Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

2021 ◽  
pp. 095440892110670
Author(s):  
Zahoor Iqbal ◽  
Awais Ahmed ◽  
Amina Anwar ◽  
Sivanandam Sivasankaran ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Flow Problem ◽  
Fluid Motion ◽  
Retardation Time ◽  
Linear Ordinary Differential Equations ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Time Parameters ◽  
The Impact

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

Forced convection in 3D Maxwell nanofluid flow via Cattaneo–Christov theory with Joule heating

2021 ◽  
pp. 095440892199963
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Mahnoor Sarfraz ◽  
Jawad Ahmed ◽  
Zahoor Iqbal
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Joule Heating ◽  
Energy Transport ◽  
Fluid Motion ◽  
Analytical Technique ◽  
Maxwell Nanofluid ◽  
Homotopy Analysis ◽  
Non Linear System ◽  
The Impact

In this article, an investigation of the thermal and solutal energy transport in the 3 D flow of Maxwell nanofluid through a porous medium under the influence of the magnetic field is performed. The heat generation source and chemical reaction are also taken in account as a controlling agent for the heat and mass transport in the Maxwell liquid. A novel idea of Cattaneo-Christov theory and Buongiorno model for nanofluid is employed under the impact of Joule heating for the present analysis. The governing partial differential equations (PDEs) are transformed into a non-linear system of ordinary differential equations (ODEs) by using flow similarities. The solution of similar ODEs is constructed through a well known semi-analytical technique which is the homotopy analysis method. The results of the investigation are explored in the form of graphs. It is observed that higher values of magnetic field decline the flow field. The temperature and concentration distributions decrease with the higher magnitude of thermal and solutal relaxation time phenomena, respectively. Moreover, the temperature field enhances when the Brownian motion of nanoparticles increases in flow while the concentration profile decreases. Also, it is found that the increase in resistive heating boosts up the thermal energy transport in the fluid motion.

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

scholarly journals Computational Modeling of Hybrid Sisko Nanofluid Flow over a Porous Radially Heated Shrinking/Stretching Disc

Coatings ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1242
Author(s):  
Umair Khan ◽  
Aurang Zaib ◽  
Anuar Ishak ◽  
Fahad S. Al-Mubaddel ◽  
Sakhinah Abu Bakar ◽  
...  
Keyword(s):  
Differential Equations ◽  
Flow Problem ◽  
Shear Thickening ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Shear Thinning Fluids ◽  
Water Based ◽  
New Type ◽  
The Impact ◽  
The Magnetic Field

The present study reveals the behavior of shear-thickening and shear-thinning fluids in magnetohydrodynamic flow comprising the significant impact of a hybrid nanofluid over a porous radially shrinking/stretching disc. The features of physical properties of water-based Ag/TiO2 hybrid nanofluid are examined. The leading flow problem is formulated initially in the requisite form of PDEs (partial differential equations) and then altered into a system of dimensionless ODEs (ordinary differential equations) by employing suitable variables. The renovated dimensionless ODEs are numerically resolved using the package of boundary value problem of fourth-order (bvp4c) available in the MATLAB software. The non-uniqueness of the results for the various pertaining parameters is discussed. There is a significant enhancement in the rate of heat transfer, approximately 13.2%, when the impact of suction governs about 10% in the boundary layer. Therefore, the heat transport rate and the thermal conductivity are greater for the new type of hybrid nanofluid compared with ordinary fluid. The bifurcation of the solutions takes place in the problem only for the shrinking case. Moreover, the sketches show that the nanoparticle volume fractions and the magnetic field delay the separation of the boundarylayer.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

scholarly journals On the MHD Casson Axisymmetric Marangoni Forced Convective Flow of Nanofluids

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1087 ◽  
Author(s):  
Anum Shafiq ◽  
Islam Zari ◽  
Ghulam Rasool ◽  
Iskander Tlili ◽  
Tahir Saeed Khan
Keyword(s):  
Differential Equations ◽  
Convective Flow ◽  
Flow Behavior ◽  
Marangoni Effect ◽  
Casson Fluid ◽  
Linear Ordinary Differential Equations ◽  
Metallic Particles ◽  
Flow Parameters ◽  
Forced Convective Flow ◽  
The Impact

The proposed investigation concerns the impact of inclined magnetohydrodynamics (MHD) in a Casson axisymmetric Marangoni forced convective flow of nanofluids. Axisymmetric Marangoni convective flow has been driven by concentration and temperature gradients due to an infinite disk. Brownian motion appears due to concentration of the nanosize metallic particles in a typical base fluid. Thermophoretic attribute and heat source are considered. The analysis of flow pattern is perceived in the presence of certain distinct fluid parameters. Using appropriate transformations, the system of Partial Differential Equations (PDEs) is reduced into non-linear Ordinary Differential Equations (ODEs). Numerical solution of this problem is achieved invoking Runge–Kutta fourth-order algorithm. To observe the effect of inclined MHD in axisymmetric Marangoni convective flow, some suitable boundary conditions are incorporated. To figure out the impact of heat/mass phenomena on flow behavior, different physical and flow parameters are addressed for velocity, concentration and temperature profiles with the aid of tables and graphs. The results indicate that Casson fluid parameter and angle of inclination of MHD are reducing factors for fluid movement; however, stronger Marangoni effect is sufficient to improve the velocity profile.

Mixed convective 3D flow of Maxwell nanofluid induced by stretching sheet: Application of Cattaneo-Christov theory

2020 ◽  
pp. 095440622097324
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Jawad Ahmed ◽  
Asia Anjum ◽  
Sohail Nadeem
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Maxwell Fluid ◽  
Brownian Diffusion ◽  
Flow Mechanism ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Text Component

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.

scholarly journals Numerical Simulation on Convection and Thermal Radiation of Casson Fluid in an Enclosure with Entropy Generation

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 229 ◽  
Author(s):  
A. K. Alzahrani ◽  
S. Sivasankaran ◽  
M. Bhuvaneswari
Keyword(s):  
Numerical Simulation ◽  
Aspect Ratio ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Energy Transport ◽  
Casson Fluid ◽  
Radiation Parameter ◽  
Fluid Parameter ◽  
The Impact ◽  
Thermal Energy Transport

The goal of the current numerical simulation is to explore the impact of aspect ratio, thermal radiation, and entropy generation on buoyant induced convection in a rectangular box filled with Casson fluid. The vertical boundaries of the box are maintained with different constant thermal distribution. Thermal insulation is executed on horizontal boundaries. The solution is obtained by a finite volume-based iterative method. The results are explored over a range of radiation parameter, Casson fluid parameter, aspect ratio, and Grashof number. The impact of entropy generation is also examined in detail. Thermal stratification occurs for greater values of Casson liquid parameters in the presence of radiation. The kinetic energy grows on rising the values of Casson liquid and radiation parameters. The thermal energy transport declines on growing the values of radiation parameter and it enhances on rising the Casson fluid parameter.

Entropy generation analysis of electrical magnetohydrodynamic flow of TiO2-Cu/H2O hybrid nanofluid with partial slip

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Venkata Subba Rao M. ◽  
B.J. Gireesha ◽  
Kotha Gangadhar ◽  
Manasa Seshakumari P. ◽  
S. Sindhu
Keyword(s):  
Differential Equations ◽  
Electric Field ◽  
Entropy Generation ◽  
Numerical Solutions ◽  
Fluid Motion ◽  
Partial Slip ◽  
Hybrid Nanofluid ◽  
Local Similarity ◽  
Content Type ◽  
Linear Ordinary Differential Equations

Purpose This paper aims to address the magnetohydrodynamic boundary layer flow of hybrid mixture across a stretching surface under the influence of electric field. Design/methodology/approach The local similarity transformations are implemented to reformulate the governing partial differential equations into coupled non-linear ordinary differential equations of higher order. The numerical solutions are obtained for the simplified governing equations with the aid of finite difference technique. Findings The velocity, temperature and entropy generation are examined thoroughly for the effects of different budding parameters related to present analysis by means of graphs. It is obtained that owing to the effect of magnetic field along with slip factor, the fluid motion slowdown. However, the flow velocity enhances for the rising estimations of an electric field which tends to resolve sticky effects. Originality/value The three-dimensional plots are drawn to understand the nature of physical quantities. To ensure the precision, the obtained solutions are compared with the existing one for certain specific conditions. A good concurrence is observed between the proposed results and previously recorded outcomes.

UNSTEADY MHD FLOW OF SOME NANOFLUIDS PAST AN ACCELERATED VERTICAL PLATE EMBEDDED IN A POROUS MEDIUM

2016 ◽  
Vol 78 (2) ◽  
Author(s):  
Abid Hussanan ◽  
Ilyas Khan ◽  
Hasmawani Hashim ◽  
Muhammad Khairul Anuar ◽  
Nazila Ishak ◽  
...  
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Vertical Plate ◽  
Fluid Motion ◽  
Mhd Flow ◽  
Transform Method ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer ◽  
The Laplace Transform ◽  
Infinite Vertical Plate

The present paper deals with the unsteady magnetohydrodynamics (MHD) flow and heat transfer of some nanofluids past an accelerating infinite vertical plate in a porous medium. Water as conventional base fluid containing three different types of nanoparticles such as copper (Cu), aluminum oxide (Al2O3) and titanium oxide (TiO2) are considered. By using suitable transformations, the governing partial differential equations corresponding to the momentum and energy are converted into linear ordinary differential equations. Exact solutions of these equations are obtained with the Laplace Transform method. The influence of pertinent parameters on the fluid motion is graphically underlined. It is found that the temperature of Cu-water is higher than those of Al2O3-water and TiO2-water nanofluids.   

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