Analytical and numerical approaches for Falkner–Skan flow of MHD Maxwell fluid using a non-Fourier heat flux model

Purpose This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects. Design/methodology/approach Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method. Findings The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models. Research limitations/implications An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux. Originality/value Current problem even in case of Newtonian fluid has not been attempted previously.

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Non-Fourier thermal analysis on transport of heat and momentum in viscoelastic fluid over convectively heat surface in the presence of thermal memory effects

Multidiscipline Modeling in Materials and Structures ◽

10.1108/mmms-05-2020-0114 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Saima Batool ◽

Muhammad Nawaz ◽

Mohammed Kbiri Alaoui

Keyword(s):

Heat Flux ◽

Relaxation Time ◽

Heat Generation ◽

Thermal Relaxation ◽

Maxwell Fluid ◽

Literature Survey ◽

Hybrid Nanofluid ◽

Content Type ◽

Flux Model ◽

Heat Flux Model

PurposeThis study presents a mathematical approach and model that can be useful to investigate the thermal performance of fluids with microstructures via hybrid nanoparticles in conventional fluid. It has been found from the extensive literature survey that no study has been conducted to investigate buoyancy effects on the flow of Maxwell fluid comprised of hybrid microstructures and heat generation aspects through the non-Fourier heat flux model.Design/methodology/approachNon-Fourier heat flux model and non-Newtonian stress–strain rheology with momentum and thermal relaxation phenomena are used to model the transport of heat and momentum in viscoelastic fluid over convectively heated surface. The role of suspension of mono and hybrid nanostructures on an increase in the thermal efficiency of fluid is being used as a medium for transportation of heat energy. The governing mathematical problems with thermo-physical correlations are solved via shooting method.FindingsIt is noted from the simulations that rate of heat transfer is much faster in hybrid nanofluid as compare to simple nanofluid with the increasing heat-generation coefficient. Additionally, an increment in the thermal relaxation time leads to decrement in the reduced skin friction coefficient; however, strong behavior of Nusselt number is shown when thermal relaxation time becomes larger for hybrid nanofluid as well as simple nanofluid.Originality/valueAccording to the literature survey, no investigation has been made on buoyancy effects of Maxwell fluid flow with hybrid microstructures and heat generation aspects through non-Fourier heat flux model. The authors confirm that this work is original, and it has neither been published elsewhere nor is it currently under consideration for publication elsewhere.

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Effect of Viscous Dissipation on Upper - Convected Maxwell Fluid with Cattaneo-Christov Heat Flux Model Using Spectral Relaxation Method

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.388.146 ◽

2018 ◽

Vol 388 ◽

pp. 146-157 ◽

Cited By ~ 2

Author(s):

K. Gangadhar ◽

Chintalapudi Suresh Kumar ◽

S. Mohammed Ibrahim ◽

Giulio Lorenzini

Keyword(s):

Boundary Layer ◽

Heat Flux ◽

Relaxation Time ◽

Thermal Relaxation ◽

Relaxation Method ◽

Maxwell Fluid ◽

Spectral Relaxation Method ◽

Flux Model ◽

Spectral Relaxation ◽

Heat Flux Model

The study observes the flow and heat transfer in upper-convected Maxwell fluid over a rapidly stretching surface with viscous dissipation. Cattaneo-Christov heat flux model has been used in the preparation of the energy equation. The model is used in guessing the impacts of thermal relaxation time over boundary layer. Similarity method has been used to keep normal the supervising boundary layer equations. Local similarity solutions have been obtained through spectral relaxation method. The fluid temperature has a relation with thermal relaxation time inversely and our calculations have shown the same.. In addition the fluid velocity is a receding activity of the fluid relaxation time. A comparative study of Fourier’s law and the Cattaneo-Christov’s law has been done and inserted in this.

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Chemical reaction, thermal relaxation time and internal material parameter effects on MHD viscoelastic fluid with internal structure using the Cattaneo-Christov heat flux equation

The European Physical Journal Plus ◽

10.1140/epjp/i2017-11599-0 ◽

2017 ◽

Vol 132 (8) ◽

Author(s):

Sabeel M. Khan ◽

M. Hammad ◽

D. A. Sunny

Keyword(s):

Heat Flux ◽

Relaxation Time ◽

Internal Structure ◽

Chemical Reaction ◽

Viscoelastic Fluid ◽

Material Parameter ◽

Thermal Relaxation ◽

Thermal Relaxation Time

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

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-08-2016-0323 ◽

2017 ◽

Vol 27 (10) ◽

pp. 2207-2222 ◽

Cited By ~ 12

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.

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Influence of Cattaneo–Christov Heat Flux on MHD Jeffrey, Maxwell, and Oldroyd-B Nanofluids with Homogeneous-Heterogeneous Reaction

Symmetry ◽

10.3390/sym11030439 ◽

2019 ◽

Vol 11 (3) ◽

pp. 439 ◽

Cited By ~ 18

Author(s):

Anwar Saeed ◽

Saeed Islam ◽

Abdullah Dawar ◽

Zahir Shah ◽

Poom Kumam ◽

...

Keyword(s):

Magnetic Field ◽

Heat Flux ◽

Relaxation Time ◽

Prandtl Number ◽

Schmidt Number ◽

Concentration Field ◽

Thermal Relaxation ◽

Heterogeneous Reactions ◽

Thermal Relaxation Time ◽

The Impact

This research article deals with the determination of magnetohydrodynamic steady flow of three combile nanofluids (Jefferey, Maxwell, and Oldroyd-B) over a stretched surface. The surface is considered to be linear. The Cattaneo–Christov heat flux model was considered necessary to study the relaxation properties of the fluid flow. The influence of homogeneous-heterogeneous reactions (active for auto catalysts and reactants) has been taken in account. The modeled problem is solved analytically. The impressions of the magnetic field, Prandtl number, thermal relaxation time, Schmidt number, homogeneous–heterogeneous reactions strength are considered through graphs. The velocity field diminished with an increasing magnetic field. The temperature field diminished with an increasing Prandtl number and thermal relaxation time. The concentration field upsurged with the increasing Schmidt number which decreased with increasing homogeneous-heterogeneous reactions strength. Furthermore, the impact of these parameters on skin fraction, Nusselt number, and Sherwood number were also accessible through tables. A comparison between analytical and numerical methods has been presented both graphically and numerically.

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Micropolar mixed convective flow with Cattaneo-Christov heat flux: Non-fourier heat conduction analysis

Thermal Science ◽

10.2298/tsci181220167h ◽

2020 ◽

Vol 24 (2 Part B) ◽

pp. 1345-1356 ◽

Cited By ~ 1

Author(s):

Abid Hussanan ◽

Ilyas Khan ◽

Waqar Khan ◽

Zhi-Min Chen

Keyword(s):

Heat Flux ◽

Relaxation Time ◽

Mixed Convection ◽

Thermal Relaxation ◽

Relaxation Parameter ◽

Rotation Parameter ◽

Thermal Relaxation Time ◽

Convection Flow ◽

Fluid Temperature ◽

The Impact

The purpose of this study is to investigate the impact of thermal relaxation time on the mixed convection flow of non-Newtonian micropolar fluid over a continuously stretching sheet of variable thickness in the presence of transverse magnetic field. An innovative and modified form of Fourier?s law, namely, Cattaneo-Christov heat flux is employed in the energy equation to study the characteristics of thermal relaxation time. The governing equations are transformed into ODE, using similarity transformations. Fourth order Runge-Kutta numerical method is used to solve these equations. The effects of relevant parameters such as a micro-rotation parameter, magnetic parameter, thermal relaxation parameter, Prandtl number, surface thickness parameter, and mixed convection parameter, on the physical quantities are graphically presented. Results illustrate that fluid temperature enhances with the rise of thermal relaxation parameter, but it reduces with an increase in micro-rotation parameter. The skin friction decreases with a rise in micro-rotation and micro-element parameters. However, variation in the rate of heat transfer is quite significant for small values of thermal relaxation parameter.

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