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Krishnendu Bhattacharyya - One of the best experts on this subject based on the ideXlab platform.
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reactive solute transfer in a stagnation point flow over a shrinking sheet with a diffusive mass flux
Journal of Applied Mechanics and Technical Physics, 2015Co-Authors: Krishnendu BhattacharyyaAbstract:Reactive solute transfer in a boundary-layer stagnation-point flow over a shrinking sheet with a uniform diffusive mass flux is investigated. The first-order chemical reaction is considered. By similarity transformations, the governing partial differential equations are converted into self-similar nonlinear ordinary differential equations. Then the transformed equations are solved numerically by using the shooting method. Dual solutions for the solute distribution are found. The study shows that the concentRation at the point increases with increasing Velocity Ratio Parameter for the first solution and decreases for the second solution. Due to an increase in the Schmidt number and reaction rate Parameter, the concentRation and concentRation boundary layer thickness decrease in the presence of the mass flux.
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mhd stagnation point flow of casson fluid and heat transfer over a stretching sheet with thermal radiation
Journal of Thermodynamics, 2013Co-Authors: Krishnendu BhattacharyyaAbstract:The two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If Velocity Ratio Parameter (B) and magnetic Parameter (M) increase, then the Velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the Velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson Parameter (β). The Velocity Ratio Parameter, Casson Parameter, and magnetic Parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of Velocity Ratio Parameter. The rate of heat transfer is enhanced with increasing magnetic Parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.
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heat transfer analysis in unsteady boundary layer stagnation point flow towards a shrinking stretching sheet
Ain Shams Engineering Journal, 2013Co-Authors: Krishnendu BhattacharyyaAbstract:Abstract The heat transfer in unsteady boundary layer stagnation-point flow over a shrinking/stretching sheet is investigated. The surface temperature of the sheet is taken time dependent. The governing equations are transformed into self-similar ordinary differential equations by adopting similarity transformations and then the converted equations are solved numerically by shooting method. The study reveals that in addition to the Velocity field, for the temperature distribution the dual solutions exist for some values of Velocity Ratio Parameter. The heat transfer rate enhances due to the unsteadiness of the flow. The temperature for first solution decreases with unsteadiness Parameter, and for second solution the temperature initially decreases, but it increases at large distance from the sheet. Moreover, for dual solutions as well as unique solution cases, the heat transfer rate increases with the Prandtl number in presence of unsteadiness.
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stagnation point flow and heat transfer over an exponentially shrinking sheet
Communications in Nonlinear Science and Numerical Simulation, 2012Co-Authors: Krishnendu Bhattacharyya, K VajraveluAbstract:Abstract An analysis is carried out to investigate the stagnation-point flow and heat transfer over an exponentially shrinking sheet. Using the boundary layer approximation and a similarity transformation in exponential form, the governing mathematical equations are transformed into coupled, nonlinear ordinary differential equations which are then solved numerically by a shooting method with fourth order Runge–Kutta integRation scheme. The analysis reveals that a solution exists only when the Velocity Ratio Parameter satisfies the inequality −1.487068 ⩽ c/a. Also, the numerical calculations exhibit the existence of dual solutions for the Velocity and the temperature fields; and it is observed that their boundary layers are thinner for the first solution (in comparison with the second). Moreover, the heat transfer from the sheet increases with an increase in c/a for the first solution, while the heat transfer decreases with increasing c/a for the second solution, and ultimately heat absorption occurs.
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mhd boundary layer stagnation point flow and mass transfer over a permeable shrinking sheet with suction blowing and chemical reaction 1
2012Co-Authors: Krishnendu Bhattacharyya, Golam Arif, Wazed Ali PramanikAbstract:An analysis is made to study the mass transfer with chemical reaction in MHD boundary layer stagnation-point flow of an electrically conducting viscous incompressible fluid over a shrinking sheet with suction or blowing. The flow is permeated by an externally applied magnetic field normal to the plane of flow. The self-similar equations corresponding to the Velocity and concentRation fields are obtained by similarity transformations and are then solved numerically by the finite dierence method using quasilinearization technique. The study reveals that the momentum and solute boundary layer thicknesses decrease with Velocity Ratio Parameter and magnetic field strength. Furthermore, it is noted that due to larger shrinking Velocity of the sheet and for variable concentRation distribution along the sheet, the mass absorption occurs in some cases.
G C Layek - One of the best experts on this subject based on the ideXlab platform.
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effects of suction blowing on steady boundary layer stagnation point flow and heat transfer towards a shrinking sheet with thermal radiation
International Journal of Heat and Mass Transfer, 2011Co-Authors: Krishnendu Bhattacharyya, G C LayekAbstract:In this paper, the effects of suction/blowing and thermal radiation on steady boundary layer stagnation-point flow and heat transfer over a porous shrinking sheet are investigated. The existence of dual solutions, unique solution and non-existence of solution for self-similar equations of the flow and heat transfer are analyzed numerically. It is noted that the range of Velocity Ratio Parameter where the solution exists increases/decreases with increasing suction/blowing. With increasing suction, temperature at the wall is found to increase (decrease) for the first (second) solution. Due to increasing Prandtl number and thermal radiation Parameter the thermal boundary layer thickness becomes thinner.
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slip effects on boundary layer stagnation point flow and heat transfer towards a shrinking sheet
International Journal of Heat and Mass Transfer, 2011Co-Authors: Krishnendu Bhattacharyya, Swati Mukhopadhyay, G C LayekAbstract:Abstract In the present study, we analyze the effects of partial slip on steady boundary layer stagnation-point flow of an incompressible fluid and heat transfer towards a shrinking sheet. Similarity transformation technique is adopted to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This investigation explores the conditions of the non-existence, existence, uniqueness and duality of the solutions of self-similar equations numerically. Due to the increase of slip Parameter ( δ ), the range of Velocity Ratio Parameter ( c / a ) where the similarity solution exists, increases.
Ali J Chamkha - One of the best experts on this subject based on the ideXlab platform.
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Non-similar Solutions of MHD Mixed Convection over an Exponentially Stretching Surface: Influence of Non-uniform Heat Source or Sink
'Geophysical Center of the Russian Academy of Sciences', 2021Co-Authors: P.m. Patil, D.n. Latha, Ali J ChamkhaAbstract:In this paper, an analysis of magnetohydrodynamic (MHD) mixed convection over an exponentially stretching surface in the presence of a non-uniform heat source/sink and suction/injection is presented. The governing boundary layer equations are transformed into a set of non-dimensional equations by using a group of non-similar transformations. The resulting highly non-linear coupled partial differential equations are solved by using the implicit finite difference method in combination with the quasilinearization technique. Numerical results for the Velocity, temperature and concentRation profiles, as well as the skin friction coefficient, wall heat transfer and mass transfer rates are computed and presented graphically for various Parameters. The results indicate that the Velocity profile reduces, while the temperature profile increases in presence of the effects of magnetic field and suction at the wall. The Velocity Ratio Parameter increases the skin-friction coefficient and the Schmidt number decreases the wall mass transfer rate. The temperature profile increases for the positive values of Eckert number and space as well as temperature dependent heat source/sink Parameters, while the opposite behavior is observed for negative values of same Parameters
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heat transfer on the cross flow of micropolar fluids over a thin needle moving in a parallel stream influenced by binary chemical reaction and arrhenius activation energy
European Physical Journal Plus, 2019Co-Authors: Fazle Mabood, Ali J Chamkha, M K NayakAbstract:Emerging engineering and industrial needs made the prime concern of this article to investigate the thermal management on the cross flow of micropolar fluids over a thin needle moving in a parallel stream. The flow is subject to binary chemical reaction and Arrhenius activation energy. The mathematical model of the considered physical problem consists of coupled nonlinear partial differential equations: conservation of mass, momentum, energy, and concentRation equation. The dimensionless transformed governing equations subject to the given boundary conditions have been solved directly by the Runge-Kutta Fehlberg fourth- fifth-order method followed by the shooting technique. Graphical results relative to the interaction effects of dynamic thermo-physical dimensionless Parameters such as Richardson Parameter, Dufour number, Soret number, Prandtl number, temperature Ratio Parameter, nondimensional activation energy, chemical reaction Parameter and Velocity Ratio Parameter controlling the flow, heat and mass transfer features are presented and analyzed. It can be seen, from the study, that the skin friction due to angular Velocity reduces with increase in size of the needle and it upsurges due to the increase in material Parameter. The obtained numerical results revealed that the augmented Richardson Parameter is in favor of a greater heat transfer enhancement. The obtained results show a better agreement of this model with the previously published results.
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unsteady mhd boundary layer flow of tangent hyperbolic two phase nanofluid of moving stretched porous wedge
International Journal of Numerical Methods for Heat & Fluid Flow, 2018Co-Authors: A Mahdy, Ali J ChamkhaAbstract:Purpose The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish. Design/methodology/approach The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique. Findings Numerical calculations point out that pressure gradient Parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentRation. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and Velocity Ratio Parameter reduce the skin friction coefficient. Again, the horizontal Velocity component enhances with upgrading power law index, unsteadiness Parameter, Velocity Ratio Parameter and Darcy number and it reduces with rising values of Weissenberg number. Originality/value A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.
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impact of nonlinear thermal radiation on stagnation point flow of a carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy
Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 2018Co-Authors: Aurang Zaib, Ali J Chamkha, M M Rashidi, Nurul Farahain MohammadAbstract:This research peruses the characteristics of nanoparticles on stagnation point flow of a generalized Newtonian Carreau fluid past a nonlinear stretching sheet with nonlinear thermal radiation. The process of mass transfer is modeled using activation energy and binary chemical reaction along with the Brownian motion and thermophoresis. For energy activation a modified Arrhenius function is invoked. With regard to the solution of the governing differential equations, suitable transformation variables are used to obtain the system of nonlinear ordinary differential equations before being numerically solved using the shooting method. Graphical results are shown in order to scrutinize the behavior of pertinent Parameters on Velocity, temperature profiles, and concentRation of nanoparticle. Also, the behavior of fluid flow is investigated through the coefficient of the skin friction, Nusselt number, Sherwood number, and streamlines. Results showed that the Velocity Ratio Parameter serves to increase the velocit...
Ch Kishore - One of the best experts on this subject based on the ideXlab platform.
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effects of exothermic chemical reaction with arrhenius activation energy non uniform heat source sink on mhd stagnation point flow of a casson fluid over a nonlinear stretching sheet with variable fluid properties and slip conditions
Journal of the Nigerian Mathematical Society, 2017Co-Authors: M Monica, J Sucharitha, Ch KishoreAbstract:In this analysis, effects of exothermic chemical reactions with Arrhenius activation energy, non-uniform heat source/sink on magnetohydrodynamic stagnation point flow of a Casson fluid over a nonlinear stretching sheet with variable viscosity, thermal conductivity and slip boundary conditions have been investigated. An appropriate similarity transformations were used to transform the governing partial differential equations into coupled nonlinear ordinary differential equations. The transformed ordinary differential equations were then solved by efficient numerical technique known as Keller Box method. The various Parameters such as Prandtl number (Pr), Eckert number (Ec), Magnetic Parameter (M), Casson Parameter (β), thermal radiation (R), non-uniform heat source/sink ($A^∗$, $B^∗$) , Velocity Ratio Parameter(λ), nonlinear stretching Parameter (n), chemical reaction rate constant (α), activation energy (E) , temperature dependent viscosity (ξ) , temperature dependent thermal conductivity ($\epsilon$) and slip Parameters ($S_1$, $S_2$, $S_3$ ) determining the Velocity, temperature and concentRation distributions, the local Skin friction coefficient, the local Nusselt number and the local Sherwood number governing such a flow were also analyzed. On analysis it has been found that the Skin friction coefficient, Local Nusselt number and Local Sherwood number decreases with respect to Velocity, thermal and concentRation slips respectively.
Tasawar Hayat - One of the best experts on this subject based on the ideXlab platform.
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the role of γal2o3 h2o and γal2o3 c2h6o2 nanomaterials in darcy forchheimer stagnation point flow an analysis using entropy optimization
International Journal of Thermal Sciences, 2019Co-Authors: Ijaz M. Khan, Tasawar Hayat, M Waqas, Faisal Shah, A AlsaediAbstract:Abstract Nanomaterials belong to a new class of materials with increased thermo-physical characteristics and heat transport performance. A comprehensive spectrum of applications in science and mechanical engineering could possibly help from them. Therefore keeping such effectiveness in mind we pointed to explore the characteristics of nanomaterial in non-Darcy mixed convective flow of viscous nanofluid through effective and without effective Prandtl number towards a stretched surface. Through implementation of second thermodynamics law total entropy rate is obtained. Stagnation point flow is pointed out. Shooting technique is implemented to tackle the nonlinear equations for numerical results. The variations in entropy geneRation, Velocity, Bejan number and temperature fields for different estimations of flow Parameters like mixed convection Parameter (0.0–0.4), inverse Darcy number (0.0–0.4), Inertia Parameter (1.0–5.8), Velocity Ratio Parameter (0.0–0.4) and nanoparticle volume fraction (0.00–0.8) are discussed and the results are graphically presented. Skin friction and Nusselt number of considered flow are discussed via graphically sketch. Moreover, it is examined that Velocity of fluid particles increases for both effective and without effective Prandtl number with rising estimations of nanoparticles volume fractions. It is also examined that entropy rate shows dual behavior verses nanoparticles volume fraction. Entropy rate enhances in case of effective Prandtl number, while decays in case without effective Prandtl number.
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magneto hydrodynamical numerical simulation of heat transfer in mhd stagnation point flow of cross fluid model towards a stretched surface
Physics and Chemistry of Liquids, 2018Co-Authors: Ijaz M. Khan, Tasawar Hayat, M Waqas, A AlsaediAbstract:ABSTRACTHere formulation and computations are presented to introduce the novel concept of activation energy in chemically reacting stagnation point flow towards a stretching sheet. Constitutive expression for Cross liquid is taken into account. Magnetic field is utilised in the transverse direction. Application of suitable variables generates the non-linear differential systems. Numerical solution by Runge–Kutta–Fehlberg approach is presented. Characteristics for the significant variables like Weissenberg number, Hartmann number, Schmidt number, activation energy chemical reaction Parameter, Velocity Ratio Parameter and Prandtl number on the physical quantities are addressed through graphs and tables. Our computations reveal that species concentRation rises via larger activation energy Parameter whereas it decays when Schmidt number is incremented. The Weissenberg number has opposite characteristics for local Nusselt and Sherwood numbers when compared with surface drag force.
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mhd stagnation point flow of jeffrey fluid over a convectively heated stretching sheet
Computers & Fluids, 2015Co-Authors: Tasawar Hayat, Sadia Asad, M Mustafa, A AlsaediAbstract:Abstract Two-dimensional stagnation-point flow of Jeffrey fluid over an exponentially stretching sheet is studied. Convective boundary condition is used for the analysis of thermal boundary layer. In addition the combined effects of thermal radiation and magnetic field are taken into consideRation. The developed nonlinear problems have been solved for the series solution. The convergence of the series solutions is carefully analyzed. The behaviors of various physical Parameters such as viscoelastic Parameter ( β ), magnetic field Parameter ( M ), radiation Parameter ( R ), Biot number (Bi) and Velocity Ratio Parameter ( α ) are examined through graphical and numerical results of Velocity and temperature distributions.
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on model for three dimensional flow of nanofluid an application to solar energy
Journal of Molecular Liquids, 2014Co-Authors: Junaid Ahmad Khan, Tasawar Hayat, M Mustafa, A Alsaedi, Asif M Farooq, Shijun LiaoAbstract:Abstract Laminar three-dimensional flow of nanofluid over a bi-directional stretching sheet is investigated. Convective boundary conditions are used for the analysis of thermal boundary layer. Mathematical model containing the combined effects of Brownian motion and thermophoretic diffusion of nanoparticles is adopted. The formulated differential system is solved numerically using a shooting method with fourth–fifth-order Runge–Kutta integRation technique. The solutions depend on various interesting Parameters including Velocity Ratio Parameter (λ), Brownian motion Parameter (Nb), thermophoresis Parameter (Nt), Prandtl number (Pr), Lewis number (Le) and the Biot number (γ). It is noticed that fields are largely influenced with the variations of these Parameters. The results are compared with the existing studies for the two-dimensional flows and found in an excellent agreement. The study reveals that nanoparticles in the base fluid offer a potential in improving the convective heat transfer performance of various liquids.
