scholarly journals Homotopic Solution for 3D Darcy–Forchheimer Flow of Prandtl Fluid through Bidirectional Extending Surface with Cattaneo–Christov Heat and Mass Flux Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shamaila Batool ◽  
A. M. Alotaibi ◽  
Waris Khan ◽  
Ahmed Hussein Msmali ◽  
Ikramullah ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Mass Flux ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Thermal Relaxation ◽  
Nonlinear Pdes ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Analytical Technique ◽  
Similarity Relations

The 3D Prandtl fluid flow through a bidirectional extending surface is analytically investigated. Cattaneo–Christov fluid model is employed to govern the heat and mass flux during fluid motion. The Prandtl fluid motion is mathematically modeled using the law of conservations of mass, momentum, and energy. The set of coupled nonlinear PDEs is converted to ODEs by employing appropriate similarity relations. The system of coupled ODEs is analytically solved using the well-established mathematical technique of HAM. The impacts of various physical parameters over the fluid state variables are investigated by displaying their corresponding plots. The augmenting Prandtl parameter enhances the fluid velocity and reduces the temperature and concentration of the fluid. The momentum boundary layer boosts while the thermal boundary layer mitigates with the rising elastic parameter ( α 2 ) strength. Furthermore, the enhancing thermal relaxation parameter ( γ e )) reduces the temperature distribution, whereas the augmenting concentration parameter ( γ c ) drops the strength of the concentration profile. The increasing Prandtl parameter declines the fluid temperature while the augmenting Schmidt number drops the fluid concentration. The comparison of the HAM technique with the numerical solution shows an excellent agreement and hence ascertains the accuracy of the applied analytical technique. This work finds applications in numerous fields involving the flow of non-Newtonian fluids.

scholarly journals Role of Cattaneo–Christov heat flux in an MHD Micropolar dusty nanofluid flow with zero mass flux condition

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Hina Gul ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
M. Y. Malik
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Mass Flux ◽  
Fluid Velocity ◽  
Particle Interaction ◽  
Thermal Relaxation ◽  
Salient Feature ◽  
Thermal Profile ◽  
Flux Flow ◽  
Zero Mass

AbstractThis investigation aims to look at the thermal conductivity of dusty Micropolar nanoliquid with MHD and Cattaneo–Christov heat flux flow over an elongated sheet. The novelty of the envisioned mathematical model is augmented with the added impacts of the heat source/sink, chemical reaction with slip, convective heat, and zero mass flux boundary conditions. The salient feature of the existing problem is to discuss the whole scenario with liquid and dust phases. The graphical depiction is attained for arising pertinent parameters by using bvp4c a built-in MATLAB function. It is noticed that the thermal profile and velocity field increases for greater values of liquid particle interaction parameter in the case of the dust phase. An escalation in the thermal profile of both liquid and dust phases is noticed for the magnetic parameter. The rate of mass transfer amplifies for large estimates of the Schmidt number. The thickness of the boundary layer and the fluid velocity are decreased as the velocity slip parameter is augmented. In both dust and liquid phases, the thermal boundary layer thickness is lessened for growing estimates of thermal relaxation time. The attained results are verified when compared with a published result.

Flow between Stretchable Rotating Disks in an Anisotropic Porous Medium with Cattaneo Christov Heat Flux

2019 ◽  
Vol 393 ◽  
pp. 138-148
Author(s):  
K. Gowthami ◽  
P. Hari Prasad ◽  
B. Mallikarjuna ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Thermal Relaxation ◽  
Relaxation Parameter ◽  
Transport Processes ◽  
Rotation Parameter ◽  
Physical Parameters ◽  
Fluid Temperature ◽  
Anisotropic Porous Medium ◽  
Physical Quantities

A study on fully developed fluid flow between 2two stretchable disks in a 1porous medium is presented. The porous medium is assumed to be an anisotropic porous medium and described using Darcy’s model. Moreover Cattaneo - Christov heat flux 1model is used for heat transport processes. Numerical method 1is used to compute the solutions of non-dimensionalized equations and obtained results are discussed with the aid of graphs and table values on physical quantities (fluid velocity, fluid temperature, skin frication coefficients and Nusselt numbers) for various values of physical parameters, Darcy’ number in different directions, stretchable disk parameters, rotation parameter and thermal relaxation parameter. Increasing stretchable disks parameter reports opposite behavior on physical quantities at different disks. Positive and negative values of rotation parameter impact on physical quantities are presented and discussed. As increase in thermal relaxation parameter fluid temperature transfers in different directions between disks and Nusselt number values are enhanced at both disks.

scholarly journals Numerical investigation of mixed convection boundary layer flow for nanofluids under quasilinearization technique

2021 ◽  
Vol 3 (11) ◽  
Author(s):  
Srimanta Maji ◽  
Akshaya K. Sahu
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Dual Solutions ◽  
Nonlinear Pdes ◽  
Convection Boundary Layer ◽  
Physical Parameters ◽  
Layer Flow

AbstractThe study of boundary layer flow under mixed convection has been investigated numerically for various nanofluids over a semi-infinite flat plate which has been placed vertically upward for both buoyancy-induced assisting and buoyancy-induced opposing flow cases. To facilitate numerical calculations, a suitable transformation has been made for the governing partial differential equations (PDEs). Then, similarity method has been applied locally to approximate the nonlinear PDEs into a coupled nonlinear ordinary differential equations (ODEs). Then, quasilinearization method has been taken for linearizing the nonlinear terms which are present in the governing equations. Thereafter, implicit trapezoidal rule has been taken for integration numerically along with principle of superposition. The effect of physical parameters which are involved in the study are analyzed on the flow and heat transfer characteristics. This study reveals the presence of dual solutions in case of opposing flow. Further, this study shows that with increasing $$\phi$$ ϕ and Pr, the range of existence of dual solutions becomes wider. Also, it has been noted that nanofluids enhance the process of heat transfer for buoyancy assisting flow and it delays the separation point in case of opposing flow.

scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

scholarly journals Thermophoresis and Brownian Effect for Chemically Reacting Magneto-Hydrodynamic Nanofluid Flow across an Exponentially Stretching Sheet

Energies ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 143
Author(s):  
Mubashar Arshad ◽  
Azad Hussain ◽  
Ali Hassan ◽  
Qusain Haider ◽  
Anwar Hassan Ibrahim ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Chemical Reaction ◽  
Chemical Change ◽  
Fluid Motion ◽  
Fluid Temperature ◽  
Similarity Transformations ◽  
Chemically Reacting ◽  
First Order Chemical Reaction ◽  
Buongiorno Model

This comparative research investigates the influence of a flexible magnetic flux and a chemical change on the freely fluid motion of a (MHD) magneto hydrodynamic boundary layer incompressible nanofluid across an exponentially expanding sheet. Water and ethanol are used for this analysis. The temperature transmission improvement of fluids is described using the Buongiorno model, which includes Brownian movement and thermophoretic distribution. The nonlinear partial differential equalities governing the boundary layer were changed to a set of standard nonlinear differential equalities utilizing certain appropriate similarity transformations. The bvp4c algorithm is then used to tackle the transformed equations numerically. Fluid motion is slowed by the magnetic field, but it is sped up by thermal and mass buoyancy forces and thermophoretic distribution increases non-dimensional fluid temperature resulting in higher temperature and thicker boundary layers. Temperature and concentration, on the other hand, have the same trend in terms of the concentration exponent, Brownian motion constraint, and chemical reaction constraint. Furthermore, The occurrence of a magnetic field, which is aided by thermal and mass buoyancies, assists in the enhancement of heat transmission and wall shear stress, whereas a smaller concentration boundary layer is produced by a first-order chemical reaction and a lower Schmidt number.

scholarly journals HEAT TRANSFER IN GRADIENT LAMINAR FLOWS

2021 ◽  
Vol 43 (3) ◽  
pp. 30-35
Author(s):  
A.A. Avramenko ◽  
A.O. Tyrinov ◽  
N.P. Dmitrenko ◽  
Yu.Yu. Kovetska
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Group Analysis ◽  
Laminar Flows ◽  
Physical Parameters ◽  
Symmetry Groups ◽  
Heat Conducting ◽  
Transfer Coefficients ◽  
Analytical Technique ◽  
Analytical Relations

The development of new areas of research in the field of theoretical thermophysics requires reliable analytical solutions that could take into account the main aspects of physical parameters in the studied objects. One such analytical technique is symmetry groups. On the basis of symmetry groups the problem of heat transfer in gradient laminar flows is solved in the paper. For the first time, the symmetries of the energy equation for the boundary layer at an arbitrary changing velocity at marching direction are obtained. Examples of the use of group analysis methods for the study of heat transfer in the boundary layer of an incompressible fluid are demonstrated. The problems of heat transfer in the boundary layer on a heat-conducting wall with a constant temperature and on a heat-insulated wall are considered. Analytical relations for temperature and heat transfer coefficients distribution are obtained.

scholarly journals Thermal Radiations and Mass Transfer Analysis of the Three-Dimensional Magnetite Carreau Fluid Flow Past a Horizontal Surface of Paraboloid of Revolution

Processes ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 656
Author(s):  
T. Abdeljawad ◽  
Asad Ullah ◽  
Hussam Alrabaiah ◽  
Ikramullah ◽  
Muhammad Ayaz ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Shear Stress ◽  
Brownian Motion ◽  
Standard Procedure ◽  
Fluid Velocity ◽  
Nonlinear Pdes ◽  
Fluid Temperature ◽  
State Variables ◽  
Carreau Fluid ◽  
Grashof Number

The dynamics of the 3-dimensional flow of magnetized Carreau fluid past a paraboloid surface of revolution is studied through thermal radiation and mass transfer analysis. The impacts of Brownian motion and chemical reaction rate are considered on the flow dynamics. The system of nonlinear PDEs are converted to coupled ODEs by employing suitable transformation relations. The developed ODEs are solved by applying the standard procedure of homotopy analysis method (HAM). The impacts of various interesting parameters on the state variables of the Carreau fluid (velocity components, temperature, concentration, and shear stress) are explained through various graphs and tables. It is found that the horizontal velocity components augment with the rising magnetic parameter and Grashof number values. The fluid temperature augments with the higher values of the pertinent parameters except Prandtl number. The Nusselet number and fluid concentration enhance with the augmenting Brownian motion parameter. The shear stress augments with the rising Grashof number. The agreement of the obtained and published results validate the accuracy of the employed technique.

Rotating flow of Oldroyd-B fluid over stretchable surface with Cattaneo – Christov heat flux

2017 ◽  
Vol 27 (10) ◽  
pp. 2207-2222 ◽  
Author(s):  
M. Mustafa ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Relaxation Time ◽  
Three Dimensional ◽  
Thermal Relaxation ◽  
Thermal Relaxation Time ◽  
Rotating Flow ◽  
Fluid Temperature ◽  
Conduction Model ◽  
Content Type

Purpose The purpose of this paper is to analyze the heat transfer effects on the stretched flow of Oldroyd-B fluid in a rotating frame. Cattaneo–Christov heat conduction model is considered, which accounts for the influence of thermal relaxation time. Design/methodology/approach Based on scale analysis, the usual boundary layer approximations are used to simplify the governing equations. The equations so formed have been reduced to self-similar forms by similarity transformations. A powerful analytic approach, namely, homotopy analysis method (HAM), has been applied to present uniformly convergent solutions for velocity and temperature profiles. Findings Suitable values of the so-called auxiliary parameter in HAM are obtained by plotting h-curves. The results show that boundary layer thickness has an inverse relation with fluid relaxation time. The rotation parameter gives resistance to the momentum transport and enhances fluid temperature. Thermal boundary layer becomes thinner when larger values of thermal relaxation time are chosen. Originality/value To the authors’ knowledge, this is the first attempt to study the three-dimensional rotating flow and heat transfer of Oldroyd-B fluid.

scholarly journals On the Analysis of the Non-Newtonian Fluid Flow Past a Stretching/Shrinking Permeable Surface with Heat and Mass Transfer

Coatings ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 566
Author(s):  
Shahid Khan ◽  
Mahmoud M. Selim ◽  
Aziz Khan ◽  
Asad Ullah ◽  
Thabet Abdeljawad ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Analytical Procedure ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Shrinking Sheet ◽  
Fluid Temperature ◽  
Carreau Fluid ◽  
Similarity Relations

The 3D Carreau fluid flow through a porous and stretching (shrinking) sheet is examined analytically by taking into account the effects of mass transfer, thermal radiation, and Hall current. The model equations, which consist of coupled partial differential equations (PDEs), are simplified to ordinary differential equations (ODEs) through appropriate similarity relations. The analytical procedure of HAM (homotopy analysis method) is employed to solve the coupled set of ODEs. The functional dependence of the hydromagnetic 3D Carreau fluid flow on the pertinent parameters are displayed through various plots. It is found that the x-component of velocity gradient (f′(η)) enhances with the higher values of the Hall and shrinking parameters (m,ϱ), while it reduces with magnetic parameter and Weissenberg number (M,We). The y-component of fluid velocity (g(η)) rises with the augmenting values of m and M, while it drops with the augmenting viscous nature of the Carreau fluid associated with the varying Weissenberg number. The fluid temperature θ(η) enhances with the increasing values of radiation parameter (Rd) and Dufour number (Du), while it drops with the rising Prandtl number (Pr). The concentration field (ϕ(η)) augments with the rising Soret number (Sr) while drops with the augmenting Schmidt number (Sc). The variation of the skin friction coefficients (Cfx and Cfz), Nusselt number (Nux) and Sherwood number (Shx) with changing values of these governing parameters are described through different tables. The present and previous published results agreement validates the applied analytical procedure.

scholarly journals Peristaltic Flow with Heat Transfer for Nano-Coupled Stress Fluid through Non-Darcy Porous Medium in the Presence of Magnetic Field

Coatings ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 910
Author(s):  
Wael Abbas ◽  
Nabil T. M. Eldabe ◽  
Rasha A. Abdelkhalek ◽  
Nehad A. Zidan ◽  
Samir. Y. Marzouk
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Porous Medium ◽  
Couple Stress ◽  
Fluid Velocity ◽  
Fluid Motion ◽  
Physical Parameters ◽  
Linear Partial Differential Equations ◽  
Nanoparticles Concentration ◽  
Coupled Stress

In this paper, the peristaltic motion of nano-coupled stress fluid through non-Darcy porous medium is investigated, and the heat transfer is taken into account. The system is stressed by an external magnetic field. The Ohmic and viscous couple stress dissipations, heat generation and chemical reaction are considered. This motion is modulated mathematically by a system of non-linear partial differential equations, which describe the fluid velocity, temperature and nanoparticles’ concentration. These equations are transformed to non-dimensional form with the associated appropriate boundary conditions. The homotopy perturbation method is used to find the solutions of these equations as a function of the physical parameters of the problem. The effects of the parameters on the obtained solutions are discussed numerically and illustrated graphically. It is found that these parameters play an important role to control the solutions. Significant outcomes from graphical elucidation envisage that the inclusion of more magnetic field strength increases the resistance of the fluid motion. Intensification of the couple stress parameter attenuates the temperature values, while it increases with increasing thermophoresis parameter.

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