximum velocity by 19.07% and average velocity by 1.09%. The average fluid temperature increases by 100.92% with wall expansion and decreases by 51.47% with a Prandtl number change from 0 to 7.Originality/valueUnderstanding fluid dynamics in various environments is crucial for engineering and natural systems. This research emphasizes the critical role of wall movements in fluid dynamics and offers valuable insights for designing systems requiring fluid flow and heat transfer. The study presents new findings on heat transfer and fluid flow in a rectangular channel with two parallel, porous walls capable of expansion and contraction, which have not been previously reported.

An Analytical Analysis of Mixed Convective MHD Casson Flow with Ramped Wall Temperature

This research discusses the behavior of magnetohydrodynamic Casson fluid subjected to a ramped wall temperature along an infinitely inclined plate. Non-Newtonian fluid, specifically the Casson fluid, is employed to characterize fluid behavior in this research. The effects of porous media, chemical reactions, and radiation are considered. In practical applications, non-Newtonian fluids find use in lubrication such as grease, engine oil, etc. The Laplace transform technique has been applied during this study where ordinary differential equations are converted from the governing partial differential equations with suitable boundary conditions. These transformed dimensionless equations are subsequently solved numerically with Mathematica, and we have achieved the exact solutions of momentum, followed by energy and finally concentration. In the results section, we have analyzed the behavior of flow features under varying conditions of key parameters, including the governing parameters, the unsteadiness parameter, and the Casson parameter. All the results are shown and analyzed in graphs.

Non-similar solution of Casson fluid flow over a curved stretching surface with viscous dissipation; Artificial neural network analysis

PurposeThe main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.Design/methodology/approachThe non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.FindingsThe results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.Originality/valueAI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

A numerical study on MHD Casson fluid flow in a non-uniform rough channel with temperature-dependent properties using OHAM

This study explores the complex dynamics of magnetohydrodynamic (MHD) Casson fluid in a non-uniform rough channel, focusing on the effects of temperature-dependent viscosity and variable thermal conductivity under no-slip boundary conditions. The study employs an innovative approach by utilising a rough surface with irregular textures to analyse flow patterns and assess drag forces on channel objects. A novel mathematical model, governed by continuity, momentum, and heat transfer equations, is developed and transformed into dimensionless, nonlinear Ordinary Differential Equations (ODEs) using non-dimensional quantities and fundamental assumptions. The Optimal Homotopy Analysis Method (OHAM) is applied to solve these equations to enhance convergence speed and accuracy. The research explores the impact of surface roughness on velocity profiles and temperature distributions under various physical constraints. Numerical simulations are conducted to determine skin friction coefficients and Nusselt numbers. Furthermore, the study examines the influence of confined boluses on fluid flow in diverse physiological conditions. A comprehensive analysis is performed to elucidate the combined effects of surface roughness on fluid passage, including flow separation, pattern alterations, pressure distribution and drop, heat transfer characteristics, and flow resistance. The intricate interplay between temperature-dependent viscosity, varying thermal conductivity, and surface roughness is thoroughly investigated to explain the complex dynamics of MHD Casson fluid movement in non-uniform channels. Implementing a magnetic field over the rough, non-uniform channel is found to provide stability and prevent fluid overflow. This research has significant real-world applications, including soil erosion prevention, blood flow regulation in arteries, and optimisation of hydropower channels and penstocks. By enhancing our understanding of flow dynamics through rough and non-uniform channels, this study contributes valuable insights into both theoretical fluid mechanics and practical engineering applications.

Effect of Thermal Radiation on Fractional MHD Casson Flow with the Help of Fractional Operator

This study examines the effects of Newtonian heating along with heat generation, and thermal radiation on magnetohydrodynamic Casson fluid over a vertical plate. At the boundary, the Newtonian heating phenomena has been employed. The problem is split into two sections for this reason: momentum equation and energy equations. To transform the equations of the given model into dimensionless equations, some particular dimensionless parameters are defined. In this article, generalized Fourier’s law and the recently proposed Caputo Fabrizio fractional operator are applied. The corresponding results of non-dimensional velocity and heat equations can be identified through the application of Laplace transform. Moreover, Tzou’s algorithm as well as Stehfest’s algorithm is implemented to recognize the inverted Laplace transform of heat and momentum equations. Finally, a graphical sketch is created using Mathcad 15 software to demonstrate the results of numerous physical characteristics. It has been reported that the heat and velocity drop with rising Prandtl number values, whereas the fluid’s velocity has been seen to rise with increasing Grashof number values. Additionally, current research has shown that flow velocity and temperature increase with rising values of a fractional parameter.

Exact solutions of non-singularized MHD Casson fluid with ramped conditions: A comparative study

The study of magnetohydrodynamic (MHD) fluids has significant implications across various scientific disciplines, particularly in understanding complex phenomena in astrophysics, engineering, and geophysics. The Casson fluid model stands as a crucial tool for describing non-Newtonian behaviors observed in certain fluid systems. The current work shows an analytical analysis to determine the ramped effect on the fractionalized MHD Casson fluid over an vertical plate. Fractional partial differential equations are used to formulate the problem along with initial and boundary conditions. The governing equations are transformed into the dimensionless form and developed fractional models like Caputo-Fabrizio and Atangana-Baleanu Derivative. We used the Laplace transform technique to find the closed form solution of the dimensionless governing equation analytically. MATHCAD software is being used for numerical computations and the physical attributes of material and fractional parameters are discussed. To analyze their behavior clearly, two-dimensional graphical results are plotted for velocity profile and temperature as well. It has been concluded that the fluid’s velocity are reduced for larger values of the fractional parameter and Prandtl number and is maximum for small values of both parameters.

Magnetohydrodynamics bio-convection flow at Casson fluid stagnation point in porous medium: Cross-diffusion effect and heat production

This study examines the effect of heat production and radiation absorption on the magnetohydrodynamic Casson fluid flow at the stagnation point in a porous medium. We convert the group of fluid flow equations, which are non-linear partial differential equations with suitable boundary constraints, into a set of non-linear ordinary differential equations using similarity transformations. The homotopy analysis method (HAM) solves the converted system of ordinary differential equations. We draw graphs for numerous values of non-dimensional parameters and tables of surface drag force, rates of heat transfer, and mass transfer to analyze the relationship between velocity field, temperature field, concentration field, and other essential parameters involved in the study. We have proven that the Dufour number, radiation parameter, and heat generation parameter elevate the fluid temperature, whereas the magnetic parameter lowers it. The Casson fluid parameter, buoyancy force parameter, and mixed convection parameter all promote fluid movement throughout the flow field. The presented tabular data allows us to see the trend of heat and mass transfer rates, as well as drag force rates, against important parameters, enhancing our understanding of these rates.

Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach

The present analysis examines the magnetohydrodynamic (MHD) flow of non-Newtonian Casson fluid on an exponentially shrinking surface under constant and exponentially varying wall temperature with suction. The main objective is to investigate multiple solutions of self-similar coupled nonlinear ordinary differential equations derived semi-numerically via the shifted Chebyshev collocation approach. The occurrence of a dual solution is found and variations in the velocity and temperature profiles are analyzed under different physical flow governing factors. The stability analysis is performed and it confirms that the first solution is stable and the second solution is unstable. The obtained results are confirmed by comparing them with earlier published results and show good agreement. The skin friction coefficient and wall temperature gradient increase for the first solution and decline for the second solution with enhancement in Hartmann number and suction parameter in case of exponentially varying surface temperature. Whereas, for constant surface temperature, increasing the Hartmann number and suction parameter results in the intensification of the wall temperature gradient. The velocity and temperature profiles decrease with improving the Casson parameter. As the Prandtl number strengthens, the heat transfer rate in a constant surface temperature situation is comparatively higher than exponentially varying surface temperature situation.

Series solution of time-fractional mhd viscoelastic model through non-local kernel approach

The study of ramped condition in the context of unsteady incompressible magnetohydrodynamic Casson fluid flow over a moving vertical plate is a complex and important topic in fluid dynamics and heat transfer. This scenario combines several physical phenomena and has practical applications in various engineering and scientific fields. In this study, Casson fluid is considered unsteady under the influence of magnetic field. The fractional mathematical model is proposed by considering the effect of chemical reaction parameter of the flowing fluid. The governing equations are transformed into the dimensionless form and developed fractional models like Caputo-Fabrizio and Atangana-Baleanu Derivative. We used the Laplace transform technique to find the solution of the dimensionless governing equation analytically. The transformed solutions for velocity, energy and momentum balances developed in terms of series. MATHCAD software is being used for numerical computations and the physical attributes of material and fractional parameters are discussed. To analyze their behavior clearly, two-dimensional graphical results are plotted for velocity profile and temperature as well. It has been concluded that the fluid’s velocity are reduced for larger values of the fractional parameter and Prandtl number and is maximum for small values of both parameters. Further, the velocity behavior becomes larger for isothermal condition as compared to ramped conditions.

Effects of viscous dissipation, gravity modulation and Joule heating on MHD Casson fluid flow over a vertically moving plate with second-order slip velocity

The study of magnetohydrodynamic flow problems for non-Newtonian fluids is significant in many engineering problems. The current inquiry is concerned with a time-dependent, incompressible magnetohydrodynamic Casson fluid flow in a vertically moving plate. The aim of this study is to analyse the effect of viscous dissipation, gravity modulation, heat source and Joule heating with second-order slip velocity. Governing equations are converted to non-dimensional ones using appropriate similarity transformations. To solve the altered equations, the perturbation method is applied, together with MATLAB software. The important physical outcome of this research is that the gravity modulation parameter increases the temperature and velocity of fluid inside the boundary layer. The Eckert number enhances the fluid velocity, concentration boundary layer, skin friction and Nusselt number, whereas the temperature boundary layer reduces for heat sink parameter. The permeability of the porous parameter raises the fluid’s concentration. The work of Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] has been expanded in this study by adding the novel effects of gravity modulation, Joule heating and viscous dissipation. In addition, the boundary condition includes second-order slip velocity. The obtained results are compared with Kodi et al. [2021. “Investigation of MHD Casson Fluid Flow Past a Vertical Porous Plate Under the Influence of Thermal Diffusion and Chemical Reaction.” Heat Transfer 51 (1): 377–394] and it shows an excellent agreement when added effects are neglected.

Implementing the multistep adams-bashforth numerical approach on magnetohydrodynamic radiated casson fluid with darcy forchheimer, dissipation and activation energy

The main goal behind the conduction of this work is to use the Adams-Bashforth method in the field of fluid dynamics to solve the Navier–Stokes equations based on the boundary layer flow of magnetohydrodynamic Casson fluid passing on the upper horizontal parabolic surface with variable fluid characteristics and Darcy-Forchheimer effect. The temperature flow rate and mass rate are also investigated with the help of thermal radiation, viscous dissipation, heat generation and activation energy. The Adams-Bashforth technique is widely used in numerical analysis, scientific computing, fluid dynamics, chemical kinetics, astrophysics and is particularly useful in solving the stiff ODEs, where other methods may fail to converge. It is particularly useful for simulating the flow of fluids around complex geometries, such as aircraft wings or turbine blade. The equations of basic governing laws (Momentum, temperature and concentration) are achieved in the form of PDE’s. These PDEs are then transmuted into ODEs via similarity variables and the numerical behaviors of these ODEs are obtained with Adam-Bashforth (Predictor-Corrector) along with RK-4 technique on the Matlab software. The initial guesses are modified by using secant method. Graphical analyses are used to explain how different parameters affect the temperature, velocity and mass transport rate. The finding of results revealed that the inertia coefficient, Hartmann number and fluid parameter make the decrement in the velocity field. The amplification in temperature of fluid is noted for varying the radiation coefficient, dissipation and thermal generation coefficient. The solutal field drops due to activation energy and reaction coefficient. The findings are useful to observe the flow attributes, behaviors and helpful in the designing of thermal equipment in the thermal industries.

A Fractional Study of MHD Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel

Abstract The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang–Abdel-Aty–Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u 0. The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as α, β, Pr , Q, Gr, M, Nr and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.

MHD Casson Fluid Flow in Stagnation-Point over an Inclined Porous Surface

Motivated by the need to comprehend and optimize complex fluid flow phenomena in various engineering and industrial applications, this paper investigates the magnetohydrodynamic (MHD) Casson fluid flow characteristics in the vicinity of a stagnation point over an inclined porous surface. The study addresses the interplay of permeability, viscous dissipation, buoyancy, and volumetric heat source, chemical reaction of the diffusion species, thermal slip, and obliqueness at the bounding surface. The governing equations are transformed into a dimensionless form using appropriate similarity transformations. The resulting nonlinear ordinary differential equations are solved numerically using the fourth-order Runge-Kutta method, coupled with the shooting technique as coded into the bvp4c solver of MATLAB 2021a. Findings from this study show that instability arises due to reduced velocity at low permeability, and Biot number enhances the Newtonian cooling at the surface, a requirement for the design of heat exchangers.

Heat transfer in MHD convective stagnation point flow over a stretching surface with thermal radiations

In this study, we have conducted an analysis of steady, incompressible, and magnetohydrodynamic (MHD) Casson fluid flow over a stretching sheet. The primary focus of this research is to investigate the effects of thermal radiation and velocity slip along a stretching sheet. The governing equations for this study are a system of Partial Differential Equations (PDEs) that converted to the Ordinary Differential Equations (ODEs) using similarity transformations. To solve these equations, we have employed the RK–Fehlberg method for solving ordinary differential equations. Governing equations are discretized using the RK–Fehlberg method, and the resulting system of algebraic equations is solved iteratively. These simulations have been conducted under various flow and heat transfer conditions, including variations in the convective number, Prandtl number, and diffusion parameter. The analysis of our results reveals several important findings. Increasing the chemical reaction parameter has been found to reduce the thickness of the concentration boundary layer, while an increase in the Schmidt number leads to an expansion of this boundary layer. These findings are critical for understanding heat transfer in stagnation point flow over a stretching sheet, and they encompass aspects such as temperature distribution, heat transfer rates, boundary layer characteristics, velocity profiles, and the potential for implementing heat transfer enhancement techniques.

Radiation Absorption and Diffusion Thermo Effects on Unsteady MHD Casson Fluid Flow Past a Moving Inclined Plate Embedded in Porous Medium in the Presence of Chemical Reaction and Thermal Radiation

The aim of the present paper is to investigate the effects of Radiation absorption and diffusion thermo on unsteady magnetohydrodynamic Casson fluid flow past an inclined permeable moving plate in Presence of thermal radiation, heat absorption and homogenous chemical reaction. The plate is assumed to be embedded in a uniform porous medium and Moves with a constant velocity in the flow direction in the presence of a transverse magnetic Field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. Also discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity and temperature distribution is observed to increase with an increase in radiation absorption and Dufour parameter, whereas diminishes with enhances of Magnetic field, heat absorption coefficient, radiation parameter and chemical reaction parameter in respective velocity, temperature and concentration distributions.

Numerical examination of the Darcy–Forchheimer Casson model with instigation energy and second-order momentum slip: Thermal features

In this study, the Darcy–Forchheimer model is examined in relation to magnetohydrodynamic (MHD) Casson fluid flow over a stretchable exponential surface. The investigation incorporates several factors not previously considered, including Arrhenius activation/instigation energy, second-order slip, Joule heating, thermal radiation, viscous dissipation, and chemical reactions. The Darcy–Forchheimer model is employed to characterize flows within permeable materials under the influence of instigation energy. Additionally, we analyze the electrically conducting flows induced by an exponentially stretched and dissipated sheet. To transform the partial differential equations (PDEs) into ordinary differential equations (ODEs), appropriate similarity transformations are applied. Numerical and graphical results are presented using the Lobatto IIIA technique across various system scenarios, demonstrating the effectiveness of this approach as a reliable, accurate, and viable solver. Through the utilization of the BVP4C technique in MATLAB, a numerical representation of the formulation is achieved. Graphs are generated, illustrating the variations in ongoing parameters such as concentration velocity. This velocity increases with higher values of E and Γ , but decreases with σ . The fluid temperature rises with larger values of R , and it responds positively to first-order slip while decreasing with second-order slip.

Numerical study of transient chemical reactive magnetized Casson fluid flow in the presence of Newtonian heating

ABSTRACT The numerical results of transient magnetohydrodynamic (MHD) Casson fluid flow under Soret-Dufour aspects are illustrated in this research. The governing dimensional equations of considered Casson fluids are first converted into dimensionless partial differential equations (PDEs) by utilizing the proper similar variables. The obtained system is then computed through the finite element method (FEM). The impact of dimensionless parameters is visualized on fluid velocity, skin friction, temperature, Nusselt number, concentration, and Sherwood number through the curves and tables. Both the temperature and velocity are risen against the higher Dufour number. It has been observed that the velocity profiles step up with the increment in various parameters. Comparisons are made with the available results in the open literature. These results are in good agreement with the previously published reports.

Multiple Lie symmetry solutions for effects of viscous on magnetohydrodynamic flow and heat transfer in non-Newtonian thin film

Abstract Numerous flow and heat transfer studies have relied on the construction of similarity transformations which map the nonlinear partial differential equations (PDEs) describing the flow and heat transfer, to ordinary differential equations (ODEs). For these reduced equations, one finds multiple analytic and approximate solution procedures as compared to the flow PDEs. Here, we aim at constructing multiple classes of similarity transformations that are different from those already existing in the literature. We adopt the Lie symmetry method to derive these new similarity transformations which reveal new classes of ODEs corresponding to flow equations when applied to them. With these multiple classes of similarity transformations, one finds multiple reductions in the flow PDEs to ODEs. On solving these ODEs analytically or numerically, we obtain different kinds of flow and heat transfer patterns that help in determining optimized solutions in accordance with the physical requirements of a problem. For the said purpose, we derive Lie point symmetries for the magnetohydrodynamic Casson fluid flow and heat transfer in a thin film on an unsteady stretching sheet with viscous dissipation. Linear combinations of these Lie symmetries that are again the Lie symmetries of the flow model are employed here to construct new similarity transformations. We derive multiple Lie similarity transformations through the proposed procedure which lead us to more than one class of reduced ODEs obtained by applying the deduced transformations. We analyze the flow and heat transfer by deriving analytic solutions for the obtained classes of systems of ODEs using the homotopy analysis method. Magnetic parameters and viscous dissipation influences on the flow and heat transports are investigated and presented in graphical and tabulated formats.