Hartman Number Research Articles

Heat Transfer Analysis and Magnetohydrodynamics Effect on Peristaltic Transport of Ree–Eyring Fluid in Rotating Frame

This paper discusses Ree–Eyring fluid’s peristaltic transport in a rotating frame and examines the impacts of Magnetohydrodynamics (MHD). The results deal with systematically (analytically) applying each of the governing equations of Ree–Eyring fluid, the axial and secondary velocities, flow rate due to auxiliary stream, and bolus. The effects of some distinctive variables, such as Hartman number, heat source/sink, and amplitude ratio, are taken under consideration and illustrated through graphs.

Numerical Study of Ion-Slip and Hall Effect on Couette Flow of Two Immiscible Micropolar and Micropolar Dusty Fluid (Fluid-Particle Suspension) with Heat Transfer

In this paper, the unsteady magnetohydrodynamic (MHD) Couette flow of two non-Newtonian immiscible fluids micropolar and micropolar dusty (fluid-particle suspension) are considered in the horizontal channel with heat transfer. A comprehensive mathematical model and computational simulation with the modified cubic B-Spline-Differential Quadrature method (MCB-DQM) is described for unsteady flow. The coupled partial differential equation for fluid and particle-phase are formulated and the effect of viscous dissipation, Joule heating, Hall current, and other hydrodynamic and solutal parameters i. e. Reynolds number, Eckert number, particle concentration parameter, Eringen micropolar material parameter, time, viscosity ratio, and density ratio on the flow rate, micro rotation, and temperature characteristics were investigated. The analysis of obtained results reveals that the fluids and particle velocities are slightly decreasing with Hartmann number, and increasing with time, ion-slip, and Hall parameters. Microrotation declined with Microrotations dropped significantly with ion-slip and Hall parameter and grown Hartman number. The temperature begins to rise as time, Hartman number, and Eckert number grow and declined with Ion-slip and Hall parameter.

MHD peristaltic transportation of radiative MWCNT-Ag/C2H6O2 hybrid nanofluid with variable characteristics

Present study addresses the flow and heat transportation for peristalsis of MWCNT-Ag/C2H6O2 hybrid nanofluid. Effects of temperature dependent thermal conductivity, viscosity, thermal radiation, inclined magnetic field, Joule heating and mixed convection are considered. Shape effects of nanomaterials are also addressed. A hybrid nanomaterial system is used with a 2% concentration of nanomaterials (50:50) in ethylene glycol. Thermal and velocity slip conditions are also employed. The mathematical model is simplified by using lubrication theory. The obtained dimensionless model is then numerically solved. Results reveal that temperature of hybrid nanofluid decreases with an increment in nanoparticles volume fraction. Heat transfer rate at the wall decays by increasing radiation parameter. The thermal efficiency of hybrid nanofluid (MWCNT-Ag/C2H6O2) is more pronounced as compared to ordinary nanofluid (MWCNT/C2H6O2) and base fluid (C2H6O2). Velocity increases with an increase in viscosity parameter. Pressure gradient declines with an augmentation in Hartman number and nanoparticles volume fraction.

Computational investigation of an unsteady non-Newtonian and non-isothermal fluid between coaxial contracting channels: A PCM approach

The essential element of this paper is to research the porous and squeezed characteristics of time varying heats that modify the flow speed and enhance the refrigerating/boiling performance of the materials, optimize the tracers flows and minimalized instability in the non-Newtonian fluids. In the presence of no-slip velocity and convective circumstances, squeezing disks tempting laminar, unsteady and incompressible non-Newtonian fluid. The convective formulation for the equations of Navier Stokes, energy and concentration are modeled on flat disks to investigate and execute both analytical and numerical analysis of heat flow and mass transfer, which transmuted further into extremely non-linear system of ordinary differential equation with the help of similarity transformations. Regarding smears, self-similar equations with adequate starting estimates and supporting parameters are resolved by utilizing the Homotopy Analysis Method (HAM) to generate an expedited and guaranteed convergence procedure. Comparisons between HAM and the BVP4c numerical solver program demonstrate the validity and precision of HAM results. It is found by increasing or decreasing the Hartman number reduces the capillary area, making the Lorentz force influence quite visible for small non-Newtonian parameter. The concentration rate at the lower end disk rises rapidly as the thermal diffusivity rises. The radial velocity also declines because of the rise in the outflow rate from the flow domains. The suction parameter also declines. Additionally, increasing the parameter of non-Newtonian enhances the flow of temperature/mass and skin friction. In the suction/injection case, all physical factors have a reverse influence upon fluid flow patterns.

Mixed convection peristalsis of hybrid nanomaterial flow in thermally active symmetric channel

We aim to investigate hybrid nanofluid effects on peristaltic motion of MHD nanofluid. Symmetric channel with slip boundary constraints is taken. Mixed convection, Hall parameter and variable viscosity are also taken into account. Energy equation includes dissipation, Ohmic heating and thermal radiation. Dimensionless equations are simplified under the observation of long wavelength approximation. Final forms of equations are solved via numerical approach. Pressure gradient and flow pattern are graphically observed. The comparative analysis of velocity, temperature and heat transport process are evaluated numerically through tabulated values. Temperature field enhances for higher Hartman number while opposite trend is observed for Hall effects. The inclusion of silver nanomaterial in copper nanofluid can more facilitate heat transport characteristics.

Flow dynamics of a time-dependent non-Newtonian and non-isothermal fluid between coaxial squeezing disks

The goal of this research is to investigate the behaviours of porosity and squeezing phenomena in the presence of time-dependent heat flow that affect the flow rate and improve the system’s heating/cooling mechanism, reduce non-Newtonian fluid turbulence and scale-up flow tracers. Squeezing discs in the presence of no-slip velocity and convective surface boundary conditions induces a laminar, unstable and incompressible non-Newtonian fluid. The convective form of the momentum, concentration and energy equations are modelled for smooth discs to evaluate and offer an analytical and numerical examination of the flow for heat and mass transfer, which are further transformed to a highly non-linear system of ordinary differential equation using similarity transformations. In the case of smooth disks, the self-similar equations are solved using Homotopy Analysis Method (HAM) with appropriate initial guesses and auxiliary parameters to produce an algorithm with an accelerated and assured convergence. The comparison of HAM solutions with numerical solver programme BVP4 c proves the validity and correctness of HAM results. It is found that increasing or bypassing the Hartman number reduces the capillary region, making the Lorentz force effect more visible for small values of non-Newtonian parameter. The concentration rate at the bottom disc rises rapidly as the thermal diffusivity rises. In addition, because the rate of outflow from the flow domain increases, the suction/injection parameter lowers the radial velocity. Additionally, as the non-Newtonian parameter is increased, skin friction and heat/mass flux rise. In the suction/injection situation, all physical characteristics have the opposite effect on flow field profiles.

Stagnation Point Heat Flow and Mass Transfer in a Casson Nanofluid with Viscous Dissipation and Inclined Magnetic Field

Influence of slip and inclined magnetic field on stagnation-point flow with chemical reaction are studied. Implementation of the similarity transformations, transformed the fluid non-linear ordinary differential equations and numerical computation is performed to solve those equations using Spectral Collocation Method. Various pertinent parameters on fluid flow, temperature and concentration distributions of the Casson nanofluid flow as well as the local skin friction coefficient, local Nusselt number, and Sherwood number are graphically displayed. The results indicate that thermophoresis parameter N_t enhanced the temperature and nanoparticle concentration profiles, because a rise in thermophoresis parameter enhances the thermophoresis force within the flow regime. Values of both local Nusselt and Sherwood numbers are enhanced with an increase in Hartman number (magnetic field parameter). The present results are compared with previously reported ones and are found to be in excellent agreement.

Entropy Optimized Hydro-Magnetic Flow Darcy-Forchheimer Viscous Fluid

Here hydromagnetic flow of an incompressible Dary-Forchheimer fluid over a curved stretching surface is addressed. Heat source/sink and dissipation effects are considered in heat equation. Entropy generation is discussed through thermodynamics law. Bejan number is calculated. The proposed system are modeled in curvilinear coordinates. Partial differential system are reduced to ordinary one through transformation. ND-solve method is implemented to solve the given system. Graphical outcomes of velocity, entropy rate, temperature and Bejan number against flow variables are discussed. Numerical outcomes of drag force against pertinent variables are examined through table. Higher Hartman number decreases velocity field. A reverse effect for velocity is observed through porosity and curvature variables. An improvement in temperature is seen for curvature variable. An augmentation in entropy rate is noted for Brinkman number.

Mathematical Analysis of Thermal Energy Distribution in a Hybridized Mixed Convective Flow

The mixed convective flow of hybrid nanofluid (SWCNT-MWCNT/EG) containing micropolar fluid past a Riga surface embedded in porous medium is explored in detail throughout this study. In the momentum equation, the Darcy Forchheimer effect is used. The heat transfer phenomenon is exploited with viscous dissipation and thermal stratification over a non-Fourier heat flux model. PDEs are transformed into the necessary governing equations using transformations. The numerical results of non-linear governing equations are collected using Matlab function bvp4c. Graphical representations of the effects of relevant parameters on velocity, skin friction, and temperature are shown. The comparison of simple nanofluid and hybrid nanofluid is discussed in graphs. The temperature field is higher for hybrid nanofluid than simple nanofluid when solid volume fraction enhances. With increasing solid volume fraction, porosity parameter, and mixed convection parameter, the axial friction factor rises. The momentum boundary layer is inversely proportional to the slip parameter, Hartman number, variable viscosity and the porosity parameter.

Entropy generation of peristaltic Eyring–Powell nanofluid flow in a vertical divergent channel for biomedical applications

Exploring the movement of blood in a blood vessel has been fascinated by clinicians and biomedical researchers because it is predominant in cell tissue engineering, drug targeting and various treatments like hypothermia, hyperthermia, and cancer. It is noticed that numerous non-Newtonian rheological fluids like Carreau fluid, tangent hyperbolic fluid, Eyring–Powell fluid and viscoelastic fluid manifest the characteristics of blood flow. Further, the investigation of entropy generation can be used to raise the performance of medical equipments. Consequently, the present mathematical model scrutinizes the transport characteristics and entropy generation of the peristaltic Eyring–Powell nanofluid in a permeable vertical divergent channel in the presence of dissipation and linear radiation. The non-similar variables are employed to convert the dimensional partial differential equations into dimensionless form which are tackled by the Homotopy perturbation method. The impacts of emerging parameters like Eyring–Powell parameters, left and right wall amplitudes, thermophoresis, mean flow rate, radiation, permeability parameter, Brownian motion, Eckert number, Hartman number on Eyring–Powell nanofluid axial velocity, temperature, and concentration are manifested. Present results disclose that the thermal Grashof number highly inflates the pressure rise. Eyring–Powell nanofluid temperature reduces for uplifting the linear radiation parameter. Growing values of the non-uniform parameter lead to move the trapping bolus towards the left and right wall. The total entropy generation diminishes for magnifying the temperature difference parameter.

Dynamics of Cattaneo-Christov Double Diffusion (CCDD) and arrhenius activation law on mixed convective flow towards a stretched Riga device

Background Current paper elaborate the impact of MHD flow of Newtonian liquid over a extendable Riga sheet. Cattaneo-Christov (CC) heat and mass flux models in formulation are taken here. Fluid filling porous medium is considered. Influences of activation energy is also considered. Boundary layer approximation is used in obtaining partial differential equations (PDEs). Applying suitable transformation to reduce the given PDEs into ordinary differential (ODEs) system. Method Homotopy method is utilized to solve non-linear differential system. Results The impacts of influencing parameters like modified Hartman number, mixed convection parameter, inverse Darcy parameter, non-dimensional parameter, Biot number, non-dimensional activation energy, Eckert number, thermal relaxation and solutal concentration variables are examined through graphs. Conclusions Velocity profile enhances for larger estimation of ratio parameter and modified Hartman number. Temperature distribution is higher for Eckert and Biot number. Concentration profile is enhancing for more values of nondimensional activation energy.

Radiative peristaltic transport of Ree-Eyring fluid through porous medium in asymmetric channel subjected to combined effect of inclined MHD and convective conditions

This study emphasizes the flow phenomenon of trapped bolus traveling along the interior walls of asymmetric inclined channels contains a non-Newtonian Ree-Eyring. The flow was exposed to influenced by inclined MHD field, thermal heat radiative, and porous media. Further, no slip and convective thermal conditions are considered. Mathematical expression for governing equations are reformulated and in accordance with lubrication approximations, nonlinear partial differential equations of the flow reduced into a system of ordinary differential equations associated with boundary conditions an approximate solution is deduced by implementing perturbation strategy for tiny A Ree-Eyring fluid parameter. Finally, a graphical description is presented to figure out the elevation behavior of flow quantities i.e. velocity profile, temperature distribution, pressure rise, and streamlines formulation due to variation of emerging involved parameters. The study analyzed that the velocity profile reveals mixed behavior via increment of Ree-Eyring parameters η, A as well as Hartman number H and Darcy number Da. whereas the thermal radiative parameter Rn accelerates the temperature distribution profile. The study calculations are made by the “Mathematica 11.3” package.

Numerical investigation of thermally developed MHD flow with pulsation in a channel with multiple constrictions

This article concerns heat transfer analysis in pulsating flow in a channel with walls having multiple symmetric constrictions. The flow is influenced by Lorentz force and thermal radiation. The unsteady governing equations, simplified for low conducting fluids, are solved by the finite difference method using the stream–vorticity function formulation. The effects of the emerging parameters, including the magnetic field parameter (Hartman number), Reynolds number, Prandtl number, and radiation parameter on various flow profiles, are studied. The profiles of dimensionless axial velocity, temperature, wall shear stress (WSS), skin friction coefficient, and local Nusselt number are discussed graphically. The profiles are examined at various prominent axial locations and time instants of the pulse cycle. The WSS has a direct relation with the Hartmann and Strouhal numbers. The WSS generated at the first constriction is higher than that at the second constriction. The WSS increases with an increase in the Strouhal number in the accelerating phase and decreases in the decelerating phase on both the constrictions. The temperature decreases with an increase in the Hartman and Prandtl numbers at the constricted portion of the channel. The radiation parameter directly affects the temperature and inversely affects the Nusselt number at the constricted part of the channel. However, in general, the flow profiles exhibit irregular patterns downstream of the constriction. The Nusselt profiles are higher at the first encountered constriction bump than that at the next bumps.

Numerical Investigation of MHD Pulsatile Flow of Micropolar Fluid in a Channel with Symmetrically Constricted Walls

This article presented an analysis of the pulsatile flow of non-Newtonian micropolar (MP) fluid under Lorentz force’s effect in a channel with symmetrical constrictions on the walls. The governing equations were first converted into the vorticity–stream function form, and a finite difference-based solver was used to solve it numerically on a Cartesian grid. The impacts of different flow controlling parameters, including the Hartman number, Strouhal number, Reynolds number, and MP parameter on the flow profiles, were studied. The wall shear stress (WSS), axial, and micro-rotation velocity profiles were depicted visually. The streamlines and vorticity patterns of the flow were also sketched. It is evident from the numerical results that the flow separation region near constriction as well as flattening of the axial velocity component is effectively controlled by the Hartmann number. At the maximum flow rate, the WSS attained its peak. The WSS increased in both the Hartmann number and Reynolds number, whereas it declined with the higher values of the MP parameter. The micro-rotation velocity increased in the Reynolds number, and it declined with increment in the MP parameter.

Magnetohydrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect

AbstractIn this study, we analyze the magnetohydrodynamic flow of magnetite‐engine oil nanofluid in the presence of nonidentical shaped nanoparticles subject to the porous medium and velocity slip effect. Energy analysis is carried out with the Ohmic heating and thermal radiation impacts. The system of partial differential equations are transformed into the system of ordinary differential equations using similarity variable. The Hamilton–Crosser model is used. The exact solutions for the momentum and heat transport analysis are found. The impact of various emerging parameters on the velocity and temperature profiles are analyzed by graphs. Furthermore, the local skin friction and heat transfer rate are examined graphically. It is examined that the velocity field increases with an increment in the magnitude of ϕ and L. An increase in the value of Hartman number enhancing the temperature profile.

Impact of Lorentz Force in Thermally Developed Pulsatile Micropolar Fluid Flow in a Constricted Channel

This work aimed to analyze the heat transfer of micropolar fluid flow in a constricted channel influenced by thermal radiation and the Lorentz force. A finite difference-based flow solver, on a Cartesian grid, is used for the numerical solution after transforming the governing equations into the vorticity-stream function form. The impact of various emerging parameters on the wall shear stress, axial velocity, micro-rotation velocity and temperature profiles is discussed in this paper. The temperature profile is observed to have an inciting trend towards the thermal radiation, whereas it has a declining trend towards the Hartman and Prandtl numbers. The axial velocity profile has an inciting trend towards the Hartman number, whereas it has a declining trend towards the micropolar parameter and Reynolds number. The micro-rotation velocity escalates with the micropolar parameter and Hartman number, whereas it de-escalates with the Reynolds number. The Nusselt number is observed to have a direct relationship with the Prandtl and Reynolds numbers.

Finite element simulation for free convective flow in an adiabatic enclosure: Study of Lorentz forces and partially thermal walls

This article contains the free convective flow in a rectangular cavity having partially heated vertical wall. Further it is assumed that flow and thermal profiles are influenced by Lorentz forces applied in the perpendicular direction to the flow distribution. This physical setup is translated in mathematical form, which is expressed as differential equation. Finite element method is adopted to get the solution of these partial differential equations, the results against various flow controlling variables are presented in contour plots and line graphs. Results depict that at various heated length streamlines distribution gets stronger due to stronger buoyancy effects. Higher values of Rayleigh number correspond to maximum Nusselt number and temperature profile. Moreover, the streamlines pattern is reduced by increasing Hartman number and resulting the conduction mode of heat transportation.

Irreversibility analysis of nanofluid flow induced by peristaltic waves in the presence of concentration‐dependent viscosity

AbstractThe present study employs irreversibility analysis for the peristaltic movement of a nanofluid. The viscosity of the nanofluid is assumed to vary with the local concentration of colloidal particles. Impacts of thermophoresis, magnetic field, Brownian motion, Ohmic heating, viscous dissipation, and buoyant forces are considered in the flow analysis. Equations representing the flow and heat/mass transfer are prepared by employing Buongiorno's model for nanofluids. The lubrication approach is used to simplify the governing equations. The resulting system of differential equations is numerically solved with the aid of NDSolve in Mathematica. Results for entropy generation, Bejan number, velocity, temperature, and concentration are graphically presented. Outcomes show that entropy generation and temperature reduce by increasing the values of viscosity parameter. By increasing buoyancy forces due to temperature difference, the entropy generation increases, whereas the concentration profile shows a decreasing behavior. Maximum velocity reduces with an increment in the Hartman number.

Effects of Joule Heating and Viscous Dissipation on Magnetohydrodynamic Boundary Layer Flow of Jeffrey Nanofluid over a Vertically Stretching Cylinder

This article investigates unsteady magnetohydrodynamic (MHD) mixed convective and thermally radiative Jeffrey nanofluid flow in view of a vertical stretchable cylinder with radiation absorption and heat; the reservoir was addressed. The mathematical formulation of Jeffrey nanofluid is established based on the theory of boundary layer approximations pioneered by Prandtl. The governing model expressions in partial differential equations (PDEs) form was transformed into dimensionless form via similarity transformation technique. The set of nonlinear nondimensional partial differential equations are solved with the help of the homotopic analysis method. For the purpose of accuracy, the optimizing system parameters, convergence, and stability analysis of the analytical algorithm (CSA) were performed graphically. The velocity, temperature, and concentration flow are studied and shown graphically with the effect of system parameters such as Grashof number, Hartman number, Prandtl number, thermal radiation, Schmidt number, Eckert number, Deborah number, Brownian parameter, heat source parameter, thermophoresis parameter, and stretching parameter. Moreover, the consequence of system parameters on skin friction coefficient, Nusselt number, and Sherwood number is also examined graphically and discussed.

Comments on “Dynamism of magnetohydrodynamic cross nanofluid with particulars of entropy generation and gyrotactic motile microorganisms”

Corrections to the units of magnetic field strength (B0) and electrical conductivity (σ) in Nomenclature are given so that the momentum equation is correct and the Hartman number (Ha) is dimensionless. The similarity variable (η) depends only on r. From the equations of energy and concentration, temperature (T) and concentration (C and n) depend on r, z. In addition, the temperature θ(η) depends only on r while RHS depends on r, z. Hence, there is a discrepancy between LHS & RHS so that the equation of temperature is not valid. Also, the concentration φ(η) and ξ(η) depend only on r while RHS depends on r, z. Hence, there is a discrepancy between LHS & RHS so that the equations of concentration are not valid. Furthermore, a correct Be form is given.