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1

Shape effects on steady flow and heat transfer of Cu-nanofluid over a nonlinear stretching surface with Joule heating

Ali Ramzan, Mitalipova Ainura, Hussan Syed Wajeeh Ul, Kurbanaliev Abdikerim, Shahzad Azeem, Abduzhabbarov Mukhammadmuso

Archives of Thermodynamics

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2025

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Vol. 46, no. 3

89--104

EN

Nanofluids have garnered significant interest in various fields due to their numerous advantages and potential applications. The appeal of ethylene glycol (EG)-based Cu-nanofluid lies in its excellent thermal conductivity, stability, and ability to enhance heat transfer properties, making it a promising candidate for diverse industrial applications. In this study, we analyse the flow behaviour of EG-based copper (Cu) nanofluid over a nonlinear stretching surface under the influence of Joule heating effects. The research involves the development of a mathematical model and formulating of governing equations represented as system of partial differential equations, which are subsequently transformed into nonlinear ordinary differential equations through suitable transformations. A numerical framework based on MATLAB bvp4c solver technique is employed to obtain approximate solutions. The study examines the influence of dimensionless parameters on velocity and thermal distributions. The findings for the local Nusselt number and skin friction are presented in tabular form, highlighting the effects of key parameters. The results are benchmarked against three different sources from existing literature, showing strong agreement in the case of reduced Nusselt number.

2

Unsteady flow of silica nanofluid over a stretching cylinder with effects of different shapes of nanoparticles and Joule heating

Ali Ramzan, Iqbal Azhar, Abbass Tasawar, Arshad Touqeer, Shahzad Azeem

Archives of Thermodynamics

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2024

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Vol. 45, no. 3

115--126

EN

Indeed, nanofluids have garnered significant interest in various fields due to their numerous advantages and potential applications. The appeal of SiO2 nanofluid, in particular, lies in its low preparation cost, simple production process, controlled chemistry, environmental safety and its exceptional ability to be homogeneously suspended in the base fluid, which makes it a promising candidate for a variety of applications. In this study, we investigate the flow analysis of a water based silicon dioxide nanofluid, passing over a stretched cylinder while subjected to a continuous magnetic field, including Joule heating effects. The research involves the development of a mathematical model and the formulation of governing equations represented as partial differential equations. These equations are subsequently transformed into non-linear ordinary differential equations through suitable transformations. To obtain a numerical solution, the MATLAB bvp4c solver technique is employed. The study investigates the implications of dimensionless parameters on velocity and thermal distributions. It is observed that the velocity distribution f'(η) exhibits a direct relationship with the volumetric fraction ϕ and an inverse relationship with the unsteadiness parameter S, the magnetic parameter M, and the temperature distribution θ(η) shows an enhancement for the increasing ϕ and M, as well as the Eckert number. However, it declines against S and the Prandtl number. The results for local Nusselt number and skin frictions are depicted in Tables.

3

Evaluating the mixed convection flow of Casson fluid from the semi-infinite vertical plate with radiation absorption effect

Sonam, Yadav Rajendra Singh

Archives of Thermodynamics

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2024

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Vol. 45, no. 4

45--59

EN

This study examines a steady laminar Casson fluid flow induced by a semi-infinite vertical plate under the impact of the Darcy-Forchheimer relation and thermal radiation. The features of mixed convection, cross-diffusion, radiation absorption, heat generation, chemical reactions and viscous dissipation are also considered to explain the transport phenomenon. The resultant system of equations, concerned with the problem under consideration, is transformed into a group of non-linear ordinary differential equations (ODEs) by means of similarity variables. The bvp4c method, an instrument popular for its numerical accomplishments, is utilized to solve this problem. The effect of flow parameters on heat transfer, concentration and velocity is evaluated via diagrams. To validate our code, we have compared the present outcomes to the prevenient literature, and stable consent has been detected. Moreover, the friction coefficient 𝐶𝑓𝑥 , Nusselt number Nu𝑥, and Sherwood number Sh𝑥 are also computed to assess velocity gradient, efficiency of heat transfer and mass transfer process, respectively.

4

Stability analysis of MHD stagnation flow over a permeable heated rotating disk with heat generation/absorption

Mendil F., Mamache S., Bouda F. N.

Archives of Mechanics

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2024

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Vol. 76, nr 5

471--494

EN

The stagnation point flow of an incompressible viscous electrically conducting fluid impacting orthogonally on a heated rotating disk is studied with internal volumetric heat generation/absorption in the presence of a uniform magnetic field. A uniform suction or injection is applied through the surface of the disk. Appropriate similarity transformations are used to reduce the governing differential equations of the problem into a system of nonlinear ordinary differential equations and then solved numerically using the fourth-order Runge-Kutta method. In the second step, the work is oriented towards linear stability analysis by considering infinitesimally small disturbances within the boundary layer. Using normal mode decomposition in the Görtler-Hammerlin framework, the resulting eigenvalue problem is then solved numerically by means of the pseudo-spectral method using Laguerre’s polynomials. As a result, the critical conditions for the onset of thermal instability are described and discussed in detail using multiple configurations. It is found that the presence of a magnetic field and suction/injection act to increase the stability of the basic flow. However, the rotation parameter and the internal heat generation/absorption contribute significantly to destabilizing the basic flow.

5

Numerical solution of MHD channel flow in a porous medium with uniform suction and injection in the presence of an inclined magnetic field

Chutia Muhim

Journal of Applied Mathematics and Computational Mechanics

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2022

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Vol. 21, nr 2

5--13

EN

In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette-Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number (M), suction/injection parameter (S), permeability parameter (α) and angle of inclination (θ) on the flow are discussed and presented graphically.

6

Wavelet-based numerical solution for MHD boundary-layer flow due to stretching sheet

Karkera Harinakshi, Katagi Nagaraj N.

International Journal of Applied Mechanics and Engineering

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2021

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Vol. 26, no. 3

84--103

EN

In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters Mand βare calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter ()M1< which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods.

7

Transient heat and mass transfer of hydromagnetic effects on the flow past a porous medium with movable vertical permeablesheet

Okedoye A. M., Salawu S. O.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 4

175--190

EN

An unsteady flow of heat and species transport through a porous medium in an infinite movable vertical permeable flat surface is considered. The hydromagnetic chemical reactive fluid flow is stimulated by the thermal and solutant convection, and propelled by the movement of the surface. The formulated nonlinear flow equations in time space are solved analytically by asymptotic expansions to obtain solutions for the flow momentum, energy and chemical concentration for various thermo-physical parameters. The existence of flow characteristic is defined with the assistance of the flow parameters. In the study, the impact of some pertinent flow terms is reported and discussed. The study revealed that the species boundary layer increases with a generative chemical reaction and decreases with a destructive chemical reaction. Also, arise in the generative species reaction term reduces the flow momentum for the cooling surface. The impact of other flow governing parameters is displayed graphically as well as the fluid wall friction, wall energy and species gradients. The results of this study are important in chemical thermal engineering for monitoring processes to avoid solution blow up.

8

Mixed convection in MHD flow and heat transfer rate near a stagnation-point on a non-linear vertical stretching sheet

Fenuga O. J., Hassan A. R., Olanrewaju P. O.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

37--51

EN

This work investigates the mixed convection in a Magnetohydrodynamic (MHD) flow and heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the fourth order Runge-Kutta method with shooting technique. The influence of pertinent flow parameters on velocity, temperature, surface drag force and heat transfer rate are computed and analyzed. Graphical and tabular results are given to examine the nature of the problem. The heat transfer rate at the surface increases with the mixed convection.

9

Effects of radiation and Eckert number on MHD flow with heat transfer rate near a stagnation point over a non-linear vertical stretching sheet

Fenuga O. J., Hassan A. R., Olanrewaju P. O.

International Journal of Applied Mechanics and Engineering

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2020

|

Vol. 25, no. 1

27--36

EN

This work investigates the effects of radiation and Eckert number on an MHD flow with heat transfer rate near a stagnation-point region over a nonlinear vertical stretching sheet. Using a similarity transformation, the governing equations are transformed into a system of ordinary differential equations which are solved numerically using the sixth order Runge-Kutta method with shooting technique. Tabular and graphical results are provided to examine the physical nature of the problem. Heat transfer rate at the surface decreases with radiation, Eckert number and as radiation increases, the flow temperature also increases for velocity ratio parameters […].

10

Perturbation solutions for magnetohydrodynamics (MHD) flow of in a non-Newtonian fluid between concentric cylinders

Yurusoy M., Guler O. F.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 1

199--211

EN

The steady-state magnetohydrodynamics (MHD) flow of a third-grade fluid with a variable viscosity parameter between concentric cylinders (annular pipe) with heat transfer is examined. The temperature of annular pipes is assumed to be higher than the temperature of the fluid. Three types of viscosity models were used, i.e., the constant viscosity model, space dependent viscosity model and the Reynolds viscosity model which is dependent on temperature in an exponential manner. Approximate analytical solutions are presented by using the perturbation technique. The variation of velocity and temperature profile in the fluid is analytically calculated. In addition, equations of motion are solved numerically. The numerical solutions obtained are compared with analytical solutions. Thus, the validity intervals of the analytical solutions are determined.

11

Numerical solution through mathematical modelling of unsteady MHD flow past a semi-infinite vertical moving plate with chemical reaction and radiation

Bhandari A.

Studia Geotechnica et Mechanica

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2018

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Vol. 40, nr 4

270--281

EN

In the present manuscript, unsteady magnetohydrodynamic (MHD) flow over a moving porous semi-infinite vertical plate with time-dependent suction has been studied in the presence of chemical reaction and radiation parameters. Time-dependent partial differential equations in the dimensionless form are solved numerically through mathematical modelling in COMSOL Multiphysics. The results are obtained for velocity, temperature and concentration profiles at different times. Steady state results are also presented for different values of physical parameters. The parameters involved in the problem are useful to change the characteristics of velocity, heat transfer and concentration profiles. The numerical solution of partial differential equations involved in the problem is obtained without sacrificing the relevant physical phenomena.

12

Soret and Dufour effects on MHD micropolar fluid flow over a linearly stretching sheet, through a non-Darcy porous medium

Reddy G. V. R., Krishna Y. H.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 2

485--502

EN

In this paper, we discuss the Soret and Dufour effects on an MHD micropolar fluid flow over a linearly stretching sheet, through a non-Darcy porous medium, where stretching velocity of the sheet varies linearly with distance from the origin, and, temperature and concentration vary non-linearly in the boundary layer region. By suitable similarity transformations, the governing boundary layer equations are transformed to ordinary differential equations. These equations are solved by numerical computations with bvp4c along with the shooting technique method. The effects of the magnetic parameter, Soret number and Dufour number on velocity profiles, microrotation profile, heat transfer, and concentration, skin-friction, Nusselt number and Sherwood number are computed, discussed and analysed numerically and presented through tables and graphs.

13

Effect of thermal radiation, chemical reaction and viscous dissipation on MHD flow

Zigta B.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 3

787--801

EN

This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

14

Effects of Radiation and Porosity of the Medium on MHD Flow Past an Inclined Plate in the Presence of Hall Current

Rajput U. S., Kumar G.

Computational Methods in Science and Technology

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2017

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Vol. 23, No. 2

93--103

EN

The present study deals with an analysis of the effects of radiation and porosity of the medium on unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively started inclined plate under the influence of transversely applied uniform magnetic field and Hall current. The medium of the flow is taken as porous. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The results obtained are discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof Number, Prandtl number, Hall current, radiation, permeability, magnetic field parameter and Schmidt number. The numerical values obtained for skin-friction and Nusselt number have been tabulated. The objective of this study is to analyze radiation and the porosity of the medium in the MHD flow model. In the study we found that the velocity in the boundary layer increases with the values of radiation and porosity of the medium. It is also observed that radiation and porosity of the medium increases the skin-friction at the wall surface. The results of the study are found to be in agreement with the actual flow. The importance of the problem can be seen in cooling of electronic components of a nuclear reactor, bed thermal storage and heat sink in the turbine blades.

15

Hall effects and rotation effects on MHD flow past an exponentially accelerated vertical plate with combined heat and mass transfer effects

Thamizhsudar M., Pandurangan J., Mathucumaraswamy R.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 3

605--616

EN

A theoretical solution of flow past an exponentially accelerated vertical plate in the presence of Hall current and MHD relative to a rotating fluid with uniform temperature and mass diffusion is presented. The dimensionless equations are solved using the Laplace method. The axial and transverse velocity, temperature and concentration fields are studied for different parameters such as the Hall parameter (m), Hartmann number (M), Rotation parameter (Ω), Schmidt number, Prandtl number, thermal Grashof number (Gr) and mass Grashof number (Gc). It has been observed that the temperature of the plate decreases with increasing values of the Prandtl number and the concentration near the plate increases with decreasing values of Schmidt number. It is also observed that both axial and transverse velocities increase with decreasing values of the magnetic field parameter or rotation parameter, but the trend gets reversed with respect to the Hall parameter. The effects of parameters m, M, […], Gr and Gc on the axial and transverse velocity profiles are shown graphically.

16

Influence of convective heat and mass conditions in MHD flow of nanofluid

Shehzad S. A., Hayat T., Alsaedi A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

|

Vol. 63, nr 2

465--474

EN

This article aims to investigate the two-dimensional magnetohydrodynamic (MHD) boundary layer flow of nanofluid. Convective mass condition is introduced. Analysis has been discussed in the presence of an applied magnetic field. The Brownian motion and thermophoresis effects are incorporated. The arising nonlinear problems are first converted to ordinary differential equations and then series solutions are constructed. Convergence of series solutions is examined through plots and numerical values. Results are plotted and discussed for the temperature and concentration. Numerical computations for skin-friction coefficient, local Nusselt and Sherwood numbers are performed and analyzed. Comparison with the previous limiting case is noted in an excellent agreement.

17

Closed form solutions of heat and mass transfer in the flow of a MHD visco-elastic fluid over a porous stretching sheet

Ashokkunar K., Veena P. H., Pravin V. K.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

989--1002

EN

The problem of heat and mass transfer in a visco-elastic fluid flow over a stretching sheet in the presence of a uniform magnetic field is examined. The important physical quantities such as the skin friction coefficient, heat transfer co-efficient and the mass transfer co-efficient are determined. It is found that the heat and mass transfer distribution decreases with the increasing values of the visco-elastic parameter k1.

18

Three dimensional free convection MHD flow in a vertical channel through a porous medium with heat source and chemical reaction

Rath P. K., Kar M., Dash G. C., Das M.

International Journal of Applied Mechanics and Engineering

|

2012

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Vol. 17, no. 4

1253-1266

EN

The present study is devoted to a three dimensional free convective MHD flow in a vertical channel packed with a porous material having uniform porosity in the presence of a heat source and chemical reaction. One of the walls of the channel is impermeable whereas the other is permeable. The heat, mass and momentum transfer phenomena are coupled due to the presence of convective terms associated with buoyancy effects. Moreover, the presence of a heat source and chemical reaction of the diffusing species makes the study interesting. Though the method of solution is straightforward and valid for a flow with a small Reynolds number still the discussion reveals some answers to awaited queries. The presence of diffusing species with chemical reaction prevents back flow of cross flow velocity. It is interesting to note that the absence of a magnetic field with a low Reynolds number as well as the presence of a magnetic field with a moderately large Reynolds number gives rise to back flow.

19

Numerical solutions for heat and mass transfer effects of an unsteady MHD free convective flow past an infinite vertical plate with constant suction (injection) and heat source

Ambethkar V.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no. 1

67-89

EN

The objective of this work is to study heat and mass transfer in an unsteady MHD free convective flow past an infinite vertical plate with constant suction (injection) and heat source numerically. Dimensionless governing equations of the problem have been solved by using the finite difference technique. Numerical solutions for temperature, velocity, concentration have been obtained for suitable parameters like the Grashof number, mass Grashof number, Prandtl number, Schmidt number and Eckert number. The rates of heat transfer and mass transfer are studied. The results obtained are discussed with the help of graphs and tables to observe the effect of various parameters concerned in the problem under investigation. Effects of suction, the Eckert number and heat source parameter on velocity and temperature distributions are discussed. Stability and convergence of the finite difference scheme is established.

20

MHD fully developed mixed convection between two long vertical parallel plates

Dubewar A. V., Soundalgekar V. M.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no. 4

941-948

EN

The effect of a transversely applied magnetic field on an MHD fully developed mixed convection between two long vertical parallel plates is studied. Velocity, pressure gradient and bulk-temperature profiles are shown graphically and the effects of different parameters like M (Hartmann number), (buoyancy parameter), (wall temperature difference ratio) on the flow are discussed.