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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

Keywords

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

Keywords

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…

93

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

Keywords

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

Keywords

Article
Publication date: 26 May 2020

Debarati Mahanty, Reeba Babu and B. Mahanthesh

In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal…

Abstract

Purpose

In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.

Design/methodology/approach

The flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.

Findings

It is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.

Originality/value

The effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.

Details

Multidiscipline Modeling in Materials and Structures, vol. 16 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

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

Keywords

Article
Publication date: 6 May 2020

S. Sindhu and B.J. Gireesha

Thermal features of hybrid nanoliquid consist of Cu–Ti, CuO–TiO2 and C71500–Ti6Al4V/H2O as hybrid mixtures of nano-sized particles in a base fluid through a microchannel…

Abstract

Purpose

Thermal features of hybrid nanoliquid consist of Cu–Ti, CuO–TiO2 and C71500–Ti6Al4V/H2O as hybrid mixtures of nano-sized particles in a base fluid through a microchannel are inspected. In this study, flow model of Darcy–Forchheimer is hired to examine the flow of hybrid composition.

Design/methodology/approach

The equations which delineate the physical occurrence of the flow are resolved via Runge–Kutta–Fehlberg scheme united through shooting procedure.

Findings

It is established that flow velocity of hybrid nano composition satisfies the identity U_(CuO-TiO2/water)>U_(Cu–Ti/water)>U_(C71500–Ti6Al4V/water).

Originality/value

Hybrid nanofluid flow of Cu–Ti, CuO–TiO2 and C71500–Ti6Al4V/H2O hybrid mixtures in a base fluid through a microchannel are inspected.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 18 April 2018

R. Sivaraj, I.L. Animasaun, A.S. Olabiyi, S. Saleem and N. Sandeep

The purpose of this paper is to provide an insight into the influence of gyrotactic microorganisms and Hall effect on the boundary layer flow of 29 nm CuO-water mixture on…

Abstract

Purpose

The purpose of this paper is to provide an insight into the influence of gyrotactic microorganisms and Hall effect on the boundary layer flow of 29 nm CuO-water mixture on the upper pointed surface of a rocket, over the bonnet of a car and upper pointed surface of an aircraft. This is true since all these objects are examples of an object with variable thickness.

Design/methodology/approach

The simplification of Rosseland approximation (Taylor series expansion of T4 about T) is avoided; thus, two different parameters relating to the study of nonlinear thermal radiation are obtained. The governing equation is non-dimensionalized, parameterized and solved numerically.

Findings

Maximum vertical and horizontal velocities of the 29 nm CuO-water nanofluid flow is guaranteed at a small value of Peclet number and large value of buoyancy parameter depending on the temperature difference. When the magnitude of thickness parameter χ is small, cross-flow velocity decreases with the velocity index and the opposite effect is observed when the magnitude of χ is large.

Originality/value

Directly or indirectly, the importance of the fluid flow which contains 29 nm CuO nanoparticle, water, and gyrotactic microorganisms in the presence of Hall current has been pointed out as an open question in the literature due to its relevance in imaging, ophthalmological and translational medicine informatics.

Details

Multidiscipline Modeling in Materials and Structures, vol. 14 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 4 September 2017

Syed Tauseef Mohyud-Din, Naveed Ahmed and Umar Khan

The purpose of this study is to investigate numerically the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with…

Abstract

Purpose

The purpose of this study is to investigate numerically the influence of nonlinear thermal radiation on the flow of a viscous fluid. The flow is confined in a channel with deformable porous walls.

Design/methodology/approach

Two numerical schemes, namely, Galerkin’s method (GM) and Runge–Kutta–Fehlberg (RKF) method have been used to obtain solutions after reducing the governing equations to a system of nonlinear ordinary differential equations.

Findings

Heat transfer rate falls at the upper wall owing to the decreasing values of the permeability parameter. However, at the lower wall, the same rate rises. Increment in θw increases the rate of heat transfer at both walls. Nusselt number also increases with the increasing values of Rd. Rd also uplifts the temperature distribution, except for the case where it falls near the lower wall owing to the contraction coupled with injection.

Originality/value

It is confirmed that the presented work is original.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 9
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 5 November 2019

Salman Ahmad, Muhammad Ijaz Khan, Tasawar Hayat, Muhammad Waqas and Ahmed Alsaedi

The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian…

Abstract

Purpose

The purpose of this paper is to study entropy generation in magneto-Jeffrey nanomaterial flow by impermeable moving boundary. Adopted nanomaterial model accounts Brownian and thermophoretic diffusions. Modeling is arranged for thermal radiation, nonlinear convection and viscous dissipation. In addition, the concept of Arrhenius activation energy associated with chemical reaction are introduced for description of mass transportation.

Design/methodology/approach

Homotopy algorithms are used to compute the system of ordinary differential equations.

Findings

The afore-stated analysis clearly notes that simultaneous aspects of activation energy and entropy generation are not yet investigated. Therefore, the intention here is to consider such effects to formulate and investigate the magneto-Jeffrey nanoliquid flow by impermeable moving surface.

Originality/value

As per the authors’ knowledge, no such work has yet been published in the literature.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of over 1000