M.M. Rashidi, T. Hayat, M. Keimanesh and A.A. Hendi
The purpose of this paper is to discuss the natural convection flow of an incompressible third grade fluid between two parallel plates. The basic equations governing the flow are…
Abstract
Purpose
The purpose of this paper is to discuss the natural convection flow of an incompressible third grade fluid between two parallel plates. The basic equations governing the flow are reduced to a nonlinear ordinary differential equation.
Design/methodology/approach
The resulting nonlinear ordinary differential equation is solved by multi‐step differential transform method (MDTM).
Findings
The obtained solutions in comparison with the numerical solutions (fourth‐order Runge‐Kutta) admit a remarkable accuracy.
Originality/value
The analysis illustrates the validity and the great potential of the MDTM in solving nonlinear differential equations.
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Tasawar Hayat, Muhammad Farooq and A. Alsaedi
– The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects.
Abstract
Purpose
The purpose of this paper is to focus on the stratified phenomenon through vertical stretching cylinder in the region of stagnation point with slip effects.
Design/methodology/approach
Homotopy analysis method is used to find the series solutions of the governing equations.
Findings
Velocity profile decreases with an increase in stratified parameters due to temperature and concentration. Velocity and thermal slips cause a reduction in the velocity profile. Thermally stratified and thermal slip parameters reduce the temperature field.
Originality/value
The present analysis has not been existed in the literature yet.
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The purpose of this paper is to focus on convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic…
Abstract
Purpose
The purpose of this paper is to focus on convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. The walls of the microchannel are subjected to constant asymmetric heat fluxes and also the first order catalytic reaction. To represent the non-equilibrium region near the surfaces, the Navier’s slip condition is considered at the surfaces because of the non-adherence of the fluid-solid interface and the microscopic roughness in microchannels.
Design/methodology/approach
Employing the Brinkman model for the flow in the porous medium and the “clear fluid compatible” model as a viscous dissipation model, the conservative partial differential equations have been transformed into a system of ordinary ones via the similarity variables. Closed form exact solutions are obtained analytically based on dimensionless parameters of velocity, temperature and species concentration.
Findings
Results show that the addition of Cu-nanoparticles to the fluid has a significant influence on decreasing concentration, temperature distribution at the both walls and velocity profile along the microchannel. In addition, total heat transfer in microchannel increases as nanoparticles add to the fluid. Slip parameter and Hartmann number have the decreasing effects on concentration and temperature distributions. Slip parameter leads to increase velocity profiles, while Hartmann number has an opposite trend in velocity profiles. These two parameters increase the total heat transfer rate significantly.
Originality/value
In the present study, a comprehensive analytical solution has been obtained for convective heat and mass transfer characteristics of Cu-water nanofluid inside a porous microchannel in the presence of a uniform magnetic field. Finally, the effects of several parameters such as Darcy number, nanoparticle volume fraction, slip parameter, Hartmann number, Brinkman number, asymmetric heat flux parameter, Soret and Damkohler numbers on total heat transfer rate and fluid flow profiles are studied in more detail. To the best of author’s knowledge, no study has been conducted to this subject and the results are original.
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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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J. Rajakumar, P. Saikrishnan and A. Chamkha
The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field.
Abstract
Purpose
The purpose of this paper is to consider axisymmetric mixed convection flow of water over a sphere with variable viscosity and Prandtl number and an applied magnetic field.
Design/methodology/approach
The non-similar solutions have been obtained from the origin of the streamwise co-ordinate to the point of zero skin friction using quasilinearization technique with an implicit finite-difference scheme.
Findings
The effect of M is not notable on the temperature and heat transfer coefficient when λ is large. The skin friction coefficient and velocity profile are enhance with the increase of MHD parameter M when λ is small. Viscous dissipation has no significant on the skin friction coefficient under MHD effect. For M=1, the movement of the slot or slot suction or slot injection do not cause any effect on flow separation. The slot suction and the movement of the slot in downstream direction delay the point of zero skin friction for M=0.
Originality/value
The present results are original and new for water boundary-layer flow over sphere in mixed convection flow with MHD effect and non-uniform mass transfer. So this study would be useful in analysing the skin friction and heat transfer coefficient on sphere of mixed convection flow of water boundary layer with MHD effect.
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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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T. Hayat, S.A. Shehzad and A. Alsaedi
– The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink.
Abstract
Purpose
The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink.
Design/methodology/approach
Similarity transformations are utilized to reduce the nonlinear partial differential equations into ordinary differential equations. The governing nonlinear problems are solved by homotopy analysis method.
Findings
The paper found that the velocities decrease while temperature increases for higher Hartman number. It is also seen that the thermal boundary layer thickness and temperature are increased with an increase in variable thermal conductivity parameter and heat source/sink parameter.
Practical implications
Heat transfer analysis with heat source/sink has pivotal role in many industrial applications like cooling of an infinite metallic plate in a cooling bath, drawing of plastic films, nuclear plants, gas turbines, various propulsion devices for missiles, space vehicles and processes occurring at high temperatures.
Originality/value
This study discusses the magnetohydrodynamic three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. No such analysis exists in the literature yet.
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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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Abderrahmane Baïri, Juan Mario García de María, Nacim Alilat, Najib Laraqi and Jean-Gabriel Bauzin
The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such…
Abstract
Purpose
The purpose of this paper is to propose correlations between Nusselt and Rayleigh numbers for the case of inclined and closed air-filled hemispherical cavities. The disk of such cavities is subjected to a constant heat flux. The study covers a wide range of Rayleigh numbers from 5×107 to 2.55×1012.
Design/methodology/approach
Correlations are obtained from numerical approach validated by experimental measurements on some configurations, valid for several angles of inclination of the cavity between 0° (horizontal disk) and 90° (vertical disk) in steps of 15°.
Findings
The statistical analysis of a large number of calculations leads to reliable results covering laminar, transitional and turbulent natural convection heat transfer zones.
Practical implications
The proposed correlations provide solutions for applications in several fields of engineering such as solar energy, aerospace, building, safety and security.
Originality/value
The new relations proposed are the first published for high Rayleigh numbers for this type of geometry. They supplement the knowledge of natural convection in hemispherical inclined cavities and constitute a useful tool for application in various engineering areas as solar energy (thermal collector, still, pyranometer, albedometer, pyrgeometer), aerospace (embarked electronics), building, safety and security (controlling and recording sensors).
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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.