M.M. Rashidi, M. Keimanesh and S.C. Rajvanshi
The purpose of this study is to investigate the problem of pulsatile flow in a porous annulus for small Reynolds number.
Abstract
Purpose
The purpose of this study is to investigate the problem of pulsatile flow in a porous annulus for small Reynolds number.
Design/methodology/approach
The similarity transformation for the governing equations gives a system of nonlinear ordinary differential equations which are analytically solved by the homotopy analysis method (HAM). The analytic solutions of non‐linear differential equation are constructed in the series form. The convergence of the series solutions is carefully analyzed.
Findings
Graphical results are presented to investigate the influence of different parameters on the flow behavior. Comparison between the solutions obtained by the HAM and the numerical solution shows good agreement.
Originality/value
An analysis for study on flow of an incompressible viscous fluid in the region lying between two concentric porous cylinders, under the assumption that a periodic pressure gradient is imposed across the annulus and that there is a uniform small transfer across two walls is presented. The HAM solutions are obtained for the equations governing the fluid flow.
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Rajneesh Kumar, Mandeep Kaur and S.C. Rajvanshi
The purpose of this paper is to establish a mathematical model to investigate the propagation of waves at an imperfect boundary between heat conducting micropolar elastic solid…
Abstract
Purpose
The purpose of this paper is to establish a mathematical model to investigate the propagation of waves at an imperfect boundary between heat conducting micropolar elastic solid and fluid media.
Design/methodology/approach
Wave propagation and reflection methods have been applied to solve the problem. The expressions for reflection and transmission coefficients are obtained. The corresponding derivation for the normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding has also been included.
Findings
A computer program is developed and numerical results are computed to obtain the reflection and transmission coefficients of various reflected waves with incident waves. Some special and particular cases are also discussed.
Originality/value
In this paper, stiffness effect on these amplitude ratios with the angle of incidence has been observed and depicted graphically.
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Mixed recirculatory flow in the annuli of stationary and rotatinghorizontal cylinders were studied numerically. A set of distorted‘false transient’ parameters were introduced to…
Abstract
Mixed recirculatory flow in the annuli of stationary and rotating horizontal cylinders were studied numerically. A set of distorted ‘false transient’ parameters were introduced to speed up the steady state solution of the unsteady vorticity, energy and stream function—vorticity equations. The inner cylinder of the annuli is assumed heated and rotating at Reynolds numbers that exclude the effects of centrifugal acceleration and three‐dimensional Taylor vortices. The Prandtl number considered is in the range of 0.01 to 1.0 and Rayleigh number in the range of 102 to 106. Radius ratios of the cylinders considered are 1.25, 2.5 and 5.0. For a radius ratio of 2.5, inner cylinder rotation in the Reynolds number range of 0 to 1120 was considered. Vertical eccentricities in the range of ±2/3 were studied for cases of the rotating inner cylinder. Numerical experiments show that the mean Nusselt number increases with Rayleigh number for both cases of concentric and eccentric stationary inner cylinder. At a Prandtl number of order 1.0 with a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow. At lower Prandtl number of the order 0.1 to 0.01, the mean Nusselt number remained fairly constant with respect to the rotational Reynolds number.
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Atul Kumar Ray, Vasu B., O. Anwar Beg, R.S.R. Gorla and P.V.S.N. Murthy
This paper aims to numerically investigate the two-dimensional unsteady laminar magnetohydrodynamic bioconvection flow and heat transfer of an electrically conducting…
Abstract
Purpose
This paper aims to numerically investigate the two-dimensional unsteady laminar magnetohydrodynamic bioconvection flow and heat transfer of an electrically conducting non-Newtonian Casson thin film with uniform thickness over a horizontal elastic sheet emerging from a slit in the presence of viscous dissipation. The composite effects of variable heat, mass, nanoparticle volume fraction and gyrotactic micro-organism flux are considered as is hydrodynamic (wall) slip. The Buongiorno nanoscale model is deployed which features Brownian motion and thermophoresis effects. The model studies the manufacturing fluid dynamics of smart magnetic bio-nano-polymer coatings.
Design/methodology/approach
The coupled non-linear partial differential boundary-layer equations governing the flow, heat and nano-particle and micro-organism mass transfer are reduced to a set of coupled non-dimensional equations using the appropriate transformations and then solved as an nonlinear boundary value problem with the semi-numerical Liao homotopy analysis method (HAM).Validation with a generalized differential quadrature (GDQ) numerical technique is included.
Findings
An increase in velocity slip results in a significant decrement in skin friction coefficient and Sherwood number, whereas it generates a substantial enhancement in Nusselt number and motile micro-organism number density. The computations reveal that the bioconvection Schmidt number decreases the micro-organism concentration and boundary-layer thickness which is attributable to a rise in viscous diffusion rate. Increasing bioconvection Péclet number substantially elevates the temperatures in the regime, thermal boundary layer thickness, nanoparticle concentration values and nano-particle species boundary layer thickness. The computations demonstrate the excellent versatility of HAM and GDQ in solving nonlinear multi-physical nano-bioconvection flows in thermal sciences and furthermore are relevant to application in the synthesis of smart biopolymers, microbial fuel cell coatings, etc.
Research limitations/implications
The numerical study is valid for two-dimensional, unsteady, laminar Casson film flow with nanoparticles over an elastic sheet in presence of variable heat, mass and nanoparticle volume fraction flux. The film has uniform thickness and flow is transpiring from slit which is fixed at origin.
Social implications
The study has significant applications in the manufacturing dynamics of nano-bio-polymers and the magnetic field control of materials processing systems. Furthermore, it is relevant to application in the synthesis of smart biopolymers, microbial fuel cell coatings, etc.
Originality/value
The originality of the study is to address the simultaneous effects of unsteady and variable surface fluxes on Casson nanofluid transport of gyrotactic bio-convection thin film over a stretching sheet in the presence of a transverse magnetic field. Validation of HAM with a GDQ numerical technique is included. The present numerical approaches (HAM and GDQ) offer excellent promise in simulating such multi-physical problems of interest in thermal thin film rheological fluid dynamics.
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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.
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Rajneesh Kumar and Shaloo Devi
The purpose of this paper is to deal with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with three-phase-lag (TPL…
Abstract
Purpose
The purpose of this paper is to deal with the study of plane waves and fundamental solution in a modified couple stress generalized thermoelastic solid with three-phase-lag (TPL) model of thermoelasticity.
Design/methodology/approach
It is found that for two-dimensional model, there exists two longitudinal waves, namely, longitudinal wave (P-wave), thermal wave (T-wave), and a set of coupled transverse waves (SV1 and SV2 waves). In addition, the fundamental solution for the system of differential equations for steady oscillations in terms of elementary functions has been constructed. Some properties of fundamental solution are also established. Various particular cases of interest are also deduced from the present investigations and compared with the known results.
Findings
The phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically and presented graphically to see the effect of TPL model, dual-phase-lag (DPL) model and GN-III model in the presence of couple stress parameter.
Originality/value
The results are compared with couple stress TPL model, couple stress DPL model and GN-III model.
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To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau…
Abstract
Purpose
To achieve material-invariant formulation for heat transfer of Carreau nanofluid, the effect of Cattaneo–Christov heat flux is studied on a natural convective flow of Carreau nanofluid past a vertical plate with the periodic variations of surface temperature and the concentration of species. Buongiorno model is considered for nanofluid transport, which includes the relative slip mechanisms, Brownian motion and thermophoresis.
Design/methodology/approach
The governing equations are non-dimensionalized using suitable transformations, further reduced to non-similar form using stream function formulation and solved by local non-similarity method with homotopy analysis method. The numerical computations are validated and verified by comparing with earlier published results and are found to be in good agreement.
Findings
The effects of varying the physical parameters such as Prandtl number, Schmidt number, Weissenberg number, thermophoresis parameter, Brownian motion parameter and buoyancy ratio parameter on velocity, temperature and species concentration are discussed and presented through graphs. The results explored that the velocity of shear thinning fluid is raised by increasing the Weissenberg number, while contrary response is seen for the shear thickening fluid. It is also found that heat transfer in Cattaneo–Christov heat conduction model is less than that in Fourier’s heat conduction model. Furthermore, the temperature and thermal boundary layer thickness expand with the increase in thermophoresis and Brownian motion parameter, whereas nanoparticle volume fraction increases with increase in thermophoresis parameter, but reverse trend is observed with increase in Brownian motion parameter.
Originality/value
The present investigation is relatively original as very little research has been reported on Carreau nanofluids under the effect of Cattaneo–Christov heat flux model.
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This paper aims to examine the influence of radiative nanoparticles on incompressible electrically conducting upper convected Maxwell fluid (rate type fluid) flow over a…
Abstract
Purpose
This paper aims to examine the influence of radiative nanoparticles on incompressible electrically conducting upper convected Maxwell fluid (rate type fluid) flow over a convectively heated exponential stretching sheet with suction/injection in the presence of heat source taking chemical reaction into account. Also, a comparison of the flow behavior of Newtonian and Maxwell fluid containing nanoparticles under the effect of different thermophysical parameters is elaborated. Velocity, temperature and nanoparticle volume fractions are assumed to have exponential distribution at boundary. Buongiorno model is considered for nanofluid transport.
Design/methodology/approach
The equations, which govern the flow, are reduced to ordinary differential equations using suitable transformation. The transformed equations are solved using a robust homotopy analysis method. The convergence of the homotopy series solution is explicitly discussed. The present results are compared with the results reported in the literature and are found to be in good agreement.
Findings
It is observed from the present study that larger relaxation time leads to slower recovery, which results in a decrease in velocity, whereas temperature and nanoparticle volume fraction is increased. Maxwell nanofluid has lower velocity with higher temperature and nanoparticle volume fraction when compared with Newtonian counterpart. Also, the presence of magnetic field leads to decrease the velocity of the nanofluid and enhances the skin coefficient friction. The existence of thermal radiation and heat source enhance the temperature. Further, the presence of chemical reaction leads to decrease in nanoparticle volume fraction. Higher value of Deborah number results in lower the rate of heat and mass transfer.
Originality/value
The novelty of present work lies in understanding the impact of fluid elasticity and radiative nanoparticles on the flow over convectively heated exponentially boundary surface in the presence of a magnetic field using homotopy analysis method. The current results may help in designing electronic and industrial applicants. The present outputs have not been considered elsewhere.
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R. Ellahi, Sadiq M. Sait, N. Shehzad and Z. Ayaz
The purpose of this paper is to present the investigation of the pressure-driven flow of aluminum oxide-water based nanofluid with the combined effect of entropy generation and…
Abstract
Purpose
The purpose of this paper is to present the investigation of the pressure-driven flow of aluminum oxide-water based nanofluid with the combined effect of entropy generation and radiative electro-magnetohydrodynamics filled with porous media inside a symmetric wavy channel.
Design/methodology/approach
The non-linear coupled differential equations are first converted into a number of ordinary differential equations with appropriate transformations and then analytical solutions are obtained by homotopic approach. Numerical simulation has been designed by the most efficient approach known homotopic-based Mathematica package BVPh 2.0 technique. The long wavelength approximation over the channel walls is taken into account. The obtained analytical results have been validated through graphs to infer the role of most involved pertinent parameters, whereas the characteristics of heat transfer and shear stress phenomena are presented and examined numerically.
Findings
It is found that the velocity profile decreases near to the channel. This is in accordance with the physical expectation because resistive force acts opposite the direction of fluid motion, which causes a decrease in velocity. It is seen that when the electromagnetic parameter increases then the velocity close to the central walls decreases whereas quite an opposite behavior is noted near to the walls. This happens because of the combined influence of electro-magnetohydrodynamics. It is perceived that by increasing the magnetic field parameter, Darcy number, radiation parameter, electromagnetic parameter and the temperature profile increases, and this is because of thermal buoyancy effect. For radiation and electromagnetic parameters, energy loss at the lower wall has substantial impact compared to the upper wall. Residual error minimizes at 20th order iterations.
Originality/value
The proposed prospective model is designed to explore the simultaneous effects of aluminum oxide-water base nanofluid, electro-magnetohydrodynamics and entropy generation through porous media. To the best of author’s knowledge, this model is reported for the first time.
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Aydin Zehforoosh, Siamak Hossainpour and Mohammad Mehdi Rashidi
The purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on…
Abstract
Purpose
The purpose of this study is to indicate the effect of mounting heat generating porous matrix in a close cavity on the Brownian term of CuO-water nanofluid and its impact on improving the Nusselt number.
Design/methodology/approach
Because of the presence of heat source in porous matrix, couple of energy equations is solved for porous matrix and nanofluid separately. Thermal conductivity and viscosity of nanofluid were assumed to be consisting of a static component and a Brownian component that were functions of volume fraction of the nanofluid and temperature. To explain the effect of the Brownian term on the flow and heat fields, different parameters such as heat conduction ratio, interstitial heat transfer coefficient, Rayleigh number, concentration of nanoparticles and porous material porosity were investigated and compared to those of the non-Brownian solution.
Findings
The Brownian term caused the cooling of porous matrix because of rising thermal conductivity. Mounting the porous material into cavity changes the temperature distribution and increases Brownian term effect and heat transfer functionality of the nanofluid. Besides, the effect of the Brownian term was seen to be greatest at low Rayleigh number, low-porosity and small thermal conductivity of the porous matrix. It is noteworthy that because of decrement of thermal conduction in high porosities, the impact of Brownian term drops severely making it possible to obtain reliable results even in the case of neglecting Brownian term in these porosities.
Originality/value
The effect of mounting the porous matrix with internal heat generation was investigated on the improvement of variable properties of nanofluid.