Joule heating in magnetic resistive flow with fractional Cattaneo–Maxwell model

Anwar, Muhammad Shoaib; Rasheed, Amer

doi:10.1007/s40430-018-1426-8

Cited by 29 publications

(7 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where (•) signifies Gamma function. Under the aforementioned premises, the boundary layer free convection flow with mass transfer, generalized Ohm's and Fick's laws J c σ (E F + U × B F ) and fractional Maxwell's equations [20] are given by [8,28].…”

Section: Mathematical Modeling Of Physical Processmentioning

confidence: 99%

“…The interpretation of the Caputo fractional time derivative is defined by where signifies Gamma function. Under the aforementioned premises, the boundary layer free convection flow with mass transfer, generalized Ohm’s and Fick’s laws and fractional Maxwell’s equations [ 20 ] are given by [ 8 , 28 ]. …”

Section: Mathematical Modeling Of Physical Processmentioning

confidence: 99%

“…Further, they notice the opposite effects for Pr and Sc numbers on concentration and temperature profile. One can find in the literature that many scholars have studied Maxwell fluid through multiple mechanical and thermal boundary conditions [8,16,19,39,43]. Convective flow with simultaneous heat and mass transfer, under the involvement of an electromagnetic essence and chemical reaction, has gained significant interest from scholars since this phenomenon occurs in man disciplines of engineering and innovative technologies.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Space–Time Coupled Fractional Cattaneo–Friedrich Maxwell Model with Caputo Derivatives

Khan

Rasheed

2021

Int. J. Appl. Comput. Math

Self Cite

View full text Add to dashboard Cite

In the current article, we have thoroughly investigated the collective impact of mixed convection with thermal radiation and chemical reaction on MHD flow of viscous and electrically conducting fluid (Cattaneo-Friedrich Maxwell-CFM model) over a permeable surface embedded in a porous medium. Here we have utilized the Caputo time-fractional derivatives and mechanical laws (generalized shear stress constitutive equation and generalized Fourier's and Fick's laws) are being used to fractionalize the presented model. The effects of radiative heat flux, Ohmic dissipation, and internal absorption are presented through generalized Fourier's law while Fick's law or mass transfer equation offers the effects of first order chemically reactive species. The finite element method and finite difference method are being utilized to numerically solve the nonlinear coupled differential equations. It is established, through compression of numerical and analytical solutions, that the presented model is convergent. Further, error analysis of the subject model is also carried out. Moreover, for better illustration of results, we have also offered a graphical and tabular presentation of impacts of the parameters of interest on velocity, temperature, concentration profile, local skin friction coefficient, and heat and mass transfer. It is evident from the obtained results that velocity near and away from the surface increases with the enhancement of fractional derivative parameter whereas an opposite trend is observed in the case of temperature. Furthermore, it is noticed that temperature shows a decreasing behavior for the value θ < 2 and φ < 2, on the other hand entirely opposite trend is witnessed for θ ≥ 3 and φ ≥ 3. From an engineering perspective, we have acquired comprehensive outcomes such that the heat transfer offers an increasing trend in the case of T R and thermal fractional parameter β 1 . Additionally, the chemical reaction parameter and Sc significantly contribute towards the mass transfer rate. Since, in literature, one cannot refer to such results with non-integer Caputo fractional derivatives thus the results obtained through the current assessment hold significance for future research avenues. Moreover, the numerical inferences of the subject study may contribute to an advanced thermal processing method in the food industry to swiftly increase the temperature for cooking or sterilization drives.

show abstract

Section: Mathematical Modeling Of Physical Processmentioning

confidence: 99%

Section: Mathematical Modeling Of Physical Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The Space–Time Coupled Fractional Cattaneo–Friedrich Maxwell Model with Caputo Derivatives

Khan

Rasheed

2021

Int. J. Appl. Comput. Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…In all of these industrial processes, heat transfer and flow investigation are of significant importance because the final product quality is determined on the basis of coefficient of velocity gradient (skin friction) and the rate of convective heat exchange. To understand the fluid flow along with heat transfer characteristics over a moving surface, readers are recommended to study [13,4,15,35,6,47,5,21,48]. Recently the focus of researchers shifted towards study of nanofluids flow and the process of heat transfer due to enhanced thermal properties of nanofluids [46,34,57,10,8,50].…”

mentioning

confidence: 99%

Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation

Aziz¹,

Jamshed²,

Ali³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

View full text Add to dashboard Cite

In this numerical study, researchers explore the flow, heat transfer and entropy of electrically conducting hybrid nanofluid over the horizontal penetrable stretching surface with velocity slip conditions at the interface. The non-Newtonian fluid models lead to better understanding of flow and heat transfer characteristics of nanofluids. Therefore, non-Newtonian Maxwell mathematical model is considered for the hybrid nanofluid and the uniform magnetic field is applied at an angle to the direction of the flow. The Joule heating and thermal radiation impact are also considered in the simplified model. The governing nonlinear partial differential equations for hybrid Maxwell nanofluid flow, heat transfer and entropy generation are simplified by taking boundary layer approximations and then reduced to ordinary differential equations using suitable similarity transformations. The Keller box scheme is then adopted to solve the system of ordinary differential equations. The Ethylene glycol based Copper Ethylene glycol (Cu-EG) nanofluid and Ferro-Copper Ethylene glycol (F e 3 O 4 − Cu-EG) hybrid nanofluids are considered to produce the numerical results for velocity, temperature and entropy profiles as well as the skin friction factor and the local Nusselt number. The main findings indicate that hybrid Maxwell nanofluid is better thermal conductor when compared with the conventional nanofluid, the greater angle of inclination of magnetic field offers greater resistance to fluid motion within boundary layer and the heat transfer rate act as descending function of nanoparticles shape factor.

show abstract

“…numerically explored the heat transport analysis for differential type fractional fluid model between non-isothermal boundaries Rasheed and Anwar (2018b). investigated the mechanism of heat transport by utilizing revised heat flux model in fractional sense for the Hartmann flow by considering the variable thermal conductivity Anwar and Rasheed (2018). examined the bearing of fractional Cattaneo-Maxwell model between two plates.…”

mentioning

confidence: 99%

Heat transport in the convective Casson fluid flow with homogeneous‒heterogeneous reactions in Darcy‒Forchheimer medium

Bilal¹,

Sohail²,

Naz³

2019

MMMS

View full text Add to dashboard Cite

Purpose The purpose of this paper is to highlight the studies of momentum and transmission of heat on mixed convection boundary layer Darcy‒Forchheimer flow of Casson liquid over a linear extending surface in a porous medium. The belongings of homogeneous‒heterogeneous retorts are also affianced. The mechanism of heat transmission is braced out in the form of Cattaneo‒Christov heat flux. Appropriate restorations are smeared to revolutionize coupled nonlinear partial differential equations conforming to momentum, energy and concentration of homogeneous‒heterogeneous reaction equations into coupled nonlinear ordinary differential equations (ODEs). Design/methodology/approach Numerical elucidations of the transmogrified ODEs are accomplished via a dexterous and trustworthy scheme, namely optimal homotopy analysis method. The convergence of planned scheme is exposed with the support of error table. Findings The exploration of mixed convection Darcy‒Forchheimer MHD boundary layer flow of incompressible Casson fluid by the linear stretched surface with Cattaneo‒Christov heat flux model and homogeneous‒heterogeneous reactions is checked in this research. Imitations of the core subsidized flow parameters on velocity, temperature and concentration of homogeneous‒heterogeneous reactions solutions are conscripted. From the recent deliberation, remarkable annotations are as follows: non-dimensional velocities in xa− and xb− directions shrink, whereas the non-dimensional temperature upsurges when the Casson fluid parameter ameliorates. Similar impact of Casson fluid parameter, magnetic parameter, mixed convection parameter, inertia parameter, and porosity parameter is observed for both the components of velocity field. An escalation in magnetic parameter shows the opposite attitude of temperature field as compared with velocity profile. Similar bearing of Casson fluid parameter is observed for both temperature and velocity fields. Enhancement in concentration rate is observed for growing values of (Ns) and (Sc), and it reduces for (k1). Both temperature and concentration of homogeneous‒heterogeneous upturn by mounting the magnetic parameter. Demeanor of magnetic parameter, Casson fluid parameter, heat generation parameter is opposite to that of Prandtl number and thermal relaxation parameter on temperature profile. Practical implications In many industrial and engineering applications, the current exploration is utilized for the transport of heat and mass in any system. Originality/value As far as novelty of this work is concerned this is an innovative study and such analysis has not been considered so far.

show abstract

Joule heating in magnetic resistive flow with fractional Cattaneo–Maxwell model

Cited by 29 publications

References 38 publications

The Space–Time Coupled Fractional Cattaneo–Friedrich Maxwell Model with Caputo Derivatives

The Space–Time Coupled Fractional Cattaneo–Friedrich Maxwell Model with Caputo Derivatives

Heat transfer and entropy analysis of Maxwell hybrid nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation

Heat transport in the convective Casson fluid flow with homogeneous‒heterogeneous reactions in Darcy‒Forchheimer medium

Contact Info

Product

Resources

About