Browsing by Author "Naveen Dwivedi"

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Effect of a Point/Line Heat Source on Hydromagnetic Free Convection between Vertical Walls due to Induced Magnetic Field
(Springer, 2022) Naveen Dwivedi; Ashok Kumar Singh
The hydromagnetic natural convective flow of an incompressible electrically conducting and viscous liquid amid non-conducting vertical walls with a constant point heat source/sink under the impact of the induced magnetic field has been studied. A wavelet function is used to formulate the point heat source. The considered problem is described by a group of simultaneous ODEs with significant boundary conditions, and their solutions have been acquired for the induced magnetic field, the velocity field and the temperature field by applying the Laplace technique. The skin friction, induced current density and mass flux have also been discussed. The influences of controlling parameters on the fluid flow are discussed with the tables and graphs. The valuable consequence of this investigation is that an enhancement in the length of point heat source enhances the induced magnetic field, velocity, induced current density and temperature field. © 2020, The National Academy of Sciences, India.
Effect of line/point heat source and Hall current with induced magnetic field on free convective flow in vertical walls
(Springer, 2022) Naveen Dwivedi; Ashok Kumar Singh
In this research, the hydromagnetic natural convection of an incompressible fluid with point heat source by considering the influence of Hall current and induced magnetic field between infinite vertical walls is studied. The Laplace transform procedure is utilized to determine the analytical solutions of the acquired mathematical model with the wavelet function. With the derived solution of velocity, induced magnetic field, temperature field, and induced current density, the flow character is investigated with the influence of the physical parameters (namely Hall current, Hartmann number, and point heat source) for the presented boundary conditions. Also, the skin friction and volumetric flow rate are derived through the velocity expression. Numerical and graphical results are introduced to formalize the solution of the model. The valuable result from the investigation is that an increase in the length of the point heat source leads to enhance both components of induced current density, induced magnetic field, and primary velocity profiles. Moreover, it is noticeable that an enhancement in the Hall current has a reverse connection with both components of the induced current density, induced magnetic field, while the direct connection with the primary velocity component. There are numerous engineering applications such as the metal cutting, grinding, welding, laser hardening of metals, and many others in which the calculation of temperature field is modeled as a problem involving a point heat source. © 2021, Indian Association for the Cultivation of Science.
Effect of point/line heat source and Hall current on free convective flow between two vertical walls
(Springer, 2020) Naveen Dwivedi; Ashok Kumar Singh
The influence of a point heat source and Hall current on the laminar hydromagnetic free convective flow of an incompressible and electrically conducting viscous liquid between two vertical walls has been studied. A wavelet function is utilised to mathematically formulate the point or line heat source. The incidental equations on the flow have been processed subject to the Boussinesq approximation. A unified analytical solution of basic equations like thermal energy and momentum has been derived by employing Laplace transform technique. The impacts of the pertinent physical parameters, such as Hall parameter, magnetic field and point heat source, on the velocity field are explained graphically. The valuable result from the investigation is that an increase in the length of the point heat source leads to the enhancement of the velocity profiles. Moreover, it is noticeable that an enhancement of Hall current has a direct connection with the primary factor of the volumetric flow rate and skin friction. © 2020, Indian Academy of Sciences.
Hydromagnetic free convection in a vertical channel with induced magnetic field: Open and short circuits
(Springer, 2022) Naveen Dwivedi; Ashok Kumar Singh; Pallath Chandran; Nirmal C Sacheti
This theoretical paper deals with a fully developed free convective flow of an incompressible viscous and electrically conducting fluid in an infinitely long rigid vertical channel in the presence of an externally applied magnetic field. By retaining the induced magnetic field, we have carried out a detailed analysis of the field equations and obtained a host of interesting results corresponding to both open-circuit and short-circuit arrangements. The governing PDEs, which under the chosen physical configuration get transformed to a set of ordinary differential equations together with appropriate boundary conditions, have further been subjected to non-dimensionalisation. Using the theory of simultaneous ordinary differential equations, the analytical solutions for velocity, temperature field and induced magnetic field were obtained. These solutions were used to obtain important quantities of engineering interest such as current density, wall skin friction and volumetric flux for both open and short circuits. The effect of Hartmann number on the velocity, induced magnetic field and induced current density were shown quite extensively. Furthermore, the results for the symmetric and asymmetric heating of the vertical walls of the channel for open- and short-circuit arrangements were compared. It is found that for the open-circuit arrangement, the velocity, induced current density and induced magnetic field are higher than that for the short-circuit arrangement. © 2022, Indian Academy of Sciences.
Hydromagnetic free convective flow in vertical cylinder due to point/line heat source/sink
(Springer, 2022) Naveen Dwivedi; Ashok Kumar Singh
The current study is to explore the phenomena of the hydromagnetic free convective flow of an electrically conducting and incompressible viscous fluid through an impermeable vertical cylinder, with the point heat source under the influence of the transversely applied magnetic field of uniform strength in the radial direction. The free convection phenomenon in the working fluid occurs due to the presence of the point/line heat source as it appears in many real-world mechanisms. The main motive of this analytical study is thus to examine the effect of point and line heat source on this buoyancy-dominated developing flow. The governing equations thus framed for the prescribed flow namely energy and momentum, simplify to steady linear differential equations in the physical setup assumed in this investigation. These equations, in non-dimensional forms, have been solved, in turn, employed simultaneous ordinary differential equations (ODEs) theory. The resulting closed form solutions for the physical variables, namely fluid temperature and fluid velocity have been presented in terms of Bessel, modified Bessel, and Regularized Hypergeometric functions. Additionally, skin friction coefficient, Nusselt number, and mass flow rate are numerically discussed for the involved parameters. There arises a number of pertinent physical parameters in our analysis: Heat source, Hartman number, and point heat source whose influence on the developing velocity and some temperature profiles have been illustrated through a number of plots. Major outcomes show that the enhancement in Hartmann number motivates a reduction in the velocity profile for the point and line heat source cases. In addition, the fluid motion rises due to the line and point heat source, and the velocity and temperature profiles have a higher value in the case of the line heat source as compared to the point heat source. © 2021, Indian Association for the Cultivation of Science.
Influence of Hall current on hydromagnetic natural convective flow between two vertical concentric cylinders in presence of heat source/sink
(John Wiley and Sons Inc, 2020) Naveen Dwivedi; Ashok Kumar Singh
The fully developed laminar magnetohydrodynamic free convection between two concentric vertical cylinders with Hall currents and heat source/sink, in the presence of the radial magnetic field, are studied. The governing thermal energy and momentum equations are changed into ordinary differential equations whose solutions are determined in closed-form expressions of the Bessel and modified Bessel functions of order zero. A parametric investigation illustrating the impacts of the Hall current, magnetic field, heat source, and radii ratio has been accomplished graphically to examine the changes in temperature as well as velocity while the Nusselt number, mass flux, and skin friction values have been presented in tabular forms. The results ensure that the Hall current has a strong and direct impact on the flow character, such that the influence of the Hall parameter enhances the velocity fields in the appearance of heat source and sink. The velocity remains almost constant as the Hall parameter value is greater than four. Moreover, the velocity and temperature fields have an increasing tendency due to the heat source and inversely for the heat sink. © 2020 Wiley Periodicals, Inc.
Influence of temperature dependent heat source/sink on transient MHD free convective flow in an infinite rigid impermeable vertical cylinder with chemical reaction
(KeAi Communications Co., 2023) Naveen Dwivedi; Ashok Kumar Singh; Nirmal C. Sacheti
It is increasingly apparent that the inclusion of mass transfer aspects, together with certain thermal conditions, in the momentum and energy equations governing MHD flows leads to a numbers of real life applications. Keeping this in view, we have attempted an exact analysis of heat and mass transfer aspects in transient hydromagnetic free convective flow of an incompressible viscous fluid through a vertical pipe under an externally applied magnetic field, assuming presence of chemical reaction and heat source/sink. The governing PDEs, which simplify to a set of 3 linear ODEs in the physical set up considered here, have been solved using Laplace transform technique, with solutions for key physical variables presented in the term of Bessel and modified Bessel functions. The influence of governing non-dimensional parameters, namely, Hartmann number, Schmidt number, source/sink parameter, Prandtl number and chemical reaction parameter, has been illustrated on the developing velocity and some concentration profiles. Some important quantities of engineering interest-surface skin friction and volumetric flow rates-have been computed too and analysed. Some notable finding worth mentioning are: (a) heat source presence causes higher fluid velocity as compared to the heat sink; (b) all important surface shear stress can be suitably controlled, among others, by chemical reaction parameter and Schmidt number. The key challenge of this study has been to obtain exact closed-form solutions of the field equations, including cumbersome Laplace inverses. This study finds innovative applications in the emerging fields such as magnetic materials processing, chemical processes, solar energy systems, etc. © 2023 The Authors
Natural convection between vertical walls due to point/line heat source/sink
(Springer, 2019) Naveen Dwivedi; A.K. Singh; Anand Kumar
In the present paper, we have investigated the influence of constant point/line heat source on fully developed free convective laminar flow between two infinite vertical walls of an electrically conducting and viscous incompressible fluid. The Heaviside step function is used to model the constant heat source/sink and further this function can be converted into line heat source/sink. The compact solution has been obtained by using Laplace transform method. The effects of physical parameters such as constant point/line heat source parameter and Hartmann number on the velocity and temperature fields are shown graphically while on skin friction, mass flow rate and Nusselt number of the fluid are presented in tabular form. It is found that the velocity and temperature field of the fluid increases when the point heat source changes into a line heat source. Also, we have observed that the velocity and temperature profiles increase as the value of constant point/line heat source parameter increases. © Springer Nature India Private Limited 2019.
Steady two-dimensional free convective flow in a finite non-rectangular vertical porous cavity subject to modulating temperature on a bounding surface
(Springer, 2025) Naveen Dwivedi; Ashok Kumar Singh; Nirmal C. Sacheti; Beer Singh Bhadauria; Pallath Chandran
In theoretical studies of free convective flows taking place in finite porous/non-porous geometries, boundary thermal conditions, especially time-dependent temperature conditions, significantly alter the convection currents and, hence, the resulting real-life applications. This paper has thus considered a fully developed steady buoyancy dominated flow of incompressible viscous fluid in a finite trapezoidal vertical porous cavity. It is assumed that the left vertical wall of this enclosure has been subjected to an oscillatory modulation in the temperature, while the remaining vertical/horizontal/inclined walls have been kept at either constant temperature or subjected to adiabatic thermal conditions. The set of governing PDEs, representing the momentum and thermal transport, together with the Darcy law for porous medium used, have been first transformed to another setup in terms of a stream function, velocity component and temperature in a non-dimensional form. These equations, subject to appropriate boundary conditions at 4 bounding surfaces, have then been solved numerically using an algebraic grid generation technique together with finite difference method. There arises a number of key physical or geometrical nondimensional parameters in our analysis whose effects, across various parameter ranges, have been exhibited on the physical variables of great interest, namely, contours of streamlines and isotherms. Some more aspects related to heat transfer taking place on the bounding walls, have been dealt with to highlight engineering features of this convective flow. It is worth emphasizing that assessing the effect of oscillatory time-dependent wall thermal modulation on natural convection occurring in a non-rectangular finite permeable cavity is the main objective here and first attempt in the literature. © Indian Academy of Sciences 2025.
Transient free convection of a second-grade fluid flowing in a vertical cylinder
(John Wiley and Sons Inc, 2021) Naveen Dwivedi; Arun Kumar Singh; Ashok Kumar Singh
The intention of the present article is to examine the transient effect on the free convection of the second-grade fluid flowing in a vertical cylinder. We have found the analytical solution of the derived governing partial differential equations in nondimensional form corresponding to the velocity as well as the temperature fields by applying the Laplace transformation method in terms of the Bessel function of the first kind. To obtain the impacts of the appropriate parameters related to the given equations, such as the second-grade fluid parameter and the Prandtl number, the numerical values of the velocity are discussed and displayed in graphs. Furthermore, the mass flow rate and the skin friction at the inner surface of the cylinder are given in a tabular form. The influence of the second-grade fluid parameter is to decelerate the velocity as well as the mass flow rate and to enhance the steady-state time. © 2020 Wiley Periodicals LLC
Transient free convective hydromagnetic flow in an infinite vertical cylinder with Hall current and heat source/sink
(John Wiley and Sons Inc, 2020) Naveen Dwivedi; Ashok Kumar Singh
The analysis of hydromagnetic flow has been a concern of consideration for research scientists and engineers. In this treatise, the unsteady hydromagnetic free convective flow of an incompressible, viscous, and electrically conducting fluid and heat transfer in a vertical cylinder with Hall effects and transverse magnetic field, in the presence of heat source and sink, is studied. Exact solutions of dimensionless unsteady governing equations are obtained by using the Laplace transform technique. Transient fluid velocity and temperature field are depicted by graphs, whereas heat transfer rate, mass flux, and skin-friction are computed in a tabular form for different physical parametric values, such as the source/sink parameter, Hall current parameter, Prandtl number, and Hartmann number. The valuable result from the investigation is that the Hall parameter slightly accelerates the fluid velocity and it provides resistance to the skin friction at the cylindrical surface. Moreover, it is noticeable that temperature as well as velocity enhances and finally gets to its steady state with time. To be noted, the Hall effects have been widely applied in numerous experimental engineering applications, such as constrictions of turbines, Hall accelerators, Hall sensors. © 2020 Wiley Periodicals LLC