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 micropolar…
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.
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P.K. Kameswaran, Z.G. Makukula, P. Sibanda, S.S. Motsa and P.V.S.N. Murthy
The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal…
Abstract
Purpose
The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal heat generation or absorption. The authors further introduce a new algorithm for solving heat transfer problems in fluid mechanics. The model used for the nanofluid incorporates the nanoparticle volume fraction parameter and a consideration of the chemical reaction effects among other features.
Design/methodology/approach
The partial differential equations for heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet were transformed into a system of nonlinear ordinary differential equations. Exact solutions for the boundary layer equations were obtained in terms of a confluent hypergeometric series. A novel spectral relaxation method (SRM) is used to obtain numerical approximations of the governing differential equations. The exact solutions are used to test the convergence and accuracy of the SRM.
Findings
Results were obtained for the fluid properties as well as the skin friction, and the heat and mass transfer rates. The results are compared with limiting cases from previous studies and they show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.
Originality/value
A new algorithm is used for the first time in this paper. In addition, new exact solutions for the energy and mass transport equations have been obtained in terms of a confluent hypergeometric series.
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Kazeem Babawale Kasali, Yusuf Olatunji Tijani, Matthew Oluwafemi Lawal and Yussuff Titilope Lawal
In this paper, we studied the steady flow of a radiative magnetohydrodynamics viscoelastic fluid over an exponentially stretching sheet. This present work incorporated the effects…
Abstract
Purpose
In this paper, we studied the steady flow of a radiative magnetohydrodynamics viscoelastic fluid over an exponentially stretching sheet. This present work incorporated the effects of Soret, Dufour, thermal radiation and chemical reaction.
Design/methodology/approach
An appropriate semi-analytical technique called homotopy analysis method (HAM) was used to solve the resulting nonlinear dimensionless boundary value problem, and the method was validated numerically using a finite difference scheme implemented on Maple software.
Findings
It was observed that apart from excellence agreement with the results in literature, the results obtained gave further insights into the behaviour of the system.
Originality/value
The purpose of this research is to investigate heat and mass transfer profiles of a MHD viscoelastic fluid flow over an exponentially stretching sheet in the influence of chemical reaction, thermal radiation and cross-diffusion which are hitherto neglected in previous studies.
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Olumide Falodun Bidemi and M.S. Sami Ahamed
The purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present…
Abstract
Purpose
The purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present study is to investigate the effects of Soret–Dufour on unsteady magneto-nanofluid flow.
Design/methodology/approach
Appropriate similarity transformations are used to convert the governing non-linear partial differential equations into coupled non-linear dimensionless partial differential equations. The transformed equations are then solved using spectral relaxation method.
Findings
The effects of controlling parameters on flow profiles is discussed and depicted with the aid of graphs. Results show that as the non-Newtonian Casson nanofluid parameter increases, the fluid velocity decreases. It is found that the Soret parameter enhance the temperature profile, while Dufour parameter decreases the concentration profile close to the wall.
Originality/value
The novelty of this paper is to consider the combined effects of both Soret and Dufour on unsteady Casson magneto-nanofluid flow. The present model is in an inclined plate embedded in a porous medium which to the best of our knowledge has not been considered in the past. The applied magnetic field gives rise to an opposing force which slows the motion of the fluid. A newly developed spectral method known as spectral relaxation method (SRM) is used in solving the modeled equations. SRM is an iterative method that employ the Gauss–Seidel approach in solving both linear and non-linear differential equations. SRM is found to be effective and accurate.
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D. Srinivasacharya and P. Vijay Kumar
– The purpose of this paper is to study the mixed convection in a nanofluid along an inclined wavy surface embedded in a porous medium.
Abstract
Purpose
The purpose of this paper is to study the mixed convection in a nanofluid along an inclined wavy surface embedded in a porous medium.
Design/methodology/approach
The complex wavy surface is transformed to a smooth surface by employing a coordinate transformation. Using the similarity transformation, the governing equations are transformed into a set of ordinary differential equations and then lineralized using the successive linearization method. The Chebyshev pseudo spectral method is then used to solve linearized differential equations.
Findings
The effects of Brownian motion parameter, thermophoresis parameter, amplitude of the wavy surface, angle of inclination of the wavy surface for aiding and opposing flows on the non-dimensional velocity, temperature, nanoparticle volume fraction, heat and nanoparticle mass transfer rates are studied and presented graphically.
Originality/value
This is the first instance in which mixed convection, inclined wavy surface and nanofluid is employed to model fluid flow.
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S. Sindhu, B.J. Gireesha and G. Sowmya
The influence of radiation on nanoliquid flow through a vertical microchannel in the presence of heat source is examined. This study aims to investigate the efficiency of…
Abstract
Purpose
The influence of radiation on nanoliquid flow through a vertical microchannel in the presence of heat source is examined. This study aims to investigate the efficiency of multi-walled carbon nanotube (MWCNT) considering water and engine oil as base fluid.
Design/methodology/approach
Nondimensional variables are used to obtain the dimensionless physical model. The solutions are computed numerically via Runge–Kutta–Fehlberg integration scheme.
Findings
It is established that (knf/kf)Lamina > (knf/kf)Column > (knf/kf)Tetrahedron > (knf/kf)Hexahedron > (knf/kf)Sphere.
Originality/value
Thermal conductivity of MWCNT is analyzed using different models. Also, it is remarked that Xue model exhibits higher thermal conductivity for MWCNT compared to Maxwell model, Yu-Choi model and Hamilton-Crosser model.
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Moses Sunday Dada and Cletus Onwubuoya
The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in…
Abstract
Purpose
The purpose of this paper is to consider heat and mass transfer on magnetohydrodynamics (MHD) Williamson fluid flow over a slendering stretching sheet with variable thickness in the presence of radiation and chemical reaction. All pertinent flow parameters are discussed and their influence on the hydrodynamics, thermal and concentration boundary layer are presented with the aid of the diagram.
Design/methodology/approach
The governing partial differential equations are reduced into a system of ordinary differential equations with the help of suitable similarity variables. A discrete version of the homotopy analysis method (HAM) called the spectral homotopy analysis method (SHAM) was used to solve the transformed equations. SHAM is efficient, and it converges faster than the HAM. The SHAM provides flexibility when solving linear ordinary differential equations with the use of the Chebyshev spectral collocation method.
Findings
The findings revealed that an increase in the variable thermal conductivity hike the temperature and the thermal boundary layer thickness, whereas the reverse is the case for velocity close to the wall.
Originality/value
The uniqueness of this paper is the exploration of combined effects of heat and mass transfer on MHD Williamson fluid flow over a slendering stretching sheet. The Williamson fluid term in the momentum equation is expressed as a linear function and the viscosity and thermal conductivity are considered to vary in the boundary layer.
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Sumit Kumar Mehta, Sukumar Pati, Shahid Ahmed, Prangan Bhattacharyya and Jishnu Jyoti Bordoloi
The purpose of this study is to analyze the thermal, hydraulic and entropy generation characteristics for laminar flow of water through a ribbed-wavy channel with the top wall as…
Abstract
Purpose
The purpose of this study is to analyze the thermal, hydraulic and entropy generation characteristics for laminar flow of water through a ribbed-wavy channel with the top wall as wavy and bottom wall as flat with ribs of three different geometries, namely, triangular, rectangular and semi-circular.
Design/methodology/approach
The finite element method-based numerical solver has been adopted to solve the governing transport equations.
Findings
A critical value of Reynolds number (Recri) is found beyond which, the average Nusselt number for the wavy or ribbed-wavy channel is more than that for a parallel plate channel and the value of Recri decreases with the increase in a number of ribs and for any given number of ribs, it is minimum for rectangular ribs. The performance factor (PF) sharply decreases with Reynolds number (Re) up to Re = 50 for all types of ribbed-wavy channels. For Re > 50, the change in PF with Re is gradual and decreases for all the ribbed cases and for the sinusoidal channel, it increases beyond Re = 100. The magnitude of PF strongly depends on the shape and number of ribs and Re. The relative magnitude of total entropy generation for different ribbed channels varies with Re and the number of ribs.
Practical implications
The findings of the present study are useful to design the economic heat exchanging devices.
Originality/value
The effects of shape and the number of ribs on the heat transfer performance and entropy generation have been investigated for the first time for the laminar flow regime. Also, the effects of shape and number of ribs on the flow and temperature fields and entropy generation have been investigated in detail.
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Ioan Pop, Siti Suzilliana Putri Mohamed Isa, Norihan M. Arifin, Roslinda Nazar, Norfifah Bachok and Fadzilah M. Ali
The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a…
Abstract
Purpose
The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically.
Design/methodology/approach
The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined.
Findings
Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter.
Originality/value
The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.
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Precious Sibanda, Sandile Motsa and Zodwa Makukula
The purpose of this paper is to study the steady laminar flow of a pressure driven third‐grade fluid with heat transfer in a horizontal channel. The study serves two purposes: to…
Abstract
Purpose
The purpose of this paper is to study the steady laminar flow of a pressure driven third‐grade fluid with heat transfer in a horizontal channel. The study serves two purposes: to correct the inaccurate results presented in Siddiqui et al., where the homotopy perturbation method was used, and to demonstrate the computational efficiency and accuracy of the spectral‐homotopy analysis methods (SHAM and MSHAM) in solving problems that arise in fluid mechanics.
Design/methodology/approach
Exact and approximate analytical series solutions of the non‐linear equations that govern the flow of a steady laminar flow of a third grade fluid through a horizontal channel are constructed using the homotopy analysis method and two new modifications of this method. These solutions are compared to the full numerical results. A new method for calculating the optimum value of the embedded auxiliary parameter ∼ is proposed.
Findings
The “standard” HAM and the two modifications of the HAM (the SHAM and the MSHAM) lead to faster convergence when compared to the homotopy perturbation method. The paper shows that when the same initial approximation is used, the HAM and the SHAM give identical results. Nonetheless, the advantage of the SHAM is that it eliminates the restriction of searching for solutions to the nonlinear equations in terms of prescribed solution forms that conform to the rule of solution expression and the rule of coefficient ergodicity. In addition, an alternative and more efficient implementation of the SHAM (referred to as the MSHAM) converges much faster, and for all parameter values.
Research limitations/implications
The spectral modification of the homotopy analysis method is a new procedure that has been shown to work efficiently for fluid flow problems in bounded domains. It however remains to be generalized and verified for more complicated nonlinear problems.
Originality/value
The spectral‐HAM has already been proposed and implemented by the authors in a recent paper. This paper serves the purpose of verifying and demonstrating the utility of the new spectral modification of the HAM in solving problems that arise in fluid mechanics. The MSHAM is a further modification of the SHAM to speed up converge and to allow for convergence for a much wider range of system parameter values. The utility of these methods has not been tested and verified for systems of nonlinear equations. For this reason as much emphasis has been placed on proving the reliability and validity of the solution techniques as on the physics of the problem.