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1 – 10 of over 2000The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with…
Abstract
Purpose
The purpose of this paper is to study the effects of surface mass transfer on the steady mixed convection flow from a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration.
Design/methodology/approach
An implicit finite difference scheme in combination with the quasilinearisation technique is employed to obtain non‐similar solutions of the governing boundary layer equations for momentum, temperature and concentration fields.
Findings
The numerical results are reported here to display the effects of mixed convection parameter, ratio of buoyancy forces, surface mass transfer (suction and injection), the ratio of free stream velocity to the composite reference velocity, Prandtl number and Schmidt number on velocity, temperature and concentration profiles as well as on skin friction, Nusselt number and Sherwood number.
Research limitations/implications
Thermophysical properties of the fluid in the flow model are assumed to be constant except the density variations causing a body force term in the momentum equation. The Boussinesq approximation is invoked for the fluid properties to relate density changes, and to couple in this way the temperature and concentration fields to the flow field. The concentration of diffusing species is assumed to be very small in comparison with other chemical species far away from the surface. Hence the Soret and Dufour effects are neglected. The stretching sheet is assumed to be subject to a power‐law wall temperature as well as to a power‐law wall concentration, in a parallel free stream.
Practical implications
Convective heat and mass transfer over a vertical stretching sheet in a parallel stream is very important for various design of technological process are hot rolling, wire drawing, glass‐fiber paper production, both metal and polymer sheets, for instance, in cooling of an infinite metallic plate in a cooling bath, the boundary layer along material handling conveyors, etc.
Originality/value
The paper studies the combined effects of thermal and mass diffusion over a vertical stretching sheet with surface mass transfer.
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Y.Y. Lok, I. Pop, D.B. Ingham and N. Amin
The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The…
Abstract
Purpose
The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The flow consists of a stagnation‐point flow and a uniform shear flow parallel to the surface of the sheet. The sheet is stretching with a velocity proportional to the distance from the stagnation point while the surface temperature is assumed to vary linearly. The paper attempts also to show that a similarity solution of this problem can be obtained.
Design/methodology/approach
Using a similarity transformation, the basic partial differential equations are first reduced to ordinary differential equations which are then solved numerically using the Keller box method for some values of the governing parameters. Both assisting and opposing flows are considered. The results are also obtained for both strong and weak concentration cases.
Findings
These results provide information about the effect of a/c (ratio of the stagnation point velocity and the stretching velocity), σ (shear flow parameter) and K (material parameter) on the flow and heat transfer characteristics in mixed convection flow near a non‐orthogonal stagnation‐point on a vertical stretching surface. The results show that the shear stress increases as K increases, while the heat flux from the surface of the sheet decreases with an increase in K.
Research limitations/implications
The results in this paper are valid only in the small region around the stagnation‐point on the vertical sheet. It is found that for smaller Prandtl number, there are difficulties in the numerical computation due to the occurrence of reversed flow for opposing flow. An extension of this work could be performed for the unsteady case.
Originality/value
The present results are original and new for the micropolar fluids. They are important in many practical applications in manufacturing processes in industry.
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Prabhugouda Mallanagouda Patil, Geeta Hadimani, Shashikant A., P.S. Kulkarni and Mukesh Kumar
This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of…
Abstract
Purpose
This paper aims to provide a detailed study on the influence of slip flow and thermal jump over mixed convection flow along an exponentially stretching surface. Also, impacts of suction/blowing, volumetric heat source/sink and velocity ratio parameter will be studied in this analysis.
Design/methodology/approach
The modeled governing equations for the assumed problem are dimensional nonlinear partial differential equations in nature. To reduce these equations, non-similar transformations are used to get the dimensionless nonlinear partial differential equations. Then, quasi-linearization technique is used to linearize these non-dimensional nonlinear partial differential equations. Finally, an implicit finite difference scheme is used to discretize the resulting equations.
Findings
The physical explanations are provided for the variations of various non-dimensional governing parameters over the velocity and temperature profiles. Also, the effects of these dimensionless parameters on skin friction coefficient and heat transfer rate are scrutinized in a manner which highlights their physical interpretation. The detailed discussion exhibits the fact that the streamwise co-ordinate velocity ratio parameter, partial slip parameter and the thermal jump parameter have significant influence over the flow and thermal fields.
Originality/value
This work has not been reported in the literature to the authors’ best of knowledge.
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Alessandra Borrelli, Giulia Giantesio, Maria Cristina Patria, Natalia C. Roşca, Alin V. Roşca and Ioan Pop
This paper aims to consider the influence of the temperature and of an external magnetic field on the steady oblique stagnation-point flow for a Boussinesquian nanofluid past a…
Abstract
Purpose
This paper aims to consider the influence of the temperature and of an external magnetic field on the steady oblique stagnation-point flow for a Boussinesquian nanofluid past a stretching or shrinking sheet.
Design/methodology/approach
The flow is reduced through similarity transformations to an ordinary boundary value problem, which is solved numerically in MATLAB using the bvp4c function. The behavior of the solution is discussed physically, and some analytical considerations concerning existence of the solution and the occurrence of dual solutions are drawn.
Findings
The study of the influence of an external magnetic field on the oblique stagnation-point flow of a Buongiorno's Boussinesquian nanofluid is carried out. The fluid clashes on a vertical stretching or shrinking sheet. Dual solutions appear for suitable values of the parameters.
Originality/value
The present results are new and original.
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Saeed Dinarvand, Reza Hosseini and Ioan Pop
The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting…
Abstract
Purpose
The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number.
Design/methodology/approach
The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases.
Findings
The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids.
Originality/value
Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.
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Gauri Shanker Seth, Rohit Sharma, Manoj Kumar Mishra and Ali J. Chamkha
The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick…
Abstract
Purpose
The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.
Design/methodology/approach
The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.
Findings
Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.
Originality/value
Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.
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Mahantesh M. Nandeppanavar, Kemparaju M.C. and Raveendra N.
This paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on…
Abstract
Purpose
This paper aims to find the influence of convective heat transfer, buoyancy proportions, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number on velocity, temperature and concentration profiles.
Design/methodology/approach
This paper explores the heat and mass transfer of a stagnation point stream of free convective Casson fluid over a moving vertical plate with nonlinear thermal radiation and convective boundary restrictions. The governing PDEs of stream, heat and concentration profiles were reformed into an arrangement of nonlinear ODEs by using similarity transformation. This framework was then tackled numerically by applying forth-order RK shooting strategy.
Findings
Distribution of flow, velocity and temperature profiles for different values of governing parameters are analyzed.
Originality/value
The original results are depicted in terms of plots.
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Keywords
Umair Khan, Aurang Zaib, Ioan Pop, Iskandar Waini and Anuar Ishak
Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery…
Abstract
Purpose
Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.
Design/methodology/approach
The mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.
Findings
For a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.
Originality/value
The present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.
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Keywords
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 and…
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.
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Aurang Zaib, Rizwan Ul Haq, A.J. Chamkha and M.M. Rashidi
The study aims to numerically examine the impact of nanoparticles on an unsteady flow of a Williamson fluid past a permeable convectively heated shrinking sheet.
Abstract
Purpose
The study aims to numerically examine the impact of nanoparticles on an unsteady flow of a Williamson fluid past a permeable convectively heated shrinking sheet.
Design/methodology/approach
In sort of the solution of the governing differential equations, suitable transformation variables are used to get the system of ODEs. The converted equations are then numerically solved via the shooting technique.
Findings
The impacts of such parameters on the velocity profile, temperature distribution and the concentration of nanoparticles are examined through graphs and tables. The results point out that multiple solutions are achieved for certain values of the suction parameter and for decelerating flow, while for accelerating flow, the solution is unique. Further, the non-Newtonian parameter reduces the fluid velocity and boosts the temperature distribution and concentration of nanoparticles in the first solution, while the reverse drift is noticed in the second solution.
Practical implications
The current results may be used in many applications such as biomedicine, industrial, electronics and solar energy.
Originality/value
The authors think that the current results are new and significant, which are used in many applications such as biomedicine, industrial, electronics and solar energy. The results have not been considered elsewhere.
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