A hybrid investigation on numerical and analytical solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation

2019 ◽  
Vol 30 (2) ◽  
pp. 834-854 ◽  
Author(s):  
R. Ellahi ◽  
Sadiq M. Sait ◽  
N. Shehzad ◽  
Z. Ayaz
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Aluminum Oxide ◽  
Entropy Generation ◽  
Analytical Solutions ◽  
Fluid Motion ◽  
Electromagnetic Parameter ◽  
Substantial Impact ◽  
Content Type ◽  
Thermal Buoyancy

Purpose The purpose of this paper is to present the investigation of the pressure-driven flow of aluminum oxide-water based nanofluid with the combined effect of entropy generation and radiative electro-magnetohydrodynamics filled with porous media inside a symmetric wavy channel. Design/methodology/approach The non-linear coupled differential equations are first converted into a number of ordinary differential equations with appropriate transformations and then analytical solutions are obtained by homotopic approach. Numerical simulation has been designed by the most efficient approach known homotopic-based Mathematica package BVPh 2.0 technique. The long wavelength approximation over the channel walls is taken into account. The obtained analytical results have been validated through graphs to infer the role of most involved pertinent parameters, whereas the characteristics of heat transfer and shear stress phenomena are presented and examined numerically. Findings It is found that the velocity profile decreases near to the channel. This is in accordance with the physical expectation because resistive force acts opposite the direction of fluid motion, which causes a decrease in velocity. It is seen that when the electromagnetic parameter increases then the velocity close to the central walls decreases whereas quite an opposite behavior is noted near to the walls. This happens because of the combined influence of electro-magnetohydrodynamics. It is perceived that by increasing the magnetic field parameter, Darcy number, radiation parameter, electromagnetic parameter and the temperature profile increases, and this is because of thermal buoyancy effect. For radiation and electromagnetic parameters, energy loss at the lower wall has substantial impact compared to the upper wall. Residual error minimizes at 20th order iterations. Originality/value The proposed prospective model is designed to explore the simultaneous effects of aluminum oxide-water base nanofluid, electro-magnetohydrodynamics and entropy generation through porous media. To the best of author’s knowledge, this model is reported for the first time.

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.

MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fazle Mabood ◽  
Anum Shafiq ◽  
Waqar Ahmed Khan ◽  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Design Parameters ◽  
Hybrid Nanofluid ◽  
Nonlinear Thermal Radiation ◽  
Content Type

Purpose This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source. Design/methodology/approach This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. Findings The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes. Originality/value This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

Entropy generation analysis in flow of thixotropic nanofluid

2019 ◽  
Vol 29 (12) ◽  
pp. 4507-4530 ◽  
Author(s):  
Muhammad Ijaz Khan ◽  
Salman Ahmad ◽  
Tasawar Hayat ◽  
M. Waleed Ahmad Khan ◽  
Ahmed Alsaedi
Keyword(s):  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Content Type ◽  
Flow Variables

Purpose The purpose of this paper is to address entropy generation in flow of thixotropic nonlinear radiative nanoliquid over a variable stretching surface with impacts of inclined magnetic field, Joule heating, viscous dissipation, heat source/sink and chemical reaction. Characteristics of nanofluid are described by Brownian motion and thermophoresis effect. At surface of the sheet zero mass flux and convective boundary condition are considered. Design/methodology/approach Considered flow problem is mathematically modeled and the governing system of partial differential equations is transformed into ordinary ones by using suitable transformation. The transformed ordinary differential equations system is figure out by homotopy algorithm. Outcomes of pertinent flow variables on entropy generation, skin friction, concentration, temperature, velocity, Bejan, Sherwood and Nusselts numbers are examined in graphs. Major outcomes are concluded in final section. Findings Velocity profile increased versus higher estimation of material and wall thickness parameter while it decays through larger Hartmann number. Furthermore, skin friction coefficient upsurges subject to higher values of Hartmann number and magnitude of skin friction coefficient decays via materials parameters. Thermal field is an increasing function of Hartmann number, radiation parameter, thermophoresis parameter and Eckert number. Originality/value The authors have discussed entropy generation in flow of thixotropic nanofluid over a variable thicked surface. No such consideration is yet published in the literature.

Convective heat transport in a heat generating MHD vertical layer saturated by a non-Newtonian nanofluid: a bidirectional study

2020 ◽  
Vol 16 (6) ◽  
pp. 1669-1689 ◽  
Author(s):  
M. Gnaneswara Reddy ◽  
P. Vijayakumari ◽  
L. Krishna ◽  
K. Ganesh Kumar ◽  
B.C Prasannakumara
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Nonlinear Thermal Radiation ◽  
Content Type ◽  
Thermal Buoyancy ◽  
Nonlinear Radiation ◽  
The Impact

PurposeIn this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.Design/methodology/approachInfinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.FindingsThe impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (βT, βC), mixed convection parameter (α), Hartmann number (M2), Weissenberg number (We), nonlinear radiation parameter (NR), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.Originality/valueThe velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

Non-similar solution of Sisko nanofluid flow with variable thermal conductivity: a finite difference approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ankita Bisht ◽  
Rajesh Sharma
Keyword(s):  
Thermal Conductivity ◽  
Finite Difference ◽  
Differential Equations ◽  
Velocity Ratio ◽  
Variable Thermal Conductivity ◽  
Brownian Diffusion ◽  
Control Parameters ◽  
Nanofluid Flow ◽  
Content Type ◽  
Thermal Buoyancy

Purpose The main purpose of this study is to present a non-similar analysis of two-dimensional boundary layer flow of non-Newtonian nanofluid over a vertical stretching sheet with variable thermal conductivity. The Sisko fluid model is used for non-Newtonian fluid with an exponent (n* > 1), that is, shear thickening fluid. Buongiorno model for nanofluid accounting Brownian diffusion and thermophoresis effects is used to model the governing differential equations. Design/methodology/approach The governing boundary layer equations are converted into nondimensional coupled nonlinear partial differential equations using appropriate transformations. The resultant differential equations are solved numerically using implicit finite difference scheme in association with the quasilinearization technique. Findings This analysis shows that the temperature raises for thermal conductivity parameter and velocity ratio parameter while decreases for the thermal buoyancy parameter. The thermophoresis and Brownian diffusion parameter that characterizes the nanofluid flow enhances the temperature and reduces the heat transfer rate. Skin friction drag can be effectively reduced by proper control of the values of thermal buoyancy and velocity ratio parameter. Practical implications The wall heating and cooling investigation result in the analysis of the control parameters that are related to the designing and manufacturing of thermal systems for cooling applications and energy harvesting. These control parameters have practical significance in the designing of heat exchangers and solar thermal collectors, in glass and polymer industries, in the extrusion of plastic sheets, the process of cooling of the metallic plate, etc. Originality/value To the best of authors’ knowledge, it is found from the literature survey that no similar work has been published which investigates the non-similar solution of Sisko nanofluid with variable thermal conductivity using finite difference method and quasilinearization technique.

Analysis of two approaches for an adiabatic boundary condition in porous media

2016 ◽  
Vol 26 (3/4) ◽  
pp. 977-998 ◽  
Author(s):  
Kun Yang ◽  
Xingwang You ◽  
Jiabing Wang ◽  
Kambiz Vafai
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Media ◽  
Nusselt Number ◽  
Analytical Solutions ◽  
Channel Wall ◽  
Flux Distribution ◽  
Heat Flux Distribution ◽  
Content Type ◽  
Adiabatic Boundary Condition

Purpose – The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed. Design/methodology/approach – Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium. Findings – The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕAfin increases and ϕAsub, ϕAcover decrease as Da decreases and k is held constant, ϕAsub increases and ϕAfin, ϕAcover decrease as k increases while Da is held constant; for Model B, ϕBfin increases and ϕBsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small. Research limitations/implications – Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases. Practical implications – Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement. Social implications – This work has important fundamental implications. Originality/value – In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

Mass Transport Modelling in Porous Media Using Delay Differential Equations

2006 ◽  
Vol 258-260 ◽  
pp. 586-591
Author(s):  
António Martins ◽  
Paulo Laranjeira ◽  
Madalena Dias ◽  
José Lopes
Keyword(s):  
Porous Media ◽  
Differential Equations ◽  
Mass Transport ◽  
Delay Differential Equations ◽  
Dispersion Model ◽  
Flow Characteristics ◽  
Convective Transport ◽  
Transport Modelling ◽  
Flow Field Characteristics ◽  
Delay Differential

In this work the application of delay differential equations to the modelling of mass transport in porous media, where the convective transport of mass, is presented and discussed. The differences and advantages when compared with the Dispersion Model are highlighted. Using simplified models of the local structure of a porous media, in particular a network model made up by combining two different types of network elements, channels and chambers, the mass transport under transient conditions is described and related to the local geometrical characteristics. The delay differential equations system that describe the flow, arise from the combination of the mass balance equations for both the network elements, and after taking into account their flow characteristics. The solution is obtained using a time marching method, and the results show that the model is capable of describing the qualitative behaviour observed experimentally, allowing the analysis of the influence of the local geometrical and flow field characteristics on the mass transport.

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