Hydromagnetic Flow Research Articles

Optimizing heat transfer rate with sensitivity analysis on nonlinear radiative hydromagnetic hybrid nanofluid flow considering catalytic effects and slip condition: Hamilton–Crosser and Yamada–Ota modelling

AbstractIn current investigation the optimization of heat transportation rate in a nonlinear radiative buoyancy‐driven hydromagnetic carbon nanotube (CNT) hybrid nanofluid flow is analysed. The proposed catalytic effects and slip condition is accounted for the real‐world complexities of the system. The Hamilton–Crosser (HC) and Yamada–Ota (YO) models are employed to characterize the behaviour of the nanofluid. The primary objective is to enhance the heat transmission rate, which is crucial for various engineering applications such as thermal management, energy systems and so forth. To achieve this, sensitivity analysis is performed to identify the most influential parameters affecting heat transfer in the system. By understanding the sensitivity of these parameters, the performance of the system can be improvised. The study focuses on the interplay between key factors including radiative heat transfer, buoyancy‐driven flow, magnetic field influence, catalytic effects, and slip condition. The presence of CNTs in the nanofluid adds another dimension to the complexity of the system that explores the effects of varying the concentration and size of CNTs on the heat transfer rate. By utilizing advanced mathematical modelling and numerical simulations, the performance of the system under different scenarios and identify the optimal conditions for maximizing heat transfer rate is evaluated. The findings of this research provide valuable insights into the design and optimization of heat transfer systems involving nanofluids with nonlinear radiative and hydromagnetic effects. The observation shows that, irrespective to single wall and multi wall CNT nanoparticles the fluid velocity attenuates significantly whereas it favours in enhancing the fluid temperature. Further, the comparative analysis reveals that the heat transfer augments in the case of HC model than that of YO model.

Exact solutions of hydromagnetic convective flow in a microchannel with superhydrophobic slip and temperature jump: Microfluidics applications

AbstractThe researchers explored the free convective flow of a hybrid nanofluid in a vertical microchannel with a rectangular cross‐section. Notably, both channel walls were heated alternately, and a transverse magnetic field was applied across the channel. The channel walls had unique properties, one of which was nonslip and the other was exceedingly hydrophobic. The major purpose was to investigate the effects of magnetism and superhydrophobicity on important flow parameters. The differential equations in the investigation were solved, producing accurate results. The study yielded some significant discoveries. First, when heated, the magnetic parameter reduced skin friction on both sides. Second, in both heating conditions, the magnetic field reduced flow rate and velocity. The flow rates in the two reported situations were similar at a crucial temperature jump coefficient. Furthermore, for low‐temperature jump coefficients, heating the superhydrophobic side reduced the Nusselt number whereas heating the nonslip side had no magnetic effect. The percentage change in the value of Nusselt number and velocity decreases continuously with increase in nonlinear density variation with temperature (NDT) parameter and magnetic parameter. The percentage increases in the value of skin friction with increase in temperature jump and slip length but decrease in the percentage of skin friction for the effect of magnetic term and NDT parameter. As the NDT parameter increases, the velocity percentage rises to 50.59% when the superhydrophobic surface is heated and to 84.30% when the nonslip surface is heated. The temperature jump is statistically significant for the value of the Nusselt number and skin friction for the no‐slip surface condition. These discoveries have practical consequences for the design and management of both tiny and large‐scale systems, with possible applications in microfluidics, microelectronics, nanoscience, and nanotechnology.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Impact of Arrhenius activation energy on magnetic nanofluid flow over a slendering stretchable sheet with nonlinear radiative heat transfer: A machine learning algorithm

Thermal systems in the contemporary world need effective cooling and heating methods. Heat transfer technology plays a vital role in various industries, including aerospace, electronic equipment, automobiles, and transportation. Considering the importance of effective cooling and heating processes, this framework explores the hydromagnetic stagnation point flow with binary chemical reactions, ohmic heating, Arrhenius activation energy, nonlinear thermal radiation, thermophoresis, and Brownian motion. At first, the flow equations are determined in a formal way as dimensional partial differential equations. Then, they are transformed into simpler, dimensionless ordinary differential equations using self-similar variables. The present study describes a novel approach to intelligent numerical computing, utilizing a Levenberg-Marquard algorithm-based MLP (Multi-Layer Perceptron) feed-forward back-propagation ANN (Artificial Neural Networks) implementation. The collection of data was conducted to facilitate the evaluation, validation, and instruction of the artificial neural network model. The utilization of appropriate self-similarity variables has facilitated the conversion of fluid transport equations into ordinary differential equations. The Runge–Kutta–Fehlberg (RKF) technique was used to solve these equations. The numerical results are presented visually for numerous constraints of the governing parameters. The increased values of the velocity ratio enhanced the fluid velocity. The nonlinear thermal radiation and temperature differential characteristics significantly raise the temperature of the fluid. Increasing the nonlinear radiation and magnetic field parameters improves the rate of heat transfer. The temperature of the fluid decreases as the size of stagnation increases. The skin friction coefficients decrease as the wall thickness and magnetic parameters increase.

Influence of induced magnetic field and chemically reacting on hydromagnetic Couette flow of Jeffrey fluid in an inclined channel with variable viscosity and convective cooling: A Caputo derivative approach

In this study, the influence of induced magnetic field and chemically reacting on hydromagnetic generalized Couette flow of Jeffrey fluid in an inclined channel through a porous medium with variable viscosity and convective cooling has been investigated using the Caputo fractional order derivative operator. The mathematical formulation used for the hydromagnetic Couette flow of Jeffrey fluid takes into account the effects of viscous dissipation, Soret, and Dufour. The system of nonlinear partial differential equations governing the flow were solved numerically using the explicit finite difference method. The numerical results for the behavior of various physical parameter on the flow variables are obtained and represented graphically. Moreover, effects of the flow parameters on heat and mass transfer rates are obtained and discussed numerically through tabular forms. The graphical findings show that velocity, concentration, induced magnetic field, and thermal field profiles decline with progressively increment of Jeffrey parameter. The velocity, and temperature of the fluid decline with higher values of fluid viscosity parameter. An increase in the chemical reaction parameter recede the concentration field profiles while increase with raises the values of Soret number. Increasing Biot, and Dufour numbers significantly grows the thermal field profiles. Induced magnetic field grows with larger values of fluid viscosity parameter. The findings of this study are important due to its application in magnetohydrodynamics pumps, polymer manufacturing, fins designs, and food processing.

COMSOL Multiphysics simulation of hydromagnetic flow in horizontal channels with diverse media: Insights into momentum and heat diffusion limitations

AbstractThe Darcy–Forchheimer model for a two‐dimensional hydromagnetic flow in a horizontal channel, including the dynamic interaction of porous and nonporous media, is investigated in this study due to the importance of the consequences of heat exchange in porous materials. The novelty of the current investigation is to study the hydrodynamics of fluid flowing through a channel with free and non‐Darcy porous media linked next to one another influenced by the potent Lorentz force. The prime objective of this investigation is to analyze the influence of critical nondimensional parameters on the rate of heat transfer and shear forces exerted on the walls of the channel. Numerical simulations are carried out using the finite element method within the COMSOL Multiphysics program, which offers a versatile framework to explore the behavior of velocity and isothermal contours. The essential optimal stability of this adopted model is achieved for specific scenarios employing a finely meshed grid and grid‐independent analysis. It is noteworthy that larger Prandtl numbers enhance heat transmission rates from surfaces at high temperatures, whereas greater Eckert numbers are correlated with lower Nusselt numbers. On the lower surface, the Forchheimer and magnetic drag forces reduce skin friction, whereas the top surface displays a different pattern. The aforesaid findings have a variety of engineering applications by improving the flow dynamics in porous and nonporous materials. This study can be beneficial in designing heat exchanger devices.

Numerical study of hydromagnetic bioconvection flow of micropolar nanofluid past an inclined stretching sheet in a porous medium with gyrotactic microorganism

The present article centers on the examination of novel bioconvection phenomena involving gyrotactic microorganisms and a micropolar nanofluid model with hydro-magnetic flow. The flow traversed a stretchable inclined plate within the permeable medium. Heat absorption and thermal radiation are considered. The objective of this study is to assess the rate of heat transfer exhibited by nanofluid when unicellular microorganisms are present. Mathematical complex flow model is converted to nonlinear dimensional less system of differential equation through adopting the appropriate similarity variables. For the non-linear nanofluid problem, the (FDM) finite difference method (Lobatto IIIA) is applied with a range of collocation sites and an accuracy of order 4–5. (Lobatto IIIA) excels in solving coupled differential equations, even those with high nonlinearities. Nanofluid containing gyrotactic microbes is highly applicable in bioscience, geoscience and eco science. The effects of dimensional less parameters on flow field, energy distribution, nanofluid concentration and density of microorganism concentration profiles analyzed through the graphical and tabulation representation. This basic research will aid scientists and engineers in controlling fluid flow and improving complex systems that make use of it.

Synergistic impacts of radiative flow of Maxwell fluid past a rotating disk with reactive conditions: An Arrhenius model analysis

This study presents an analysis of the hydromagnetic radiative flow of a Maxwell fluid past a rotating disk around its own axis with an angular velocity Ω0 which has enormous applications in metal casting (help to optimize the solidification and cooling of molten metals), plastic molding and aerospace engineering (cooling system of aircraft engines). The flow is constrained by boundaries that induce convection and chemical reactions described by the Arrhenius model. By applying similarity transformations, the non-linear partial differential equations, which describe the flow phenomenon, are metamorphosed into the non-dimensional system of ordinary differential equations (ODEs). The obtained ODEs are then solved numerically using ‘Keller box method’, an efficient computational technique, by implementing the finite-difference approach. The influence of different parameters, namely magnetic field strength, radiation parameter, reaction rate constant, and convective heat transfer coefficient, on the flow and heat/mass transfer characteristics are investigated. The findings suggest that the higher activation energy leads to a slower rate of reaction. As the reaction rate decreases, the consumption of reactant molecules and the reduction in their concentration also slow down. The influence of the convective heat transfer coefficient is also examined in terms of its effect on the thermal and concentration boundary layers. As the stretching parameter increases, the Maxwell fluid undergoes greater deformation, leading to greater strain and a consequent slowing of the fluid's radial velocity. Heat transfer is enhanced by thermal radiation and convective condition at the surface of rotating disk. The findings of this study provide valuable insights into the industries dealing with Maxwell fluids, enabling them to enhance process efficiency, optimize resource utilization, and develop sustainable and environmentally friendly solutions.

Analytical Investigation of Arrhenius Kinetics with Heat Source/Sink Impacts along a Heated Superhydrophobic Microchannel

Exothermic Arrhenius-controlled chemical reactions are widely employed for heating applications, such as combustion in heating systems and fuel-burning motors. These effects are critical for manufacturing high thermal systems required for high thermal performances. Therefore, this paper presents the analytical investigation into the Arrhenius-controlled heat-generating/absorbing fluid of a hydromagnetic flow along a heated upstanding plate in a microchannel. One wall had a superhydrophobic surface and temperature jump conditions, but the other was unaltered. The regular perturbation approach investigated the nonlinear, coupled governing equations. With the help of graphical plots, the impacts of crucial and relevant parameters embedded in the flow are described. This investigation concludes that chemically reacting parameters' impact significantly elevates the micro-channel's thermal and hydromagnetic flow. However, applying the heat generation parameter increases fluid velocity, whereas the heat absorption parameter produces the contrary effect. The outcomes of this study can be relevant to the field of biomedical sciences and devices for improving heat transfer efficiency, chemical synthesis, enhancing the performances of micro-electro-mechanical systems (MEMS) and mini-devices, heating and energy generation, designing efficient energy conversion processes, and so on.

Numerical and statistical analysis of unsteady hydromagnetic hybrid nanofluid flow in a porous medium over an inclined disk with dissipative heat transfer

AbstractThe present analysis deals with the three‐dimensional radiative, convective hybrid nanofluid flow over a rotating and stretching inclined disk under the action of the applied magnetic field, Joule's heating, and viscous dissipation effects. The mathematical model considers nanoparticles graphene oxide (GO) and molybdenum disulfide (MoS) suspended in water as the base fluid within a Darcy medium. The cylindrical coordinate system is used to express continuity, momentum, and energy partial differential equations, out of which momentum and energy partial differential equations are transformed into ordinary differential equations using a suitable transformation method under the boundary‐layer approximation. The transformed equations are further solved using the spectral quasi‐linearization method. Graphical and numerical data are presented to investigate the behavior of velocity and temperature under various parameters and shape factors. The nature of fluid flow at the boundary wall is determined by tables of skin friction and the Nusselt number. Statistical analysis of the parameters for axial and tangential skin friction and the Nusselt number is performed using the quadratic regression model.

Hydromagnetic peristaltic flow of convective Casson nanofluid through a vertical porous channel under the influence of Ohmic heating and viscous dissipation effects

Purpose Ohmic heating generates temperature with the help of electrical current and resists the flow of electricity. Also, it generates heat rapidly and uniformly in the liquid matrix. Electrically conducting biofluid flows with Ohmic heating have many biomedical and industrial applications. The purpose of this study is to provide the significance of the effects of Ohmic heating and viscous dissipation on electrically conducting Casson nanofluid flow driven by peristaltic pumping through a vertical porous channel. Design/methodology/approach In this analysis, the non-Newtonian properties of fluid will be characterized by the Casson fluid model. The long wavelength approach reduces the complexity of the governing system of coupled partial differential equations with non-linear components. Using a regular perturbation approach, the solutions for the flow quantities are established. The fascinating and essential characteristics of flow parameters such as the thermal Grashof number, nanoparticle Grashof number, magnetic parameter, Brinkmann number, permeability parameter, Reynolds number, Casson fluid parameter, thermophoresis parameter and Brownian movement parameter on the convective peristaltic pumping are presented and thoroughly addressed. Furthermore, the phenomenon of trapping is illustrated visually. Findings The findings indicate that intensifying the permeability and Casson fluid parameters boosts the temperature distribution. It is observed that the velocity profile is elevated by enhancing the thermal Grashof number and perturbation parameter, whereas it reduces as a function of the magnetic parameter and Reynolds number. Moreover, trapped bolus size upsurges for greater values of nanoparticle Grashof number and magnetic parameter. Originality/value There are some interesting studies in the literature to explain the nature of the peristaltic flow of non-Newtonian nanofluids under various assumptions. It is observed that there is no study in the literature as investigated in this paper.

Modeling the hydromagnetic transient three-dimensional stagnation point flow of a couple stress Casson fluid over a bi-directional stretching sheet

A numerical study is performed to examine the magnetohydrodynamic effects on the transient three-dimensional stagnation point flow of a Casson fluid along a bi-directional stretching sheet. The physical model of the flow includes a sheet which is stretched in both the tangential directions and is thus called “bi-directional stretching”. The heat transfer mechanism includes the influences of space- and time-dependent non-uniform heat generation/absorption, as well as dissipation due to viscosity. The mathematical modeling of the problem involves the constitution of a set of coupled nonlinear boundary layer equations, together with suitable boundary conditions. The mathematical model thus developed is then subjected to suitable similarity transformations to arrive at a set of ordinary differential equations, which were then treated with the successive linearization method (SLM) to obtain approximate solutions for the velocity and temperature fields. A parametric study is carried out, and the results are discussed and presented graphically to analyze the behavior of the primary and secondary velocity distributions, as well as fluid temperature, along with significant physical quantities such as skin friction and Nusselt number for various values of the nondimensional parameters. Multiple quadratic regression analysis is also carried out to investigate the significance of parameters and to estimate the skin-friction and heat transfer coefficients.

HARK formulation for entropy optimized convective flow beyond constant thermophysical properties

Background and objectiveOhmic heating has a pivotal role in food processing industry. For example, Ohmic heating in chocolate industry for cocoa beans shell is significant substrate for bioactive compounds recovery sustainability. In addition, the Soret and Dufour effects have importance in chemical and petroleum processes involving separation treatments, convective movements in lakes and solar ponds, solidification, humidity migration in building, drying processes, crystal growth and many others. In view of such applications here we discuss the hydromagnetic mixed convection flow with variable thermophysical properties. Formulation for Reiner-Rivlin material is made. Entropy generation in presence of dissipation, magnetohydrodynamics and radiation are discussed. Thermal relation consists of heat generation and dissipation. Soret and Dufour outcomes are under consideration. Ohmic heating is attended. Binary chemical reactive flow has been accounted. Convective conditions are implemented. MethodologyBy utilization of appropriate variables, we get the ordinary differential equations. ND-solve method is implemented to provide computations. ResultsEvaluation of different variables for flow, concentration, entropy rate and temperature are studied. Analysis of surface drag force and solutal and thermal transport rates via influential variables are examined. An augmentation in velocity is noted for variable viscosity and material parameters. Reverse effect holds for thermal field and flow with variation in magnetic variable. An intensification in thermal distribution and entropy is found through radiation and thermal Biot number. A reverse impact is observed for concentration through Schmidt and Soret numbers. Higher variable mass diffusivity parameter correspond to improves concentration and entropy rate. Brinkman number has increasing trend for entropy rate.

Finite element simulation of Soret-Dufour and conjugate heating effects on mixed convective heat absorbing hydromagnetic Casson fluid flow with suction/blowing from flat semi-infinite vertical porous plate

The finite element simulations of the Soret-Dufour and angled magnetic field effects on conjugate heat and mass transportation of unsteady heat absorbing hydromagnetic Casson flow across a semi-infinite flat oscillatory plate engrafted in a porous medium with suction/blowing, radiation and chemical reaction is performed. The dimensionless coupled flow guiding nonlinear PDEs of the physical structure is handled numerically by the dynamic Galerkin finite element scheme. The demeanor of the velocity, concentration and the temperature profiles due to the alterations in the regulating flow parameters are examined graphically whereas the wall-friction, mass and heat transfer rates explicated by utilizing the tabular data. The research discovered that radiation; conjugate heat transfer and diffusion thermo effects heighten the temperature and velocity distributions whereas heat absorption has a reverse effect. Likewise, conjugate mass transfer and thermo-diffusion effects intensify the concentration and velocity distributions whereas the chemical reaction display overturns aspect. Increased radiation absorption, inclined magnetic field and porosity parameter stimulate fluid velocity whereas the Casson and magnetic parameters exhibit the converse impact. In the instance of suction, the profiles of concentration, velocity and temperature displayed a downturn nature but for the case of blowing, it was noticed a reversal trend. Further, a comparative analysis between the current findings and existing research works in the literature demonstrates our results are exact and accurate.

Hydromagnetic Squeezing Nanofluid Flow between Two Vertical Plates in Presence of a Chemical Reaction

Hydromagnetic Squeezing Nanofluid Flow between Two Vertical Plates in Presence of a Chemical Reaction

Hydromagnetic flow of radiating and chemically reacting Williamson fluid in stretching cylindrical surface through porous medium in the presence of heat source/sink

Hydromagnetic flow of radiating and chemically reacting Williamson fluid in stretching cylindrical surface through porous medium in the presence of heat source/sink

Hydromagnetic radial stagnation-point flow of Casson fluid through a twisted cylinder: A computational investigation

A cylinder that performs linear torsional motion with an applied magnetic field and heat transfer is the basic aim of our computational research which is associated with the impact of radial stagnation-point flow. This improves earlier research on the motion around a cylinder experiencing linear torsional motion without heat transfer. By transforming partial differential equations to ordinary differential equations, a nonlinear and coupled system of governing equations is created under the effect of many dimensionless variables. The Bvp4c method in MATLAB is used to numerically solve these equations. The nondimensional scale variable η=r*a2 plays an important role in finding the convergent solution, especially for the velocity components. The influence of different parameters on the axial velocity f′, azimuthal velocity g and temperature profile θ are illustrated graphically. Additionally, it also shows how the diverse character of physical parameters affects the azimuthal, and axial shear stresses, as well as the heat transport rates. The key findings of the study state that the f′′1 and g′1 wall stress are the strong function of R. Further f′′1 ids a weak function of σ whereas g′1 is a strong function of σ.

Ternary cobalt ferrite (CoFeO4)-silver (Ag)-titanium dioxide (TiO2) hybrid nanofluid hydromagnetic nonlinear radiative-convective flow from a rotating disk with viscous dissipation, non-Darcy and non-Fourier effects: Swirl coating simulation

Magnetic nanoparticles are increasingly being deployed in smart coating systems due to their exceptional functionalities and abilities to be tuned for specific environmental conditions. Inspired by the emergence of tri-hybrid magnetic nanofluids which utilize three distinct nanoparticles in a single base fluid coating, the present article examines analytically and computationally the swirl coating of magnetic ternary hybrid nanofluid from a rotating disk, as a simulation of spin coating deposition processes in materials manufacturing. Owing to high temperature fabrication conditions, thermal radiative heat transfer is also considered and a Rossleand flux model deployed. -- hybrid nanoparticles are considered with Ethylene Glycol-Water () base fluid. A filtration medium is also featured (porous medium) adjacent to the disk and the Darcy-Forchheimer model is deployed to simulate both bulk matrix porous drag encountered at lower Reynolds numbers and inertial quadratic drag generated at higher Reynolds numbers. Thermal relaxation of the coating nanofluid is additionally addressed and a non-Fourier Cattaneo-Christov model is therefore implemented in the heat conservation equation. Viscous dissipation is also included in the model. The governing conservation equations for mass, momenta (radial, tangential and axial) and energy with prescribed boundary conditions are rendered into coupled nonlinear ordinary differential boundary layer equations via suitable scaling variables and the Von Karman transformations. The derived reduced boundary value problem is then solved with a Runge-Kutta numerical scheme and shooting scheme in MATLAB. Validation of solutions is included with previous studies. Radial and azimuthal velocities, temperature, radial skin-friction, azimuthal skin friction and local Nusselt number are computed for a range of selected parameters. A comparative assessment of mono nanofluid Hybrid - nanofluid and tri-Hybrid -- nanofluid is conducted. This combination of hybrid nanoparticles has never been examined previously in the literature and constitutes the significant novelty of the present work. Both radial and tangential velocity are depleted with increasing applied magnetic field whereas temperature and thermal boundary layer thickness are increased.

Analyzing the effects of suction and injection Reynolds number on the transport process in a hydromagnetic flow through a channel of reactive porous walls

The present paper analyzes the effects of suction and injection Reynolds number on the dispersion process of solute in an incompressible magneto-hydrodynamics flow through a channel. The walls of the channel are permeable and a first order heterogeneous reaction is applied on it. Also, an inclined magnetic field is employed at both walls of the channel. The unsteady convection-diffusion equation is solved semi-analytically to find out the coefficient of dispersion, skewness and kurtosis of the solute distribution for all time period. Using Hermite polynomial representation, the distribution of mean concentration is obtained. The effects of various parameters such as suction Reynolds number (R), injection Reynolds number (R′), boundary absorption parameter (β), inclination angle of the magnetic field (α), Hartmann number (M) and dispersion time (t) on dispersion process of the solute are examined. It is shown that with the increment of suction Reynolds number, the peak of the mean concentration of solute enhances prominently. But, when injection Reynolds number increases, the amplitude of the mean concentration decreases. The current research gives an insight to understand the complex behavior of transport process of the solute in a hydro-magnetic channel flow with reactive porous walls.

Thermodynamics of hydromagnetic boundary layer flow of Prandtl nanofluid past a heated stretching cylindrical surface with interface slip

BackgroundThe mathematical modelling of a non-Newtonian fluid in the backdrop of applied magnetic field against an electrically conducting liquid is recognized as magnetohydrodynamics (MHD), which has important implications in chemical engineering and the biological sciences. Illustrations of such magneto-fluids include molten metals, electrolytes, blood plasma, and salty water. The applications of flowing liquids over cylindrical geometries is a fascinating due to its wide range importance in engineering. The aforementioned uses of MHD encourage scientists and analysts to establish new mathematical modelling in the area of fluid dynamics. Therefore, we considered the Prandtl fluid flow with loaded nanoparticles over a cylindrical tube with slip triggered by wall shear stress. The transport equation involving thermophoresis and Brownian diffusions are modelled using the Buongiorno model. The modelling of energy and entropy are established considering the effects of frictional dissipation, non-uniform heat source, thermal stratification, and Ohmic heating. MethodsThe formulated mathematical model leading to a complex system of partial differential equations with numerous integrated parameters. Using numerical algorithm RK-45 with a tolerance limit of 10−6, the system of resultant ordinary differential equations is simulated. The solver is used repeatedly to select the parameters that best meet the intended boundary conditions. Significant findingThe results of the current study revealed that the influence of heat source and thermal stratification on fluid temperature are conflicting. Additionally, the magnetic variable and Brinkman parameter have an escalating relationship with the rate of entropy development. The Bejan number detract with the magnetic variable. For distinct estimations of slip factors, heat and mass transport behave identically. However, the effect of slip is higher as compared to no slip scenario. The effect of Lewis number against nanoparticles concentration is opposite.