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Article

Renato M Cotta, Carolina Palma Naveira-Cotta and Diego C. Knupp

The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary…

Abstract

Purpose

The purpose of this paper is to propose the generalized integral transform technique (GITT) to the solution of convection-diffusion problems with nonlinear boundary conditions by employing the corresponding nonlinear eigenvalue problem in the construction of the expansion basis.

Design/methodology/approach

The original nonlinear boundary condition coefficients in the problem formulation are all incorporated into the adopted eigenvalue problem, which may be itself integral transformed through a representative linear auxiliary problem, yielding a nonlinear algebraic eigenvalue problem for the associated eigenvalues and eigenvectors, to be solved along with the transformed ordinary differential system. The nonlinear eigenvalues computation may also be accomplished by rewriting the corresponding transcendental equation as an ordinary differential system for the eigenvalues, which is then simultaneously solved with the transformed potentials.

Findings

An application on one-dimensional transient diffusion with nonlinear boundary condition coefficients is selected for illustrating some important computational aspects and the convergence behavior of the proposed eigenfunction expansions. For comparison purposes, an alternative solution with a linear eigenvalue problem basis is also presented and implemented.

Originality/value

This novel approach can be further extended to various classes of nonlinear convection-diffusion problems, either already solved by the GITT with a linear coefficients basis, or new challenging applications with more involved nonlinearities.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Mohammad Niknami, Zahir Ahmed, Bashar Albaalbaki and Roger E Khayat

The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from…

Abstract

Purpose

The post-critical convective state for Rayleigh-Benard (RB) convection is studied using a nonlinear spectral-amplitude-perturbation approach in a fluid layer heated from below. The paper aims to discuss these issues.

Design/methodology/approach

In the spectral method the flow and temperature fields are expanded periodically along the layer and orthonormal shape functions are used in the transverse direction. A combined amplitude-perturbation approach is developed to solve the nonlinear spectral system in the post-critical range, even far from the linear stability threshold. Also, to leading order, the Lorenz model is recovered.

Findings

It is found that very small Prandtl numbers (Pr < 0.1) can change the Nusselt number, when terms to O(ε5/2) and higher are considered. However, to lower orders the Prandtl number does not affect the results. Variation of the Nusselt number to different orders is found to be highly consistent. Comparison with experimental results is made and a very good qualitative agreement is observed, even far from the linear threshold.

Originality/value

Unlike existing nonlinear formulations for RB thermal convection, the present combined spectral-perturbation approach provides a systematic method for mode selection. The number and type of modes to be included are directly related to the post-critical Rayleigh number. The method is not limited to the weakly nonlinear range.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25 no. 4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

C. RamReddy and P. Naveen

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a…

Abstract

Purpose

The purpose of this paper is to analyze the combined effects of thermal radiation and activation energy with a chemical reaction on the quadratic convective flow of a micropolar fluid over an inclined plate. Convective thermal boundary condition and suction/injection effects are considered at the surface of an inclined plate.

Design/methodology/approach

The convection along with nonlinear Boussinesq approximation (i.e. quadratic convection or nonlinear convection) and usual boundary layer assumptions is employed in the mathematical formulation. Highly coupled nonlinear governing equations are tackled by a combined local non-similarity and successive linearization techniques.

Findings

The behavior of various pertinent parameters on the fluid flow characteristics is conferred through graphs and it reveals that the qualitative behaviors of velocity, temperature, skin friction and heat transfer rates of a micropolar fluid are similar for Biot number and radiation parameters. The suction/injection and activation energy parameters increase the concentration of the micropolar fluid within the boundary layer, while the chemical reaction parameter reduces the concentration in the same region. Further, this quadratic convection shows a strong influence on the fluid flow characteristics and then the impact of pertinent parameters is more prominent on the physical quantities, compared therewith results of the linear convection.

Practical implications

This kind of investigation is useful in the mechanism of combustion, aerosol technology, high-temperature polymeric mixtures and solar collectors which are operated at moderate to very high temperatures.

Originality/value

This attempt is a unique contribution to the establishment of both micropolar fluid and activation energy. This kind of study even in the absence of quadratic convection is not yet noted.

Details

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

Keywords

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Article

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

Keywords

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Article

B. Mahanthesh, T. Brizlyn, SabirAli Shehzad and Gireesha B.J.

The nonlinear density thermal/solutal fluctuations in the buoyancy force term cannot be ignored when the temperature/concentration difference between the surface and fluid…

Abstract

Purpose

The nonlinear density thermal/solutal fluctuations in the buoyancy force term cannot be ignored when the temperature/concentration difference between the surface and fluid is large. The purpose of this paper is to investigate the nonlinear density fluctuations across a flowing fluid with heat mass transfer effects on a non-axial rotating plate. Therefore, the impact of nonlinear convection in the flow of Casson fluid over an oscillating plate has been analytically investigated.

Design/methodology/approach

The governing equations are modeled with the help of conservation equations of velocity, energy and concentration under the transient-state situation. The dimensional governing equations are non-dimensionalized by utilizing non-dimensional variables. Later, the subsequent non-dimensional problem has been solved analytically using Laplace transform method.

Findings

The effects of thermal Grashof number, solute Grashof number, nonlinear convection parameters, Casson fluid parameter, unsteady parameter, Prandtl number as well as Schmidt number on hydrodynamic, thermal and solute characteristics have been quantified. The numeric data for skin friction coefficient, Nusselt number and Sherwood number are presented. It is established the nonlinear convection aspect has a significant influence on heat and mass transport characteristics.

Originality/value

The effect of nonlinear convection in the dynamics of Casson fluid past an oscillating plate which is rotating non-axially is investigated for the first time.

Details

Multidiscipline Modeling in Materials and Structures, vol. 15 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

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Article

M. Mudassar Gulzar, Shagufta Jabeen, Muhammad Waqas, Sabir Ali Shehzad, Tasawar Hayat and Ahmed Alsaedi

The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by…

Abstract

Purpose

The purpose of this study is to scrutinize the effects of entropy generation and nonlinear mixed convection on the boundary layer flow of second grade fluid induced by stretching sheets. Heat transfer effects are accounted in view of viscous dissipation and nonlinear thermal radiation.

Design/methodology/approach

Optimal homotopic asymptotic method procedure is adopted to obtain the analytical solution of nonlinear ordinary differential equations.

Findings

It has been noticed that Hartmann and Brinkman number has reverse characteristics against entropy generation and Bejan number.

Originality/value

To the best of the authors’ knowledge, no such analysis has been reported to date.

Details

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

Keywords

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Article

D. Andrew S. Rees and Donald A. Nield

The purpose of this paper is to determine how the presence of an embedded, centrally placed, solid but heat-conducting block affects the onset and development of…

Abstract

Purpose

The purpose of this paper is to determine how the presence of an embedded, centrally placed, solid but heat-conducting block affects the onset and development of Darcy-Bénard convection.

Design/methodology/approach

Steady solutions are obtained using finite difference methods with SOR as the smoother. A detailed presentation is given of how the interface conditions are modelled, and how a continuity of pressure argument is used to determine the value of the streamfunction on the solid block.

Findings

The presence of the block affects strongly both the onset of convection and the nonlinear properties such as the mean Nusselt number and the strength of the fluid circulation. The smallest possible critical Darcy-Rayleigh is found to be 22.0152, which is smaller than 4π2, the value when the block is absent.

Research limitations/implications

The Darcy-Rayleigh number is restricted to values at or below 200, which is five times the critical value without a solid block, but the size and conductivity of the block vary between all admissible values.

Originality/value

This is the first investigation of the effect of internal obstacles on Darcy-Bénard convection.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

D. Andrew S. Rees

The purpose of this paper is to determine the manner in which a yield stress fluid begins convecting when it saturates a porous medium. A sidewall-heated rectangular…

Abstract

Purpose

The purpose of this paper is to determine the manner in which a yield stress fluid begins convecting when it saturates a porous medium. A sidewall-heated rectangular cavity is selected as the testbed for this pioneering work.

Design/methodology/approach

Steady solutions are obtained using a second order accurate finite difference method, line relaxation based on the Gauss-Seidel smoother, a Full Approximation Scheme multigrid algorithm with V-cycling and a regularization of the Darcy-Bingham model to smooth the piecewise linear relation between the Darcy flux and the applied body forces.

Findings

While Newtonian fluids always convect whenever the Darcy-Rayleigh number is nonzero, Bingham fluids are found to convect only when the Darcy-Rayleigh number exceeds a value which is linearly dependent on both the Rees-Bingham number and the overall perimeter of the rectangular cavity. Stagnation is always found in the centre of the cavity and in regions close to the four corners. Care must be taken over the selection of the regularization constant.

Research limitations/implications

The Darcy-Rayleigh number is restricted to values which are at or below 200.

Originality/value

This is the first investigation of the effect of yield stress on nonlinear convection in porous media.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 26 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Fabio Andrade Pontes, Emanuel Negrão Macêdo, Clauderino da Silva Batista, João Alves de Lima and João Nazareno Nonato Quaresma

The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform…

Abstract

Purpose

The purpose of this study is to show the procedure, application and main features of the hybrid numerical-analytical approach known as generalized integral transform technique by using it to study magnetohydrodynamic flow of electrically conductive Newtonian fluids inside flat parallel-plate channels subjected to a uniform and constant external magnetic field.

Design/methodology/approach

The mathematical formulation of the analyzed problem is given in terms of a streamfunction, obtained from the Navier–Stokes and energy equations, by considering steady state laminar and incompressible flow and constant physical properties.

Findings

Convergence analyses are performed and presented to illustrate the consistency of the integral transformation technique. The results for the velocity and temperature fields are generated and compared with those in the literature as a function of the main governing parameters.

Originality/value

A detailed analysis of the parametric sensibility of the main dimensionless parameters, such as the Reynolds number, Hartmann number, Eckert number, Prandtl number and electrical parameter, for some typical situations is performed.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 28 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

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Article

Muhammad Waqas, Saira Naz, Tasawar Hayat, Sabir Ali Shehzad and Ahmed Alsaedi

The purpose of this paper is to introduce the concept of improved Fourier–Fick laws subjected to variable fluid characteristics. Flow analysis in the stagnation region of…

Abstract

Purpose

The purpose of this paper is to introduce the concept of improved Fourier–Fick laws subjected to variable fluid characteristics. Flow analysis in the stagnation region of Oldroyd-B fluid is elaborated. Heat generation is present.

Design/methodology/approach

Optimal homotopy analysis method is used to obtain convergent solutions.

Findings

The outcomes reveal reduction in penetration depths of temperature and concentration due to involvement of thermal and solutal relaxation times of fluxes.

Originality/value

As per the authors’ knowledge, such analysis has not yet been reported.

Details

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

Keywords

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