Browsing by Author "Krishnendu Bhattacharyya"

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A computational description of time-dependent transport of a water-based nanofluid with hybrid nanocomposite Cu-Al2O3over a parabolic surface by Keller-box scheme: A modified Buongiorno model
(World Scientific, 2024) Sohita Rajput; Krishnendu Bhattacharyya; Dimpal Sharma; Amit Kumar Pandey; Ali J. Chamkha
This paper discusses the high heat transfer demand from application prospects. Hybrid nanofluid is a well-known liquid with higher heat transfer capabilities. Here, the time-dependent flow of hybrid nanocomposite, by hybridizing the metal (Cu) and metallic oxide (Al2O3) and inserting them into water-based nanofluid, is examined. The flow takes place over the upper half of a parabolic surface. The modified Buongiorno model is used to express the physical phenomenon in mathematical equations form. The governing system of partial differential equations (PDEs) is reduced to a system of ordinary differential equations (ODEs) by applying certain transformations. Computation of the final equations has been done by a numerical scheme, known as the Keller-box method. The significance of dimensionless flow causing physical parameters is shown through graphs and tables. The findings reveal that among the hybrid nanofluids with two types of nanoparticles varying from 0% to 5%, a nanofluid having 5% of both nanoparticles is the one with the maximum surface drag force and heat transport rate, which are 41.8% and 22.7% higher to water, respectively. A higher amount of Al2O3 than Cu results in a suitable hybrid combination for application purposes to produce higher cooling rate with less surface drag. Also, the thickness of the surface, unsteadiness, nanoparticles suspension and power index of wall temperature enhance the heat transfer rate. Thin parabolic surfaces experience less drag and have larger boundary layer thicknesses (momentum, thermal and concentration) as compared to thicker parabolic surfaces. Also, the addition of copper slows down the hybrid fluid flow field, but alumina magnifies the mobility of hybrid fluid. © 2024 World Scientific Publishing Company.
Analytical and numerical examinations on the stability investigation of Casson nanofluid flow in a permeable layer controlled by vertical throughflow
(Emerald Publishing, 2024) A.M. Mohamad; Dhananjay Yadav; Mukesh Kumar Awasthi; Ravi Ragoju; Krishnendu Bhattacharyya; Amit Mahajan
Purpose: The purpose of the study is to analytically as well as numerically investigate the weight of throughflow on the onset of Casson nanofluid layer in a permeable matrix. This study examines both the marginal and over stable kind of convective movement in the system. Design/methodology/approach: A double-phase model is used for Casson nanofluid, which integrates the impacts of thermophoresis and Brownian wave, whereas for flow in the porous matrix the altered Darcy model is occupied under the statement that nanoparticle flux is disappear on the boundaries. The resultant eigenvalue problem is resolved analytically as well as numerically with the help of Galerkin process with the Casson nanofluid Rayleigh–Darcy number as the eigenvalue. Findings: The findings revealed that the throughflow factor postpones the arrival of convective flow and reduces the extent of convective cells, whereas the Casson factor, the Casson nanoparticle Rayleigh–Darcy number and the reformed diffusivity ratio promote convective motion and also decrease the extent of convective cells. Originality/value: Controlling the convective movement in heat transfer systems that generate high heat flux is a real mechanical challenge. The proposed framework proved that the use of throughflow is one of the most important ways to control the convective movement in Casson nanofluid. To the best of the authors’ knowledge, no inspection has been established in the literature that studies the outcome of throughflow on the Casson nanofluid convective flow in a porous medium layer. However, the convective flow of Casson nanofluid finds many applications in improving heat transmission and energy efficiency in a range of thermal systems, such as the cooling of heat-generating elements in electronic devices, heat exchangers, pharmaceutical practices and hybrid-powered engines, where throughflow can play a significant role in controlling the convective motion. © 2024, Emerald Publishing Limited.
Analytical and numerical examinations on the stability investigation of Casson nanofluid flow in a permeable layer controlled by vertical throughflow
(Emerald Publishing, 2025) Abdul M. Mohamad; Dhananjay Yadav; Mukesh Kumar Awasthi; Ragoju Ravi; Krishnendu Bhattacharyya; Amit Mahajan
Purpose – The purpose of the study is to analytically as well as numerically investigate the weight of throughflow on the onset of Casson nanofluid layer in a permeable matrix. This study examines both the marginal and over stable kind of convective movement in the system. Design/methodology/approach – A double-phase model is used for Casson nanofluid, which integrates the impacts of thermophoresis and Brownian wave, whereas for flow in the porous matrix the altered Darcy model is occupied under the statement that nanoparticle flux is disappear on the boundaries. The resultant eigenvalue problem is resolved analytically as well as numerically with the help of Galerkin process with the Casson nanofluid Rayleigh–Darcy number as the eigenvalue. Findings – The findings revealed that the throughflow factor postpones the arrival of convective flow and reduces the extent of convective cells, whereas the Casson factor, the Casson nanoparticle Rayleigh–Darcy number and the reformed diffusivity ratio promote convective motion and also decrease the extent of convective cells. Originality/value – Controlling the convective movement in heat transfer systems that generate high heat flux is a real mechanical challenge. The proposed framework proved that the use of throughflow is one of the most important ways to control the convective movement in Casson nanofluid. To the best of the authors’ knowledge, no inspection has been established in the literature that studies the outcome of throughflow on the Casson nanofluid convective flow in a porous medium layer. However, the convective flow of Casson nanofluid finds many applications in improving heat transmission and energy efficiency in a range of thermal systems, such as the cooling of heat-generating elements in electronic devices, heat exchangers, pharmaceutical practices and hybrid-powered engines, where throughflow can play a significant role in controlling the convective motion. © 2024 Emerald Publishing Limited
Boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving flat plate in Darcy porous medium with a parallel free-stream: Multiple solutions and stability analysis
(Springer, 2021) Ajeet Kumar Verma; Anil Kumar Gautam; Krishnendu Bhattacharyya; Astick Banerjee; Ali J Chamkha
Two-dimensional forced convective steady boundary layer flow of non-Newtonian Eyring–Powell nanofluid over a moving plate in a porous medium in the presence of a parallel free-stream is investigated. The governing coupled non-linear partial differential equations (PDEs) along with boundary conditions are transformed into a set of non-linear coupled ordinary differential equations (ODEs) by using appropriate transformations. The obtained non-linear ODEs with modified boundary conditions are converted into a system of first-order ODEs which are solved using the classical and efficient shooting method. Dual solutions for velocity, temperature and nanoparticle concentration distributions for Eying–Powell fluids similar to Newtonian fluid in some special flow situations are obtained, when the plate and free-stream are moving along mutually opposite directions. The stability analysis of the obtained solutions is performed and it is found that the upper branch solutions are physically stable, while lower branch solutions are unstable. The impacts of different dimensionless physical parameters on velocity, temperature and nanoparticle concentration are reported in the form of graphs and tables. An important result is obtained and it reveals that the ‘dual solutions’ character has been destroyed if resistance due to the porous medium is raised up to a definite level (i.e., permeability parameter K> 0.07979), though the range of existence of unique solution becomes larger with further increase of resistance due to porous medium. It is also observed that heat transfer rate diminishes with increasing thermophoresis parameter, Brownian diffusion parameter and Lewis number in all the cases, whereas mass transfer rate enhances with thermophoresis parameter (for dual solutions), Brownian diffusion parameter (for unique solutions) and Lewis number (for unique solutions). Further, skin-friction coefficient, i.e., the surface drag force, increases with permeability parameter, suction/injection parameter and decreases with Eyring–Powell fluid parameter. Also, increments in permeability parameter and the suction/injection parameter lead to the delay in the boundary layer separation. The critical values of velocity ratio parameter beyond which the boundary layer separation appears are − 0.5476432, − 0.5987132, − 0.704862, − 0.816944, − 0.9365732, − 0.96179102, − 1.057104, − 1.062004, − 1.09222, − 1.115824, − 1.193413, − 1.591023 and − 1.898366 for K= 0 , 0.01, 0.03, 0.05, 0.07, 0.074, 0.08, 0.082, 0.085, 0.09, 0.1, 0.15 and 0.2, respectively. © 2021, Indian Academy of Sciences.
Buoyancy driven non-Newtonian Prandtl-Eyring nanofluid flow in Darcy-Forchheimer porous medium over inclined non-linear expanding sheet with double stratification
(Taylor and Francis Ltd., 2022) Ajeet Kumar Verma; Krishnendu Bhattacharyya; Sohita Rajput; Mani Shankar Mandal; Ali J. Chamkha; Dhananjay Yadav
In the existence of mixed convection and double stratification, the 2D, viscous, incompressible, steady, laminar boundary layer flow of Prandtl-Eyring nanofluid over the inclined non-linear expanding sheet in Darcy-Forchheimer porous medium is scrutinized. To analyze the impacts of Brownian motion and thermophoretic force on diffusion of nanoparticles Buongiorno model has been utilized. Flow governing equations are non-linear, higher order, coupled PDEs with no slip boundary condition, which are transforming into coupled, non-linear, higher order ODEs via suitable transformations. Obtained ODEs are solved using MATLAB bvp4c function. The impacts of flow governing parameters on flow associated distributions are acknowledged through graphs. In limiting sense, to check the credibility of numerical method, present results are compared with previously published data. The analysis reveals that fluid velocity displays an enhancement with first Prandtl-Eyring parameter α and a diminution with second Prandtl-Eyring parameter β. Whereas, due to presence of both stratifications (thermal and solutal) there is a decline in fluid velocity. Also, nanofluid temperature is augmented with Forchheimer number (Formula presented.) and inclination angle γ, whereas it declines with α and thermal stratification parameter (Formula presented.). Nanoparticle concentration escalates with γ, whereas it drops with concentration stratification parameter (Formula presented.). For larger thermophoresis parameter Nt, the nanoparticle concentration achieves higher level than its initial value in mid-region of boundary layer, while near surface it assumes lower value. The surface drag-force elevates with β and Nt. Whereas surface cooling rate enhances with (Formula presented.) and it weakens with (Formula presented.). © 2022 Informa UK Limited, trading as Taylor & Francis Group.
Chemical Reaction and Internal Heating Effects on the Double Diffusive Convection in Porous Membrane Enclosures Soaked with Maxwell Fluid
(MDPI, 2022) Dhananjay Yadav; Maimouna Al-Siyabi; Mukesh Kumar Awasthi; Salma Al-Nadhairi; Amna Al-Rahbi; Maryam Al-Subhi; Ravi Ragoju; Krishnendu Bhattacharyya
In this paper, the joint impact of the interior heating and chemical reaction on the double diffusive convective flow in porous membrane enclosures soaked by a non-Newtonian Maxwell fluid is investigated applying linear and nonlinear stability techniques. The porous enclosures are square, slender and rectangular. Using the linear stability analysis, the expression for the critical thermal Rayleigh–Darcy number, above which the convective movement occurs, is derived analytically in terms of associated physical parameters. A nonlinear stability examination reliant on the Fourier double series is executed to calculate the convective heat and mass transports of the arrangement. It is observed that the pattern of convective activity is oscillatory only in the occurrence of a relaxation parameter and the threshold value of the relaxation parameter for the occurrence of the oscillatory pattern depends on the other physical parameters. The onset of convective instability accelerates with the increasing chemical reacting parameter, the interior heating parameter, the solute Rayleigh–Darcy number, the Lewis number, the Vadasz number, and the relaxation parameter, while it delays with the heat capacity ratio. The convective heat and mass transfers increase with the solute Rayleigh– Darcy number, the Vadasz number, the relaxation parameter, and the aspect ratio (for rectangular enclosure), while it decreases with the heat capacity ratio and the aspect ratio (for slender enclosure). Additionally, the convective heat transfer enhances with the interior heating parameter, while the convective mass transfer enhances with the chemical reacting parameter and the Lewis number. The effects of Vadasz number, heat capacity ratio, and relaxation parameter are witnessed only on the oscillatory pattern of convection and unsteady convective heat and mass transfers. Further, some existing literature results are compared with the current findings. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
Comparative study of two non-Newtonian fluids with bioconvective induced MHD flow in presence of multiple slips, heat source/sink and nonlinear thermal radiation
(Elsevier B.V., 2022) Anil Kumar Gautam; Sohita Rajput; Krishnendu Bhattacharyya; Amit Kumar Pandey; Ali J. Chamkha; Momtaz Begum
The present manuscript deals with bioconvective induced magnetohydrodynamic (MHD) flow of non-Newtonian fluids with simultaneous effects of multiple slips, heat source/sink, and nonlinear thermal radiation. Flows of Maxwell and Casson fluids are considered separately, but a single governing momentum conservation equation is constructed by combining these two flow models. Transformed governing equations are solved by MATLAB solver ‘bvp4c’. The objective of the current study is to check the comparative behaviour of two non-Newtonian fluids viz., Maxwell and Casson in presence of induced MHD effect with the bioconvective phenomenon and slip effect. The main findings reveal the growth of velocity and fall of microorganisms’ motile density with induced magnetic number. With higher values of Peclet number and microorganism concentration difference parameter, the microbe's motile density significantly reduces. The temperature hike is witnessed with heat generation/absorption, thermal radiation, and temperature ratio parameters. Also, for a fixed set of values of parameters the Casson fluid velocity is more prominent than the Maxwell fluid velocity and the scenario is the opposite for the motile density of microorganisms. Velocity increases, whereas motile density decreases with raising the amount of magnetic Prandtl number. Casson fluids have more velocity than Maxwell fluids, whereas the movement of the motile density of microorganisms is showing prominency for Maxwell fluids. The magnitude of surface drag and surface cooling rate are at a higher level for Casson fluid in comparison with Maxwell fluid. The motile density number enhances with the microorganism concentration difference parameter and Peclet number. © 2022
Comparison between graphene-water and graphene oxide-water nanofluid flows over exponential shrinking sheet in porous medium: Dual solutions and stability analysis
(Elsevier B.V., 2022) Ajeet Kumar Verma; Sohita Rajput; Krishnendu Bhattacharyya; Ali J. Chamkha; Dhananjay Yadav
To achieve ultra-high cooling rate requirement of modern-day industries the combined use of nanofluid and porous medium in several engineering and industrial processes provides excellent outcomes. In present analysis, the comparison between the flows of Gr-w and GO-w nanofluids over exponential shrinking sheet inside porous medium is investigated. Governing coupled PDEs are changed into ODEs by appropriate transformations which are solved numerically with the help of shooting method with RK4; and obtained dual solutions of Darcy flow for certain enforced mass suction exist and consequently, a stability analysis is performed to test physical stability of both solutions which proves physical stability of upper solution branch and instability of lower solution branch. The impacts of several physical parameters are presented in graphical modes along with a tabular comparison. The study reveals that Gr-w nanofluid delays the boundary layer flow separation more in comparison with GO-w nanofluid and hence, the requirement of mass suction for existence of Gr-w nanofluid flow is of lower amount. Also, consideration of porous material as flow medium defers the separation phenomenon. The rise of surface-drag force is witnessed for porous medium and mass suction and it is relatively larger for Gr-w nanofluid than GO-w nanofluid in case of upper branch solution and the surface cooling rate is larger for Gr-w nanofluid in comparison with GO-w nanofluid. © 2022
Convective flow of ethylene glycol-silver Jeffery nanofluid in a Hele-Shaw cell with an influence of external magnetic field
(John Wiley and Sons Ltd, 2023) Dhananjay Yadav; Sara Al-Balushi; Mukesh Kumar Awasthi; Taif Al-Hadi; Raya Al-Abri; Jawhara Al-Wahaibi; Fatan Al-Nasseri; Sara Al-Siyabi; Ravi Ragoju; Krishnendu Bhattacharyya
This effort investigates the arrival of magnetothermal convection of ethylene glycol-silver Jeffrey nanofluid in a Hele-Shaw cell utilizing the linear stability concept. The model practiced for the Jeffrey nanofluid includes the impacts of Brownian movement and thermophoresis. The norms for both marginal and overstable modes of convections are developed analytically. The impact of magnetic Chandrasekhar number (Figure presented.), magnetic Prandtl number (Figure presented.), Jeffrey parameter (Figure presented.), Hele-Shaw number (Figure presented.), and a variety of nanofluid parameters such as the volumetric fraction of nanoparticles (Figure presented.), nanoparticle Rayleigh number (Figure presented.), adjusted diffusive ratio (Figure presented.), and Lewis number (Figure presented.) on the beginning of convective motion are investigated, and results are illustrated graphically. It is observed that the overstable approach of convection is probable below the certain threshold estimate of the magnetic Prandtl number (Figure presented.). This threshold estimate of the magnetic Prandtl number (Figure presented.) upturns with a rise in the rate of (Figure presented.), (Figure presented.), and (Figure presented.), while it drops with a surge in the nanofluid parameters. The system was found to be more stable by decreasing the Hele-Shaw number (Figure presented.), the Jeffery parameter (Figure presented.), and nanofluid parameters, while it was unstable by decreasing the magnetic Chandrasekhar number (Figure presented.) and the magnetic Prandtl number (Figure presented.). © 2023 Curtin University and John Wiley & Sons Ltd.
Divergent channel flow of Casson fluid and heat transfer with suction/blowing and viscous dissipation: Existence of boundary layer
(Elsevier B.V., 2021) Astick Banerjee; Sanat Kumar Mahato; Krishnendu Bhattacharyya; Ali J. Chamkha
The boundary layer existence in divergent porous channel of non-Newtonian Casson fluid with heat transfer in presence of suction/blowing and viscous dissipation is studied. Nonlinear coupled ODEs are obtained from governing PDEs and the conditions under which boundary layer structure for Casson fluid exists by controlling backflow are explored. Numerical solutions are also obtained using “bvp4c”, a MATLAB package. The study reveals that if mass suction exceeds a certain amount which is dependent on Casson parameter then only boundary layer flow is possible and as Casson parameter increases, the requirement of mass suction for boundary layer flow reduces. In addition, rheological characters of Casson fluid and viscous dissipation have a major impact on temperature distribution and due to these, the temperature falls lower than free stream temperature within the boundary layer region. © 2021 The Authors
Double diffusive convective motion in a reactive porous medium layer saturated by a non-Newtonian Kuvshiniski fluid
(American Institute of Physics Inc., 2022) Dhananjay Yadav; Mukesh Kumar Awasthi; M. Al-Siyabi; S. Al-Nadhairi; A. Al-Rahbi; M. Al-Subhi; Ravi Ragoju; Krishnendu Bhattacharyya
The impact of chemical reactions on the double-diffusive convective motion in a non-Newtonian viscoelastic fluid (Kuvshiniski type) saturated porous layer is examined applying both linear and nonlinear stability techniques. The Darcy model that includes the Kuvshiniski type viscoelastic effect of viscoelastic fluid and the Boussinesq estimation is employed as the momentum equation. The conditions for the occurrence of the stationary and oscillatory style of convective motions are determined by applying linear stability theory in terms of a critical thermal Rayleigh-Darcy number. Using the weakly nonlinear stability analysis, the convective heat and mass transfers are calculated. It is observed that the occurrence of oscillatory convection is possible only if the value of the solute Rayleigh-Darcy number is negative and also depends on other involved physical parameters. With rising values of the Kuvshiniski parameter and the heat capacity ratio, the range of the solute Rayleigh-Darcy number in which oscillatory convection is privileged diminishes, whereas it grows with the chemical reacting parameter and the Lewis number. The critical thermal Rayleigh-Darcy number at which the convective motion occurs increased nearly 3% with a 15% increase in the value of the Kuvshiniski parameter. Furthermore, the convective heat and mass transfers are reduced by growing the Kuvshiniski parameter and the heat capacity ratio, while both are enhanced by increasing the thermal Rayleigh-Darcy number and the solute Rayleigh-Darcy number. © 2022 Author(s).
Dual solutions of an unsteady magnetohydrodynamic stagnation-point flow of a nanofluid with heat and mass transfer in the presence of thermophoresis
(SAGE Publications Ltd, 2018) Aurang Zaib; Krishnendu Bhattacharyya; S.A. Urooj; Sharidan Shafie
The unsteady two-dimensional magnetohydrodynamic stagnation point flow of a nanofluid with thermophoresis effect is investigated numerically. The technique of similarity transformation is implemented to obtain the self-similar ordinary differential equations and then the self-similar equations are solved numerically using shooting method. This analysis explores the conditions of the existence, non-existence, uniqueness, and duality of the solutions of self-similar equations numerically. Dual solutions of velocity, temperature and concentration profiles are reported for different values of the each parameter involved for two types of nanoparticles, namely copper (Cu) and gold (Au) in the water-based fluid. It is found that the dual solutions exist for negative values of unsteady parameter A, whereas for positive values of unsteady parameter, the solution is unique. The results also indicate that the nanoparticle volume fraction reduces the skin friction coefficient, the heat transfer rate as well as mass transfer rate. Further, due to increase of thermophoresis parameter, the concentration inside the boundary layer reduces and the mass transfer rate enhances. In addition, to validate the present numerical results, comparison with published results is made and found to be in excellent agreement. © 2017, © IMechE 2017.
Dual Solutions of Non-Newtonian Casson Fluid Flow and Heat Transfer over an Exponentially Permeable Shrinking Sheet with Viscous Dissipation
(Hindawi Limited, 2016) Aurang Zaib; Krishnendu Bhattacharyya; Md. Sharif Uddin; Sharidan Shafie
The two-dimensional boundary layer flow of a non-Newtonian Casson fluid and heat transfer due to an exponentially permeable shrinking sheet with viscous dissipation is investigated. Using similarity transformations, the governing momentum and energy equations are transformed to self-similar nonlinear ODEs and then those are solved numerically by very efficient shooting method. The analysis explores many important aspects of flow and heat transfer of the aforesaid non-Newtonian fluid flow dynamics. For the steady flow of non-Newtonian Casson fluid, more amount of wall mass suction through the porous sheet is required in comparison to that of Newtonian fluid flow. Dual similarity solutions are obtained for velocity and temperature. The viscous dissipation effect has major impact on the heat transfer characteristic. In fact, heat absorption at the surface occurs and it increases due to viscous dissipation. For higher Prandtl number, the temperature inside the boundary layer reduces, but with larger Eckert number (viscous dissipation) it is enhanced. © 2016 Aurang Zaib et al.
Effect of convective boundary condition on unsteady flow of CNT-H2O nanofluid towards a stagnation-point on a shrinking/expanding flat sheet
(SAGE Publications Ltd, 2022) Sohita Rajput; Amit Kumar Pandey; Krishnendu Bhattacharyya; Ioan Pop
A model study of unsteady stagnation-point flow of most important nanoparticles, that is, carbon nanotubes suspended nanofluid towards shrinking/expanding sheet with convective boundary condition is demonstrated. Two types of carbon nanotubes, namely, single-wall and multi-wall nanotubes are carefully considered. Numerical solutions of converted equations from governing equation of the problem are obtained and those are graphically presented. Similar to without carbon nanotubes case, dual and unique solutions in specific ranges of velocity ratio parameter are achieved. Analysis disclosures that the condition on range where dual solutions exist is unaltered with solid-volume fraction and type of carbon nanotubes. The surface drag-force and heat transfer rate from wall are larger for single-walled carbon nanotubes nanofluid than multi-walled carbon nanotubes nanofluid. An increment in the parameter related to convective boundary condition generates high rate of heat transfer. After stability analysis, it is identified that in case of dual solutions, upper branch is stable and lower branch is unstable, while unique solution is always stable. © IMechE 2021.
Effect of nonlinear thermal radiation on 3D magneto slip flow of Eyring-Powell nanofluid flow over a slendering sheet with binary chemical reaction and Arrhenius activation energy
(Elsevier B.V., 2019) S.R.R. Reddy; P. Bala Anki Reddy; Krishnendu Bhattacharyya
An analysis is performed to study the combined effects of nonlinear thermal radiation, Arrhenius activation energy, chemical reaction and heat generation/absorption on the steady three-dimensional magnetohydrodynamic flow of Eyring-Powell nanofluid flow over a slendering stretchable sheet with velocity, thermal and solutal slips. The prevailing partial differential equations are transmuted into coupled non-linear ordinary differential equations via with the suitable similarity transformations. The resultant non-linear coupled differential equations are solved numerically by using the R-K 4th order method along with shooting scheme. The results are calculated to measure the influence of sundry parameters on velocity, temperature, concentration, shear stress, temperature gradient and concentration gradient are presented graphically and in tabular form. It is noticed that the temperature is more impactable for higher values of radiative heat transport. The local Sherwood number decays exponentially for all the values of the chemical reaction parameter. We compared the present results for the limiting cases with previously published results, which has shown reliability and efficiency. © 2019 Society of Powder Technology Japan
Effects of Hall current on MHD natural convection in between two vertical flat walls with induced magnetic field and heat source/sink
(Taylor and Francis Ltd., 2022) Dileep Kumar; A.K. Singh; Krishnendu Bhattacharyya; Astick Banerjee
The effects of Hall current and heat source/sink are considered on MHD natural convective flow of an electrically conducting viscous fluid in between two vertical flat walls with an induced magnetic field. The exact analytical solutions for converted flow equations from governing equations after using suitable non-dimensional variables are obtained. The effects of Hall current, heat source/sink, and magnetic field on the velocity components, induced magnetic field in flow dynamics, and the induced current density are presented through some figures and tables. The impact of the Hall current is massive on both components of velocity and those increases with Hall current. Whereas, both the components of the induced magnetic field and induced current density decrease due to Hall current. Whereas due to heat source(sink), the primary velocity enhances(reduces) and the effect is opposite for the secondary velocity. For increasing heat source parameter both primary and secondary induced magnetic field and induced current density increase, while temperature-dependent heat sink shows contrary effects. In two flat vertical walls, the variations in the skin-friction components, i.e. surface drag force components for the presence of magnetic field are opposite to each other. In addition, mass flow rate components enhance for Hall current and reduce for a stronger magnetic field. With increasing heat source parameter, the primary skin-friction component rises and secondary skin-friction component decreases at the left wall with higher temperature, while at the right wall with lower temperature both skin-friction components have increasing nature, and reverse impacts are observed for the heat sink. Due to the presence of heat source, primary (secondary) mass flow rate component enhances (reduces) and opposite effects have found for the heat sink. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
Effects of non-linearly variable heat flux and thermal radiation on heat transfer in MHD boundary layer flow over an unsteady permeable stretching sheet in Darcy porous medium
(Academy of Sciences of the Czech Republic, 2017) Gauri Shanker Seth; Aditya Kumar Singha; Astick Banerjee; Krishnendu Bhattacharyya
In this analysis, the effects variable heat flux and thermal radiation on MHD flow and heat transfer over an unsteady permeable stretching sheet in a porous medium with mass suction/injection are investigated. The basic equations of flow are converted to self-similar ordinary equations adopting suitable similarity transformations. Shooting method is used to obtain numerical solutions of the transformed self-similar equations. Simultaneous effects of variable heat flux, thermal radiation, magnetic field and resistance for porous medium on the unsteady flow and heat transfer are obtained. It is found that for magnetic field and the medium of flow being porous, the velocity decreases and temperature increases. Also, mass suction has similar effect on the velocity profile. Temperature and thermal boundary layer thickness decrease with unsteadiness, Prandtl number and variable heat flux with high rate of heat transfer from the sheet to the ambient fluid. Whereas, for stranger magnetic field the heat transfer rate reduces. © 2017 Institute of Thermomechanics CAS, v.v.i.
Entropy generation analysis of Falkner–Skan flow of Maxwell nanofluid in porous medium with temperature-dependent viscosity
(Springer, 2021) Ajeet Kumar Verma; Anil Kumar Gautam; Krishnendu Bhattacharyya; Ioan Pop
Entropy generation analysis in steady two-dimensional, viscous, incompressible forced convective Falkner–Skan flow of Maxwell nanofluid over a static wedge embedded in a porous medium with temperature-dependent viscosity is examined. The Buongiorno’s model has been utilised, to get the flow governing higher-order coupled nonlinear partial differential equations (PDEs) from mass, momentum, energy and concentration conservations. Suitable transformations have been done to convert governing PDEs into the coupled non-linear ODEs along with no-slip boundary conditions, which are then solved using the MATLAB programme bvp4c. The influences of diverse flow governing parameters on various flow properties and quantities of physical interest are displayed in graphical mode and discussed. It is found that entropy generation reduces only with Eckert number (Ec), while more entropy is generated for pressure gradient parameter (m), local Deborah number (β) , variable viscosity parameter (δ) and permeability parameter (K). Entropy generation due to heat transfer irreversibility is prominent with increase in m and δ, but it is not so for other parameters. The drag force on the wedge surface become stronger with β and m, but it reduces with δ. Rates of heat transfer and mass transfer enhance with m and δ. In addition, surface drag force and heat transfer rate diminish with Brownian motion parameter (Nb) and thermophoresis parameter (Nt). © 2021, Indian Academy of Sciences.
Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation
(Elsevier B.V., 2016) Krishnendu Bhattacharyya; M.S. Uddin; G.C. Layek
An analysis of thermal boundary layer in the flow of Casson fluid over a permeable shrinking sheet with variable wall temperature and thermal radiation is made. Using similarity transformations, self-similar nonlinear ODEs are obtained from the governing equations. Dual exact solutions of transformed velocity and energy equations are obtained. From the plotted results it can be observed that the temperature inside the boundary layer decreases with Casson parameter and wall mass transfer parameter in first solution and it increases in second solution. Whereas, temperature decreases for larger values of Prandtl number, radiation parameter and power-law exponent for inverse variation along the sheet in both solutions and it enhances with power-law exponent for direct variation along the surface. Also, thermal boundary layer thickness reduces with stronger thermal radiation and inverse variation of wall temperature along the surface and it becomes thicker with direct variation of wall temperature. The rate of heat transfer is less with increasing values of power-law exponent for direct variation along the sheet and for inverse variation it is higher. In graphical representation of temperature field, temperature overshoot is observed in certain cases. So, in some situations heat absorption at surface occurs instead of heat transfer from surface. © 2016 Faculty of Engineering, Alexandria University.
Exact solutions for 2D boundary layer flow of two types of viscoelastic fluids and heat transfer on a permeable shrinking sheet with thermal radiation and variable surface temperature: existence of multiple solutions
(Taylor and Francis Ltd., 2022) Astick Banerjee; Krishnendu Bhattacharyya; Sanat Kumar Mahato; Ajeet Kumar Verma; Anil Kumar Gautam; Ali J. Chamkha
A study with existence of multiple exact solutions has its own importance, and if the study is performed for a viscoelastic fluid, then the attraction becomes very high. So, here an attempt is performed, where the flow of two types of viscoelastic fluids and heat transfer due to shrinking of a permeable sheet is described. In the energy flow, the impacts of thermal radiation and variable temperature of the wall are simultaneously undertaken. By using similarity approach, in addition to single solution, the dual and triple closed-form solutions of the flow field and temperature are obtained in some specific flow situations of two fluids, namely, second-grade and Walters liquid B. Dual solutions for the flow of second-grade fluid are detected only for stronger mass suction with smaller viscoelastic parameter of second-grade fluid and for both weaker and stronger mass suctions (for two ranges) with larger viscoelastic parameter and unique solution in case of mass injection. However, for the flow of Walters liquid B, boundary layer solution is attained for mass suction only, and most importantly, triple solutions for some mass suction range are found. Now for heat flow, an exceptional result is witnessed: if the wall temperature distribution is assumed suitably, then the heat transfer rate is not dependent on the fluid rheology. Also, influences of involved physical parameters on velocity, temperature and other important quantities are described through some graphs. © 2022 Informa UK Limited, trading as Taylor & Francis Group.