Browsing by Author "Ajeet Kumar Verma"

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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.
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
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 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.
Existence of boundary layer nanofluid flow through a divergent channel in porous medium with mass suction/injection
(Springer, 2021) Ajeet Kumar Verma; Anil Kumar Gautam; Krishnendu Bhattacharyya; R.P. Sharma
The steady two-dimensional, laminar, viscous, incompressible boundary layer flow of Cu/Ag-H2O nanofluid in a diverging channel formed by two non-parallel walls in a Darcian porous medium is numerically studied in the presence of mass suction/injection of equal magnitude on both the walls. Here, divergent flow is generated by a line source of fluid volume at the intersection of channel walls. Using similarity transformations, the non-linear governing PDEs are transformed into self-similar coupled non-linear ODEs and they are solved numerically with the help of MATLAB-built solver “bvp4c”. The conditions for the existence of boundary layer flow structure for nanofluid through divergent channel in porous medium are obtained. The analysis reveals that when the permeability parameter K and nanofluid-volume-fraction-related parameter ϕ1 are chosen in a specific manner such that they satisfy the condition K> 2 ϕ1 then boundary layer flow exists, preventing separation for any mass suction/injection or even in the absence of mass suction/injection. A similar velocity field rises with permeability parameter, which exhibits opposite behavior with nanoparticle volume fraction. Also temperature increases with nanoparticle volume fraction, permeability parameter, and Eckert number, and decreases with power-law exponent (related to variable wall temperature). Skin-friction coefficient and heat transfer rate for Cu-water nanofluid are stronger when compared with Ag-water nanofluid. © 2021, Indian Academy of Sciences.
Existence of multiple solutions for magnetohydrodynamic flows of second-grade and Walter's B fluids due continuously contracting flat sheet with partial slip
(Elsevier B.V., 2022) Anil Kumar Gautam; Sohita Rajput; Krishnendu Bhattacharyya; Ajeet Kumar Verma; Md. Glam Arif; Ali J. Chamkha
In the present investigation, an attempt is performed to analyse the existence of multiple exact solutions for magnetohydrodynamic flows of second-grade and Walter's B fluids due continuously contracting flat sheet with partial slip condition at the boundary. After transforming basic governing equations by suitable similarity transformations, single and double closed-form exact solutions of the flow are achieved on certain restrictions on flow variables of two aforesaid fluids. The impacts of magnetic field and partial slip on existence and non-existence of solutions are revealed. The changes of flow surface drag and velocity with various involved parametric values are also explored. For both viscoelastic type fluids, i.e., second-grade and Walter's B fluids, double solutions exist for certain flow conditions. In second-grade case, if viscoelastic parameter exceeds a definite value, then double similarity solutions are achieved for any type of flow, i.e., slip flow or no-slip flow. For Walter's B fluid similar results are obtained with unique similarity slip flow solution if magnitude of viscoelastic parameter exceeds certain fixed value. Importantly, the magnetic field and its MHD effect stabilize the uncertainty situation in existence of similarity solution for both fluids and produce unique solution for a suitable choice. © 2022
IInsight of boundary layer structure with heat transfer through a diverging porous channel in Darcy-Forchheimer porous material with suction/injection: A study of separation control
(Yildiz Technical University, 2023) Astick Banerjee; Sanat Kumar Mahato; Krishnendu Bhattacharyya; Sohita Rajput; Ajeet Kumar Verma; Ali J. Chamkha
Separation control and formation of boundary layer Newtonian flow in a diverging perme-able channel in Darcy-Forchheimer porous material having suction/injection are discussed. Self-similar equations from governing equations are acquired and existence conditions for boundary layer structure are derived using nature of velocity gradient inside boundary layer. It reveals that if sum of Darcy permeability parameter and twice of Forchheimer parameter ex-ceeds 2, then the boundary layer flow always exists with all type of mass suction/injection and even without suction/injection. Also, if mass suction parameter goes beyond [Formula Presented], then there is no matter what are the values of Darcy permeability parameter and Forchheimer parameter, a boundary layer exists inside the divergent channel. In addition, obtained numerical solutions are exhibited graphically. It reveals that thicknesses of velocity and thermal boundary layers reduce with Darcy and non-Darcy resistances of porous medium and fluid temperature also diminishes. The velocity and temperature reduce with increment of mass suction and contrary results are found for mass injection. © 2021, Yıldız Technical University. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). All Rights Reserved.
Impacts of activation energy and binary chemical reaction on MHD flow of Williamson nanofluid in Darcy–Forchheimer porous medium: a case of expanding sheet of variable thickness
(Taylor and Francis Ltd., 2024) Anil Kumar Gautam; Ajeet Kumar Verma; Krishnendu Bhattacharyya; Swati Mukhopadhyay; Ali J. Chamkha
An expanding sheet problem is more relevant when the thickness of the sheet is variable and it bears frequent applications in polymer press, paper production, metallic plate cooling, etc. On the other hand, activation energy is an important phenomenon of chemical reaction in flow dynamics of Newtonian and non-Newtonian fluids. The activation energy and chemical reaction have vital applications in food preparing, the mechanism of water and oil emulsions, chemical engineering, and more. So in this project, the impacts of activation energy and binary chemical reaction on MHD two-dimensional boundary layer flow of Williamson nanofluid on an expanding surface of variable thickness embedded in Darcy–Forchheimer porous medium are investigated. Using suitable transformations, the governing equations are transformed into a set of non-linear ordinary differential equations (ODEs). Later, numerical solutions have been achieved by well-known MATLAB inbuilt function ‘bvp4c’. Several vital results are explored for variations of involved physical parameters and those are presented in graphical and tabular modes. The achieved results suggest that when wall thickness parameter increases, there is a contrast in behaviors of velocity, temperature and nanoparticle concentration if there is a condition that the shape parameter is greater than or less than unity. For the former case, the above flow properties reduce with wall thickness parameter, whereas, for the latter case, those are showing significant growth. The Brownian motion of nanoparticles causes an increase in temperature and a reduction in nanoparticle concentration, whereas due to thermophoretic force, both temperature and nanoparticle concentration rise. Due to the presence of activation energy in chemical reaction, the nanoparticle concentration enhances, while, temperature decreases(increases) near(away from) the sheet. With increasing reaction rate parameters, nanoparticle concentration diminishes, but temperature increases near the sheet. The surface drag force decreases with Williamson fluid parameter, while it increases with the magnetic parameter, inverse Darcy number, and Forchheimer parameter. On the other hand, the surface heat flux and surface mass flux are decreasing functions of Williamson fluid parameter, magnetic parameter, inverse Darcy number, and Forchheimer parameter. It also reveals that surface heat flux reduces with increasing reaction rate parameters, whereas surface mass flux increases. Finally, for the growth of activation energy parameter, initially surface heat flux rises and surface mass flux declines, but for its larger values, the quantities turn out to be constants. Also, the surface heat and mass fluxes are decreasing functions of thermophoresis parameter. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
MHD mixed convection on an inclined stretching plate in Darcy porous medium with Soret effect and variable surface conditions
(De Gruyter Open Ltd, 2021) Bidyut Mandal; Krishnendu Bhattacharyya; Astick Banerjee; Ajeet Kumar Verma; Anil Kumar Gautam
This work is concerned with a steady 2D laminar MHD mixed convective flow of an electrically conducting Newtonian fluid with low electrical conductivity along with heat and mass transfer on an isothermal stretching semi-infinite inclined plate embedded in a Darcy porous medium. Along with a strong uniform transverse external magnetic field, the Soret effect is considered. The temperature and concentration at the wall are varying with distance from the edge along the plate, but it is uniform at far away from the plate. The governing equations with necessary flow conditions are formulated under boundary layer approximations. Then a continuous group of symmetry transformations are employed to the governing equations and boundary conditions which determine a set of self-similar equations with necessary scaling laws. These equations are solved numerically and similar velocity, concentration, and temperature for various values of involved parameters are obtained and presented through graphs. The momentum boundary layer thickness becomes larger with increasing thermal and concentration buoyancy forces. The flow boundary layer thickness decreases with the angle of inclination of the stretching plate. The concentration increases considerably for larger values of the Soret number and it decreases with Lewis number. The skin friction coefficient increases for increasing angle of inclination of the plate, magnetic and porosity parameters, however it decreases for rise of thermal and solutal buoyancy parameters. In this double diffusive boundary layer flow, Nusselt and Sherweed numbers increase for rise of thermal and solutal buoyancy parameters, Prandtl number, but they behave opposite nature in case of angle of inclination of the plate, magnetic and porosity parameters. The Sherwood number increases for increasing Lewis number but it decreases for increasing Soret number. © 2020 Bidyut Mandal et al., published by De Gruyter 2020.
Nanoparticle's radius effect on unsteady mixed convective copper-water nanofluid flow over an expanding sheet in porous medium with boundary slip
(Elsevier B.V., 2022) Ajeet Kumar Verma; Sohita Rajput; Krishnendu Bhattacharyya; Ali J. Chamkha
Nanofluid and its higher thermal performance are displayed more promising outcomes when the flow medium is assumed to be a porous medium. Additionally, the radius size of nanoparticles plays a significant role in enhancing this thermal performance. So, present analysis aims to investigate the time-dependent flow of copper-water nanofluid in porous medium on an expanding sheet in presence of buoyancy force and slip phenomenon under various nanoparticle's radii. The flow is assumed to be boundary layer, two-dimensional, viscous, incompressible, laminar and unsteady. Governing coupled PDEs are changed into ODEs by suitable transformations and the converted ODEs are solved numerically. The study discloses that velocity rises with larger radius of nanoparticles and enlargement in assisting buoyancy force, whereas with unsteadiness of the flow, less permeability of porous material and boundary slip it drops. Also, magnitude of wall-drag force grows with larger radius of nanoparticles and flow unsteadiness. Importantly, for higher value of nanoparticle's radius surface-drag force massively enhances when permeability of porous medium is less. Temperature increment exhibits for boundary slip and less permeability of the porous material. Lastly, wall cooling rate intensifies with flow unsteadiness and higher value of nanoparticle's radius. © 2022
Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate
(Springer, 2020) Anil Kumar Gautam; Ajeet Kumar Verma; Krishnendu Bhattacharyya; Astick Banerjee
In this analysis, the mixed convection boundary layer MHD flow of non-Newtonian Carreau fluid subjected to Soret and Dufour effects over a moving vertical plate is studied. The governing flow equations are converted into a set of non-linear ordinary differential equations using suitable transformations. For numerical computations, bvp4c in MATLAB package is used to solve the resulting equations. Impacts of various involved parameters, such as Weissenberg number, power-law index, magnetic parameter, thermal buoyancy parameter, solutal buoyancy parameter, thermal radiation, Dufour number, Soret number and reaction rate parameter, on velocity, temperature and concentration are shown through figures. Also, the local skin-friction coefficient, local Nusselt number and local Sherwood number are calculated and shown graphically and in tabular form for different parameters. Some important facts are revealed during the investigation. The temperature and concentration show decreasing trends with increasing values of power-law index, whereas velocity shows reverse trend and these trends are more prominent for larger values of Weissenberg number. For stronger magnetic field, velocity decreases, while the temperature and concentration increase. It was also found that for shear thinning fluid the drag coefficient exhibits an increasing character when Weissenberg number increases, but for shear thickening fluid the drag coefficient shows the contrary nature. For small values of Dufour number, heat transfer rate enhances with increasing Soret number, but for higher values of Dufour number it slightly dies down with Soret number and the mass transfer rate reacts oppositely. In addition, due to increasing chemical reaction rate, the concentration and velocity decrease. © 2020, Indian Academy of Sciences.
Unsteady nonlinear mixed convective flow of nanofluid over a wedge: Buongiorno model
(Taylor and Francis Ltd., 2024) Sohita Rajput; Ajeet Kumar Verma; Krishnendu Bhattacharyya; Ali J. Chamkha
The article deals with 2D unsteady nanofluid flow past a vertical wedge along with nonlinear mixed convection. Brownian diffusion and thermophoresis effects are considered to model nanofluid flow. Convenient transformations are assumed to change the coupled nonlinear governing PDEs into ODEs. To analyze the problem, the solutions of transformed equations are numerically achieved via ‘bvp4c’, a MATLAB approach. Graphical presentation is adopted to see the impact of various influential parameters. Results reveal that nonlinear temperature and concentration convection parameters exhibit the same impact for velocity, temperature and concentration profile, though nonlinear convection parameter for temperature is more impactful than concentration. Velocity overshoot is observed for assisting flow situations. In nonlinear mixed convection flow, skin-friction coefficient, heat and mass transfer rates prominently change for favorable and adverse pressure gradient conditions. © 2021 Informa UK Limited, trading as Taylor & Francis Group.
Unsteady stagnation-point flow of CNTs suspended nanofluid on a shrinking/expanding sheet with partial slip: multiple solutions and stability analysis
(Taylor and Francis Ltd., 2022) Sohita Rajput; Krishnendu Bhattacharyya; Ajeet Kumar Verma; Mani Shankar Mandal; Ali J. Chamkha; Dhananjay Yadav
The purpose of the study of single/multi-wall carbon nanotubes (SWCNTs/MWCNTs) mixed water-based nanofluid having unsteady stagnation-point flow on shrinking/expanding sheet with velocity and thermal slip effects is to decode the heat transfer mechanism to know the high cooling rate criteria. Governing boundary layer coupled partial differential equation (PDEs) are converted into ordinary ones. The transformed equations are numerically solved by shooting method with RK-4 scheme. The impacts of different parameters are described graphically and a comparison between current and previous results is made in tabular form. Existence of multiple solutions along with unique solution appears for specific cases of shrinking and expanding velocities. The investigation also reveals that SWCNT-nanoparticles have more dominating heat and momentum transfer rates than MWCNT-nanoparticles. Velocity slip delays the boundary layer separation, but maximum surface drag-force does not alter. Thermal slip and unsteadiness reduce heat transfer rate, whereas velocity slip enhances it. For high shrinking velocity compared to free stream velocity, the surface cooling rate drops down with Prandtl number and thermal boundary layer thickness significantly reduces for all types of nanofluids and for both solution branches. For both nanofluids, the temperature near the sheet decreases with thermal slip. For non-uniqueness of the similarity solution, a linear stability analysis is conducted and it verifies that upper branch of the obtained solutions is stable, while lower branch is unstable for high shrinking velocity and the unique solution is stable for expanding and low shrinking velocities. © 2022 Informa UK Limited, trading as Taylor & Francis Group.