Mair Khan, T. Salahuddin, Muhammad Malik Yousaf, Farzana Khan and Arif Hussain
The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of…
Abstract
Purpose
The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.
Design/methodology/approach
A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.
Findings
The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.
Originality/value
This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.
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M.Y. Malik, Arif Hussain, T. Salahuddin and M. Awais
– The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.
Abstract
Purpose
The purpose of this paper is to examine the Sisko fluid model over a stretching cylinder with heat transfer and magnetohydrodynamics.
Design/methodology/approach
The boundary layer approach is employed to simplify the governing equations. Suitable similarity transformations are used to transform the governing partial differential equations into ordinary differential equations. In order to solve this system of ordinary differential equations numerically, shooting method in conjunction with Runge-Kutta-Fehlberg method is used.
Findings
The effects of physical parameters involved in velocity and temperature profiles are shown through graphs. It is observed that Sisko fluid parameter and curvature parameter enhances fluid velocity while motion of fluid is retarded by increasing magnetic field strength. Additionally temperature of fluid raise with curvature parameter while it fall down for larger values of Prandtl number. Skin friction coefficient and Nusselt number are computed and presented in graphs and tables for further analysis. It can be seen that curvature parameter increases both skin friction and Nusselt number while magnetic field and Prandtl number decayed skin friction and Nusselt number, respectively. Also Sisko parameter enlarges skin friction coefficient. The accuracy of solution is verified by comparing it with existing literature.
Originality/value
The computed results are interested for industrial and engineering processes, especially in cooling of nuclear reactors.
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Arif Hussain, Muhammad Yousaf Malik, Mair Khan and Taimoor Salahuddin
The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.
Abstract
Purpose
The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.
Design/methodology/approach
The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem.
Findings
The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations.
Originality/value
The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.
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Muhammad Sohail, Rahila Naz and Rabeeah Raza
The purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous…
Abstract
Purpose
The purpose of this paper is to address the entropy analysis of the 3D flow of Maxwell nanofluid containing gyrotactic microorganism in the presence of homogeneous–heterogeneous reactions with improved heat conduction and mass diffusion models over a stretched surface. Improved models are supported out by utilizing Cattaneo–Christov heat flux and generalized Fick’s law, respectively.
Design/methodology/approach
Governing equations which present the given flow phenomenon are modeled in the form of PDEs by applying boundary layer analysis and then suitable makeovers are engaged to transfigure prevailing partial differential equations into a set of ordinary differential equations. Transformed equations are handled via optimal homotopy analysis process in computational tool Mathematica and also a special case of already published work is substantiated and found to be in excellent settlement.
Findings
The bearing of innumerable convoluted physical parameters on velocity, temperature, concentration, reaction rate, the concentration of motile microorganism and entropy generation are presented and deliberated through graphs. Moreover, the convergence of the homotopic solution is presented in tabular form which confirms the reliability of the proposed scheme. It is perceived that mounting values of the magnetic parameter and Brinkman number boosts the irreversibility analysis and Bejan number diminishes for these parameters. Moreover, the growing values of Prandtl and Schmidt numbers reduce the temperature and concentration fields, respectively.
Practical implications
The work contained in this paper has applications in a different industry.
Originality/value
The work contained in this paper is original work and it is good for the researcher in the field of applied mathematics.
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The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a…
Abstract
Purpose
The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish.
Design/methodology/approach
The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique.
Findings
Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number.
Originality/value
A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.
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Gollapalli Shankar and Siva Reddy Sheri
This research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and…
Abstract
Purpose
This research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and electrically conductive fluid over a vertically oscillating flat plate. The study highlights the significance of magnetic fields in influencing thermal and mass transfer, particularly in the context of thermal radiation. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the finite element method (FEM) numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. Key parameters such as skin friction, temperature, concentration, velocity and Sherwood numbers are derived and analyzed. The results demonstrate that viscous dissipation significantly elevates the fluid temperature, while an increase in the radiation parameter is associated with a decrease in internal friction at the plate. These findings provide critical insights into the interplay between thermal radiation and magnetic fields in MHD flows, with potential applications in engineering systems involving heat and mass transfer, such as cooling systems and material processing. This study underscores the importance of understanding these dynamics for optimizing the performance of MHD applications in various industrial settings.
Design/methodology/approach
The mainly authorized and energetic FEM to explain the non-linear, dimensionless partial differential equations (11–13) via equation with boundary conditions (14) makes use of Bathe (36), Reddy (37), Connor (38) and Chung (39). Following are the key steps that make up the method: discretize the domain, derivation of element equation, assembly of element equation, imposition of boundary condition and solution of assembly equation.
Findings
This study examined the impact of viscid dissipative radiation and the Dufour effect on unsteady one-dimensional MHD natural convective flow of a viscous, incompressible, electrically conducting fluid past an infinite moving vertical flat plate with a chemical reaction. Numerically solving the governing equations using the FEM approach is efficient and precise, aiming to be applied to fluid mechanics and related problems. Along with their effects on temperature, concentration and velocity, the following parameters are included: the mass Grashof number, the Soret number, the Grashof number, the Prandtl number, chemical reaction, the Schmidt number, radiation and the Casson parameter. Both the Grashof numbers of thermal and mass rates (Gr, Gm) make an increment in the velocity region. The velocity decreases with an increase in the magnetic parameter. The velocity increases with an increase in the permeability of the porous medium parameter. The temperature flow rate is higher for both Dufour and Viscid dissipation, while a decrement is noted of both Prandtl number and radiation effects. The decrementing behavior of the concentration region is observed at supreme inputs of chemical reaction coefficient and Schmidt number.
Originality/value
This is an original paper and not submitted anywhere.
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Abdulaziz Alsenafi, Fares Alazemi and M. Nawaz
To improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and…
Abstract
Purpose
To improve the thermal performance of base fluid, nanoparticles of three types are dispersed in the base fluid. A novel theory of non-Fourier heat transfer is used for design and development of models. The thermal performance of sample fluids is compared to determine which types of combination of nanoparticles are the best for an optimized enhancement in thermal performance of fluids. This article aims to: (i) investigate the impact of nanoparticles on thermal performance; and (ii) implement the Galerkin finite element method (GFEM) to thermal problems.
Design/methodology/approach
The mathematical models are developed using novel non-Fourier heat flux theory, conservation laws of computational fluid dynamics (CFD) and no-slip thermal boundary conditions. The models are approximated using thermal boundary layer approximations, and transformed models are solved numerically using GFEM. A grid-sensitivity test is performed. The accuracy, correction and stability of solutions is ensured. The numerical method adopted for the calculations is validated with published data. Quantities of engineering interest, i.e. wall shear stress, wall mass flow rate and wall heat flux, are calculated and examined versus emerging rheological parameters and thermal relaxation time.
Findings
The thermal relaxation time measures the ability of a fluid to restore its original thermal state, called thermal equilibrium and therefore, simulations have shown that the thermal relaxation time associated with a mono nanofluid has the most substantial effect on the temperature of fluid, whereas a ternary nanofluid has the smallest thermal relaxation time. A ternary nanofluid has a wider thermal boundary thickness in comparison with base and di- and mono nanofluids. The wall heat flux (in the case of the ternary nanofluids) has the most significant value compared with the wall shear stresses for the mono and hybrid nanofluids. The wall heat and mass fluxes have the highest values for the case of non-Fourier heat and mass diffusion compared to the case of Fourier heat and mass transfer.
Originality/value
An extensive literature review reveals that no study has considered thermal and concentration memory effects on transport mechanisms in fluids of cross-rheological liquid using novel theory of heat and mass [presented by Cattaneo (Cattaneo, 1958) and Christov (Christov, 2009)] so far. Moreover, the finite element method for coupled and nonlinear CFD problems has not been implemented so far. To the best of the authors’ knowledge for the first time, the dynamics of wall heat flow rate and mass flow rate under simultaneous effects of thermal and solute relaxation times, Ohmic dissipation and first-order chemical reactions are studied.
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Nagisetty Jyothi and Vijaya Kumar Avula Golla
This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous…
Abstract
Purpose
This study aims to analyze the multi-slip effects of entropy generation in steady non-linear magnetohydrodynamics thermal radiation with Williamson nanofluid flow across a porous stretched sheet near a stagnation point. Also, the qualities of viscous dissipation, Cattaneo–Christove heat flux and Arrhenius activation energy are taken into account. Thermophoresis, Brownian motion and Joule heating are also considered.
Design/methodology/approach
The Navier–Stokes equation, the thermal energy equation and the Solutal concentration equations are the governing mathematical equations that describe the flow and heat and mass transfer phenomena for fluid domains. By using the proper similarity transformations, a set of ordinary differential equationss are retrieved from boundary flow equations. The classical Runge–Kutta fifth-order algorithm along with the shooting technique is implemented to solve the obtained first order differential equations.
Findings
The study concludes that the temperature distribution boosting for thermal radiation, magnetic field and Eckert number where as the velocity and entropy generation escalate for the Williamson parameter, diffusion parameter and Brinkman number. The skin-friction and heat and mass transfer rate increases with the fluid injection. In addition, tabulated values of friction drag and rate of heat and mass transfer for various values of constraints are provided.
Originality/value
The comparison of the present results is carried out with the published results and noted a good agreement.
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Muhammad Sohail, Esha Rafique and Kamaleldin Abodayeh
This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those…
Abstract
Purpose
This investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.
Design/methodology/approach
Following the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.
Findings
Remarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.
Originality/value
Available studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.
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Present investigation based on the flow of electrically conducting Williamson nanofluid embedded in a porous medium past a linearly horizontal stretching sheet. In addition to…
Abstract
Purpose
Present investigation based on the flow of electrically conducting Williamson nanofluid embedded in a porous medium past a linearly horizontal stretching sheet. In addition to that, the combined effect of thermophoresis, Brownian motion, thermal radiation and chemical reaction is considered in both energy and solutal transfer equation, respectively.
Design/methodology/approach
With suitable choice of nondimensional variables the governing equations for the velocity, temperature, species concentration fields, as well as rate shear stress at the plate, rate of heat and mass transfer are expressed in the nondimensional form. These transformed coupled nonlinear differential equations are solved semi-analytically using variation parameter method.
Findings
The behavior of characterizing parameters such as magnetic parameter, melting parameter, porous matrix, Brownian motion, thermophoretic parameter, radiation, Lewis number and chemical particular case present result validates with earlier established results and found to be in good agreement. Finally reaction parameter is demonstrated via graphs and numerical results are presented in tabular form.
Originality/value
The said work is an original work of the authors.