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Article
Publication date: 17 December 2019

Nilankush Acharya, Suprakash Maity and Prabir Kumar Kundu

Hybrid nanofluids are of significant engrossment for their considerable heat transport rate. The steady flow of an incompressible viscous electrically conducted hybrid…

Abstract

Purpose

Hybrid nanofluids are of significant engrossment for their considerable heat transport rate. The steady flow of an incompressible viscous electrically conducted hybrid nanofluid is considered over a rotating disk under a magnetic field. Titanium oxide (TiO2) and ferrous (CoFe2O4) nanoparticles are used with their physical properties and water is considered as host liquid. The purpose of this paper is to analyze how hydrothermal integrity varies for hybrid nanosuspension over a spinning disk in the presence of magnetic orientation.

Design/methodology/approach

Governing equations with boundary conditions are transformed by similarity transformations and then solved numerically with RK-4 method. A comparison of linear and nonlinear thermal radiation for the above-mentioned parameters is taken and the efficiency of nonlinear radiation is established, the same over nanofluid and hybrid nanofluid is also discussed. Heat lines are observed and discussed for various parameters like magnetic field, concentration, suction and injection parameter, radiation effect and Prandtl number.

Findings

Suction and increasing nanoparticle concentration foster the radial and cross-radial velocities, whereas magnetization and injection confirm the reverse trend. The rate of increment of radial friction is quite higher for the usual nanosuspension. The calculated data demonstrate that the rate for hybrid nanofluid is 8.97 percent, whereas for nanofluid it is 15.06 percent. Double-particle suspension amplifies the thermal efficiency than that of a single particle. Magnetic and radiation parameters aid the heat transfer, but nanoparticle concentration and suction explore the opposite syndrome. The magnetic parameter increases the heat transport at 36.58 and 42.71 percent for nonlinear radiation and hybrid nanosuspension, respectively.

Originality/value

Nonlinear radiation gives a higher heat transport rate and for the radiation parameter it is almost double. This result is very significant for comparison between linear and nonlinear radiation. Heat lines may be observed by taking different nanoparticle materials to get some diverse result. Hydrothermal study of such hybrid liquid is noteworthy because outcomes of this study will aid nanoscience and nanotechnology in an efficient way.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 4
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 11 September 2019

Muhammad Ayub, Muhammad Yousaf Malik, Misbah Ijaz, Marei Saeed Alqarni and Ali Saeed Alqahtani

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov…

Abstract

Purpose

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Design/methodology/approach

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

  • It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

  • It guarantees the convergence of series solutions for nonlinear problems.

  • It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

(1) N [ u ( x ) ] = 0 ,

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

(2) ( 1 q ) L [ u ˆ ( x ; q ) u o ( x ) ] = q h H ( x ) N [ u ˆ ( x ; q ) ] ,

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, uo(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

(3) u ˆ ( x ; 0 ) = u o ( x ) and u ˆ ( x ; 1 ) = u ( x ) ,

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

(4) u ˆ ( x ; q ) = u o ( x ) + m = 1 u m ( x ) q m , where u m ( x ) = 1 m ! m u ˆ ( x ; q ) q m | q = 0 .

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

(5) u ( x ) = u o ( x ) + m = 1 + u m ( x ) .

By defining a vector u = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

(6) L [ u ˆ m ( x ) χ m u m 1 ( x ) ] = h H ( x ) R m [ u m 1 ] ,

where:

(7) R m [ u m 1 ] = 1 ( m 1 ) ! m 1 N [ u ( x ; q ) ] q m 1 | q = 0 and χ m = | 0 m 1 1 m > 1 .

Applying L−1 on both sides of Equation (6), we get:

(8) u m ( x ) = χ m u m 1 ( x ) + h L 1 [ H ( x ) R m [ u m 1 ] ] .

In this way, we obtain um for m ⩾ 1, at mth-order, we have:

(9) u ( x ) = m = 1 M u m ( x ) .

Findings

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P1) and (P2), respectively. Moreover, temperature Θ(Ω1) enhances for greater values of Brownian motion parameter (Nb), non-uniform heat source/sink parameter (B1) and thermophoresis factor (Nt). Reverse behavior of concentration ϒ(Ω1) field is remarked in view of (Nb) and (Nt). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

Originality/value

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 1
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 29 December 2017

O.K. Koriko, I.L. Animasaun, M. Gnaneswara Reddy and N. Sandeep

The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell…

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Abstract

Purpose

The purpose of this paper is to scrutinize the effects of nonlinear thermal radiation and thermal stratification effects on the flow of three-dimensional Eyring-Powell 36 nm alumina-water nanofluid within the thin boundary layer in the presence of quartic autocatalytic kind of chemical reaction effects, and to unravel the effects of a magnetic field parameter, random motion of the tiny nanoparticles and volume fraction on the flow.

Design/methodology/approach

The chemical reaction between homogeneous (Eyring-Powell 36 nm alumina-water) bulk fluid and heterogeneous (three molecules of the catalyst at the surface) in the flow of magnetohydrodynamic three-dimensional flow is modeled as a quartic autocatalytic kind of chemical reaction. The electromagnetic radiation which occurs within the boundary layer is treated as the nonlinear form due to the fact that Taylor series expansion may not give full details of such effects within the boundary layer. With the aid of appropriate similarity variables, the nonlinear coupled system of partial differential equation which models the flow was reduced to ordinary differential equation boundary value problem.

Findings

A favorable agreement of the present results is obtained by comparing it for a limiting case with the published results; hence, reliable results are presented. The concentration of homogeneous bulk fluid (Eyring-Powell nanofluid) increases and decreases with ϕ and Pr, respectively. The increase in the value of magnetic field parameter causes vertical and horizontal velocities of the flow within the boundary layer to decrease significantly. The decrease in the vertical and horizontal velocities of Eyring-Powell nanofluid flow within the boundary layer is guaranteed due to an increase in the value of M. Concentration of homogeneous fluid increases, while the concentration of the heterogeneous catalyst at the wall decreases with M.

Originality/value

Considering the industrial applications of thermal stratification in solar engineering and polymer processing where the behavior of the flow possesses attributes of Eyring-Powell 36 nm alumina-water, this paper presents the solution of the flow problem considering 36 nm alumina nanoparticles, thermophoresis, stratification of thermal energy, Brownian motion and nonlinear thermal radiation. In addition, the aim and objectives of this paper fill such vacuum in the industry.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 2
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 18 June 2020

M. Gnaneswara Reddy, P. Vijayakumari, L. Krishna, K. Ganesh Kumar and B.C Prasannakumara

In this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of…

Abstract

Purpose

In 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/approach

Infinite 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.

Findings

The 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/value

The 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.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 4 December 2017

B.J. Gireesha, M. Archana, Prasannakumara B.C., R.S. Reddy Gorla and Oluwole Daniel Makinde

This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting…

Abstract

Purpose

This paper aims to deal with the study of heat and mass transfer on double-diffusive three-dimensional hydromagnetic boundary layer flow of an electrically conducting Casson nanofluid over a stretching surface. The combined effects of nonlinear thermal radiation, magnetic field, buoyancy forces, thermophoresis and Brownian motion are taken into consideration with convective boundary conditions.

Design/methodology/approach

Similarity transformations are used to reduce the governing partial differential equations into a set of nonlinear ordinary differential equations. The reduced equations were numerically solved using Runge–Kutta–Fehlberg fourth-fifth-order method along with shooting technique.

Findings

The impact of several existing physical parameters such as Casson parameter, mixed convection parameter, regular buoyancy ratio parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, temperature ratio parameter on velocity, temperature, solutal and nanofluid concentration profiles are analyzed through graphs and tables in detail. It is found that the solutal component increases for Dufour Lewis number, whereas it decreases for nanofluid Lewis number. Moreover, velocity profiles decrease for Casson parameter, while the Nusselt number increases for Biot number, radiation and temperature ratio parameter.

Originality/value

This paper is a new work related to three-dimensional double-diffusive flow of Casson nanofluid with buoyancy and nonlinear thermal radiation effect.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

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Article
Publication date: 16 November 2020

Mahantesh M. Nandeppanavar, Kemparaju M.C. and N. Raveendra

This paper aims to report the investigation of over heat and mass transfer of convective Casson fluid flow over a moving vertical plate with nonlinear thermal radiation

Abstract

Purpose

This paper aims to report the investigation of over heat and mass transfer of convective Casson fluid flow over a moving vertical plate with nonlinear thermal radiation and convective boundary conditions.

Design/methodology/approach

The main partial differential equations of the flow, heat and concentration profiles were rehabilitated to nonlinear ordinary differential equations by using an appropriate similarity transformation. The resultant nonlinear ordinary differential equations (ODEs) are solved numerically applying fourth-order Runge–Kutta shooting technique and functions of ODE45 from MATLAB.

Findings

The effect of convective heat transfer, buoyancy ratio parameter, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number over velocity, temperature and concentration profiles, equivalent to abundant somatic parameters were graphically scrutinized.

Originality/value

All the results are very promising and further there is got good agreement of results when compared with earlier published results at limiting conditions.

Details

World Journal of Engineering, vol. 18 no. 1
Type: Research Article
ISSN: 1708-5284

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Article
Publication date: 22 July 2021

Mahantesh M. Nandeppanavar, Kemparaju M.C. and Raveendra N.

This paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on…

Abstract

Purpose

This paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on velocity, temperature and concentration profiles.

Design/methodology/approach

This paper explores the heat and mass transfer of a stagnation point stream of free convective Casson fluid over a moving vertical plate with nonlinear thermal radiation and convective boundary restrictions. The governing PDEs of stream, heat and concentration profiles were reformed into an arrangement of nonlinear ODEs by using similarity transformation. This framework was then tackled numerically by applying forth-order RK shooting strategy.

Findings

Distribution of flow, velocity and temperature profiles for different values of governing parameters are analyzed.

Originality/value

The original results are depicted in terms of plots.

Details

Journal of Engineering, Design and Technology , vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1726-0531

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Article
Publication date: 26 May 2020

S. Sindhu, B.J. Gireesha and G. Sowmya

This report offers the detailed investigation of Couette–Poiseuille flow of nanoliquid with varying viscosity. The analysis is carried out by considering flow between two…

Abstract

Purpose

This report offers the detailed investigation of Couette–Poiseuille flow of nanoliquid with varying viscosity. The analysis is carried out by considering flow between two parallel plates in a rotating permeable channel with the aid of nonlinear thermal radiation and Hall effect. The predominant equations governing the physical phenomenon are demonstrated using the Buongiorno model.

Design/methodology/approach

Numerical computation for the demonstrated physical problem is achieved through the implementation of the Runge–Kutta–Fehlberg fourth–fifth-order method along with shooting technique.

Findings

The theoretical view of Brownian motion, nonlinear radiation, Hall effect and thermophoresis parameter is presented graphically.

Originality/value

It is revealed that flow velocity increases with the upper wall motion parameter and magnetic field. Also, it is established that an increase in the Nusselt number is achieved for increasing values of nonlinear radiation parameter.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 6
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 9 July 2019

K. Ganesh Kumar and M. Archana

The purpose of this paper is to model the boundary layer flow and heat transfer of dusty fluid with suspended nanoparticles over a stretching surface. The effect of…

Abstract

Purpose

The purpose of this paper is to model the boundary layer flow and heat transfer of dusty fluid with suspended nanoparticles over a stretching surface. The effect of multiple slip and nonlinear thermal radiation is taken into the account. Adequate similarity transformations are used to obtain a set of nonlinear ordinary differential equations to govern formulated problem. The resultant non-dimensionalized boundary value problem is solved numerically using the RKF-45 method. The profiles for velocity and temperature, which are controlled by thermophysical parameters, are presented graphically. Based on these plots, the conclusion is given and the obtained numerical results are tabulated. Observed interesting fact is that the SiO2-water nanoparticles show a thicker thermal boundary layer than TiO2-water nanoparticles.

Design/methodology/approach

The governing partial differential equations are approximated to a system of nonlinear ordinary differential equations by using suitable similarity transformations. An effective fourth–fifth-order Runge–Kutta–Fehlberg integration scheme numerically solves these equations along with a shooting technique. The effects of various pertinent parameters on the flow and heat transfer are examined.

Findings

Present results have an excellent agreement with previous published results in the limiting cases. The values of skin friction and wall temperature for different governing parameters are also tabulated. It is demonstrated that the SiO2-water nanoparticles show a thicker thermal boundary layer than TiO2-water nanoparticles. It is interesting to note that the dusty nanofluids are found to have higher thermal conductivity.

Originality/value

This paper is a new work related to comparative study of TiO2 and SiO2 nanoparticles in heat transfer of dusty fluid flow.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 5
Type: Research Article
ISSN: 1573-6105

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Article
Publication date: 6 June 2016

Md. Jashim Uddin, O. Anwar Bég and Izani Md. Ismail

The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat…

Abstract

Purpose

The purpose of this paper is to study two-dimensional nonlinear radiative-convective, steady-state boundary layer flow of non-Newtonian power-law nanofluids along a flat vertical plate in a saturated porous medium taking into account thermal and mass convective boundary conditions numerically.

Design/methodology/approach

The governing equations are reduced to a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The transformed equations are then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method with Maple 17 and Adomian decomposition method (ADM) in Mathematica.

Findings

The transformed equations are controlled by the parameter: power-law exponent, n; temperature ratio, Tr; Rosseland radiation-conduction, R; conduction-convection, Nc; and diffusion-convection, Nd. Temperature and nanoparticle concentration is enhanced with convection-diffusion parameter as are temperatures. Velocities are depressed with greater power-law rheological index whereas temperatures are elevated. Increasing thermal radiation flux accelerate the flow but to strongly heat the boundary layer. Very good correlation of the Maple solutions with previous stationary free stream and ADM solutions for a moving free stream, are obtained.

Practical implications

The study is relevant to high temperature nano-polymer manufacturing systems.

Originality/value

Lie symmetry group is used for the first time to transform the governing equations into a set of coupled nonlinear ordinary differential equations with relevant boundary conditions. The study is relevant to high temperature nano-polymer manufacturing systems.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

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