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Article
Publication date: 31 July 2023

Syed Sohaib Zafar, Aurang Zaib, Farhan Ali, Fuad S. Alduais, Afrah Al Bossly and Anwar Saeed

The modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and…

Abstract

Purpose

The modern day has seen an increase in the prevalence of the improvement of high-performance thermal systems for the enhancement of heat transmission. Numerous studies and research projects have been carried out to acquire an understanding of heat transport performance for their functional application to heat conveyance augmentation. The idea of this study is to inspect the entropy production in Darcy-Forchheimer Ree-Eyring nanofluid containing bioconvection flow toward a stretching surface is the topic of discussion in this paper. It is also important to take into account the influence of gravitational forces, double stratification, heat source–sink and thermal radiation. In light of the second rule of thermodynamics, a model of the generation of total entropy is presented.

Design/methodology/approach

Incorporating boundary layer assumptions allows one to derive the governing system of partial differential equations. The dimensional flow model is transformed into a non-dimensional representation by applying the appropriate transformations. To deal with dimensionless flow expressions, the built-in shooting method and the BVP4c code in the Matlab software are used. Graphical analysis is performed on the data to investigate the variation in velocity, temperature, concentration, motile microorganisms, Bejan number and entropy production concerning the involved parameters.

Findings

The authors have analytically assessed the impact of Darcy Forchheimer's flow of nanofluid due to a spinning disc with slip conditions and microorganisms. The modeled equations are reset into the non-dimensional form of ordinary differential equations. Which are further solved through the BVP4c approach. The results are presented in the form of tables and figures for velocity, mass, energy and motile microbe profiles. The key conclusions are: The rate of skin friction incessantly reduces with the variation of the Weissenberg number, porosity parameter and Forchheimer number. The rising values of the Prandtl number reduce the energy transmission rate while accelerating the mass transfer rate. Similarly, the effect of Nb (Brownian motion) enhances the energy and mass transfer rates. The rate of augments with the flourishing values of bioconvection Lewis and Peclet number. The factor of concentration of microorganisms is reported to have a diminishing effect on the profile. The velocity, energy and entropy generation enhance with the rising values of the Weissenberg number.

Originality/value

According to the findings of the study, a slip flow of Ree-Eyring nanofluid was observed in the presence of entropy production and heat sources/sinks. There are features when the implementations of Darcy–Forchheimer come into play. In addition to that, double stratification with chemical reaction characteristics is presented as a new feature. The flow was caused by the stretching sheet. It has been brought to people's attention that although there are some investigations accessible on the flow of Ree-Eyring nanofluid with double stratification, they are not presented. This research draws attention to a previously unexplored topic and demonstrates a successful attempt to construct a model with distinctive characteristics.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 13 December 2018

Sadia Rashid, Tasawar Hayat, Sumaira Qayyum, Muhammad Ayub and Ahmed Alsaedi

The purpose of this study is to study flow caused by rotating frame. Effects of Darcy–Forchheimer and porous medium are considered to study velocity field. Concentration field is…

Abstract

Purpose

The purpose of this study is to study flow caused by rotating frame. Effects of Darcy–Forchheimer and porous medium are considered to study velocity field. Concentration field is discussed in presence of activation energy. Darcy–Forchheimer in a rotating frame is examined. Flow because of stretched sheet fills the porous space. Binary chemical reaction is entertained. Resulting system is numerically solved. The plots are arranged for rotational parameter, porosity parameter, coefficients of inertia, Prandtl number and Schmidt number. It is revealed that rotation on velocity has opposite effects when compared with temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are numerically discussed.

Design/methodology/approach

Darcy–Forchheimer in a rotating frame is examined. Flow because of stretched sheet fills the porous space. Binary chemical reaction is entertained. Resulting system is numerically solved. The plots are arranged for rotational parameter, porosity parameter, coefficients of inertia, Prandtl number and Schmidt number. It is revealed that rotation on velocity has opposite effects when compared with temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are numerically discussed.

Findings

The major findings here are as follows: an addition in porosity λ causes decay in velocity f′(η) while there is opposite behavior for temperature θ(η) and concentration ϕ(η) fields. θ and ϕ via β have similar results qualitatively. There is an opposite behavior of Pr on temperature and concentration. Inverse behavior of λ on ϕ and wall mass flux is noted. Concentration ϕ is decreasing function of reaction rate constant σ. Skin friction coefficient has similar qualitative results for λ and β. Temperature gradient −θ(0) is decreased by λ and β.

Originality/value

Here, the authors are interested to investigate rotating flow in a porous space. Dissipation and radiation effects are neglected. Effects of activation energy are studied. This work is not done yet in literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 12 October 2018

Tasawar Hayat, Tayyaba Ayub, Taseer Muhammad, Ahmed Alsaedi and M. Mustafa

The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous medium…

Abstract

Purpose

The purpose of this paper is to construct mathematical model for squeezed flow of carbon-water nanofluid between parallel disks considering Darcy–Forchheimer porous medium. Thermal conductivity of carbon nanotubes is estimated through the well-known Xue model. Such research work is not carried out in the past even in the absence of Darcy–Forchheimer porous space. Forchheimer equation is preferred here to account for both low and high velocity inertial effects. Researchers also found that dispersion of carbon nanotubes in water elevates the thermal conductivity of resulting nanofluid by 100 per cent.

Design/methodology/approach

Homotopy analysis method (HAM) is used for the convergent series solutions of the governing system.

Findings

Nusselt number at the lower disk increases when squeezing parameter Sq enlarges. This illustrates that heat transfer rate at the lower wall can be enhanced by increasing the squeezing velocity of the lower disk. The results demonstrate a decreasing trend in temperature profile for increasing volume fraction of carbon nanotubes. Moreover, improvement in heat transfer rate because of existence of carbon nanotubes is also apparent. A significant enhancement in temperature profile is depicted when inertial permeability coefficient is enhanced. Skin friction coefficients at the lower and upper disks are higher for MWCNTs in comparison to the SWCNTs.

Originality/value

To the best of author’s knowledge, no such consideration has been given in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 20 November 2023

A.K. Abdul Hakeem, Priya S., Ganga Bhose and Sivasankaran Sivanandam

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent…

Abstract

Purpose

The purpose of this study is to provide that porous media and viscous dissipation are crucial considerations when working with hybrid nanofluids in various applications.Recent years have witnessed significant progress in optimizing these fluids for enhanced heat transfer within porous (Darcy–Forchheimer) structures, offering promising solutions for various industries seeking improved thermalmanagement and energy efficiency.

Design/methodology/approach

The first step is to transform the original partial differential equations into a system of first-order ordinary differential equations (ODEs). The fourth-order Runge–Kutta method is chosen for its accuracy in solving ODEs. The present study investigates the free convective boundary layer flow of hybrid nanofluids over a moving thin inclined needle with the slip flow brought about by inclined Lorentz force and Darcy–Forchheimer porous matrix, viscous dissipation.

Findings

It is found that slip conditions (velocity and Thermal) exist for a range of the natural convection boundary layer flow. In the hybrid nanofluid flow, which consists of Al2O3 and Fe3O4 are nanoparticles, H2OC2H6O2 (50:50) are considered as the base fluid. The consequence of the governing parameter on the momentum and temperature profile distribution is graphically depicted. The range of the variables is 1 ≤ M ≤ 4, 1 ≤ d ≤ 2.5, 1 ≤ δ ≤ 4, 1 ≤ Fr ≤ 7, 1 ≤ Kr ≤ 7 and 0.5≤λ ≤ 3.5. The Nusselt number and skin friction factors are used to calculate the numerical values of various parameters, which are displayed in Table 4. These analyses elucidate that upsurges in the value of the Fr noticeably diminish the momentum and temperature. It is investigated to see if the contemporary results are in outstanding promise with the outcomes reported in earlier works.

Practical implications

The results can be very helpful to improve the energy efficiency of thermal systems.

Social implications

The hybrid nanofluids in heat transfer have the potential to improve the energy efficiency and performance of a wide range of systems.

Originality/value

This study proposes that in the combined effects of hybrid nanofluid properties, the inclined Lorentz force, the Darcy–Forchheimer model for porous media and viscous dissipation on the boundary layer flow of a conducting fluid over a moving thin inclined needle. Assessing the potential practical applications of the hybrid nanofluids in inclined needles, this could involve areas such as biomedical engineering, drug delivery systems or microfluidic devices. In future should explore the benefits and limitations of using hybrid nanofluids in these applications.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 14 December 2018

Rai Sajjad Saif, T. Hayat, R. Ellahi, Taseer Muhammad and A. Alsaedi

The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by…

Abstract

Purpose

The purpose of present communication is to analyze Darcy–Forchheimer flow of viscous nanofluid by curved stretchable surface. Flow in porous medium is characterized by Darcy–Forchheimer relation. Brownian diffusion and thermophoresis are considered. Convective heat and mass boundary conditions are also used at the curved stretchable surface.

Design/methodology/approach

The resulting nonlinear system is solved through shooting technique.

Findings

Skin friction coefficient is enhanced for larger porosity parameter and inertia coefficient while reverse trend is noticed for curvature parameter. Local Nusselt number is enhanced for higher Prandtl number and thermal Biot number, whereas the opposite trend is seen via curvature parameter, porosity parameter, inertia coefficient, thermophoresis parameter and Brownian motion parameter. Local Sherwood number is enhanced for Schmidt number, Brownian motion parameter and concentration Biot number, while reverse trend is noticed for curvature parameter, porosity parameter, inertia coefficient and thermophoresis parameter.

Originality/value

To the best of author’s knowledge, no such consideration has been given in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 6 December 2020

S. Das, Akram Ali and R.N. Jana

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching…

Abstract

Purpose

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

Design/methodology/approach

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

Findings

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

Practical implications

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

Originality/value

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

Details

World Journal of Engineering, vol. 18 no. 2
Type: Research Article
ISSN: 1708-5284

Keywords

Article
Publication date: 17 October 2018

T. Hayat, Arsalan Aziz, Taseer Muhammad and A. Alsaedi

The purpose of this study is to examine the Darcy–Forchheimer flow of viscous nanoliquid because of a rotating disk. Thermophoretic diffusion and random motion aspects are…

80

Abstract

Purpose

The purpose of this study is to examine the Darcy–Forchheimer flow of viscous nanoliquid because of a rotating disk. Thermophoretic diffusion and random motion aspects are retained. Heat and mass transfer features are analyzed through convective conditions.

Design/methodology/approach

The governing systems are solved numerically by the shooting technique.

Findings

Higher porosity parameter and Forchheimer number Fr depict similar trend for both velocity profiles f' and g. Both temperature and concentration profiles show increasing behavior for higher Forchheimer number Fr. An increase in Prandtl number Pr corresponds to lower temperature profile, while opposite trend is noticed for thermal Biot number. Larger concentration Biot number exhibits increasing behavior for both concentration and its associated layer thickness.

Originality/value

To the best of the author’s knowledge, no such consideration has been given in the literature yet.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 28 June 2019

Muhammad Ijaz Khan, Khursheed Muhammad, Tasawar Hayat, Shahid Farooq and Ahmed Alsaedi

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as…

Abstract

Purpose

This paper aims to discuss the salient aspects of the Darcy–Forchheimer flow of viscous liquid in carbon nanotubes (CNTs). CNTs are considered as nanofluid, and water is taken as the continuous phase liquid. The flow features are discussed via curved surface. Water is taken as the base liquid. Flow is generated via nonlinear stretching. Energy expression is modeled subject to heat generation/absorption. Furthermore, convective conditions are considered at the boundary. The Xue model is used in the mathematical modeling which describes the features of nanomaterials. Both types of CNTs are considered, i.e. single-walled CNTs and multi-walled CNTs.

Design/methodology/approach

Appropriate transformations are used to convert the flow expressions into dimensionless differential equations. The bvp4c method is used for solution development.

Findings

Velocity enhances via higher estimations of nanoparticles volume fraction while decays for higher Forchheimer number, curvature parameter, behavior index and porosity parameter. Furthermore, thermal field is an increasing function of nanoparticle volume fraction, behavior index, Forchheimer number and porosity parameter.

Originality/value

Here, the authors have discussed two-dimensional CNTs-based nanomaterial Darcy–Forchheimer flow of viscous fluid over a curved surface. The authors believe that all the outcomes and numerical techniques are original and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 3 May 2019

Muhammad Ijaz Khan, Madiha Rashid, Tasawar Hayat, Niaz B. Khan and Ahmed Alsaedi

This paper aims to examine the three-dimensional (3D) flow of carbon nanotubes (CNTs) due to bidirectional nonlinearly stretching surface by considering porous medium…

Abstract

Purpose

This paper aims to examine the three-dimensional (3D) flow of carbon nanotubes (CNTs) due to bidirectional nonlinearly stretching surface by considering porous medium. Characteristics of both single-walled CNTs and multi-walled CNTs are discussed by considering Xue model. Darcy–Forchheimer model is used for flow saturating porous medium.

Design/methodology/approach

Optimal homotopy analysis method is used for the development of series solutions.

Findings

The authors deal with 3D Darcy–Forchheimer flow of CNTs over a nonlinearly stretching surface. Heat transport mechanism is discussed in the presence of Xue model. The homogeneous and heterogeneous effects are also accounted. The mathematical modeling is computed using boundary-layer approximations.

Originality/value

No such work has been done yet in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 21 January 2020

Ambreen A. Khan, S. Naeem, R. Ellahi, Sadiq M. Sait and K. Vafai

This study aims to investigate the effect of two-dimensional Darcy-Forchheimer flow over second-grade fluid with linear stretching. Heat transfer through convective boundary…

Abstract

Purpose

This study aims to investigate the effect of two-dimensional Darcy-Forchheimer flow over second-grade fluid with linear stretching. Heat transfer through convective boundary conditions is taken into account.

Design/methodology/approach

Nonlinear coupled governing equations are tackled with a homotopy algorithm, while for numerical computation the computer software package BVPh 2.0 is used. The convergence analysis is also presented for the validation of analytical and numerical results.

Findings

Valuation for the impact of key parameters such as variable thermal conductivity, Dufour and Soret effects and variable magnetic field in an electrically conducted fluid on the velocity, concentration and temperature profiles are graphically illustrated. It is observed from the results that temperature distribution rises by Dufour number whereas concentration distribution rises by Soret number. The Forchheimer number and porosity parameter raise the skin friction coefficient. The permeable medium has a vital impact and can help in reining the rate of heat transfer.

Practical implications

The permeable medium has a vital impact and can help in reining the rate of heat transfer.

Originality/value

To the best of the authors’ knowledge, this study is reported for the first time.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 30 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

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