Effect of Joule heating on MHD non‐Newtonian fluid flow past an exponentially stretching curved surface

The current endeavor examines the convective heat transfer characteristics on magnetohydrodynamic stagnation point flow of micropolar fluid past an exponential curved surface. The flow is supposed to be laminar and time‐independent. The influence of radiation, irregular heat source/sink, Joule heating, and variable thermal conductivity are supposed. Suitable similarity renovations are considered to transform the original partial differential equations as ordinary ones and then resolved by shooting and fourth‐order Runge–Kutta methods. Graphs are drawn to inspect the impacts of sundry nondimensional parameters on the distributions of velocity, microrotation, and temperature. We detect that there is an escalation in temperature with Eckert number and variable heat source/sink parameters. Also, it is motivating to comment that Biot number is an increasing function of local Nusselt number.     

Dynamics of Newtonian fluid through curved domain by considering unsteady effects

Cross-diffusion gradients, such as the Soret and Dufour effects, play a big role in the formation of binary alloys, the movement of oil and groundwater contaminants, and the separation of gas mixtures. Other applications where cross-diffusion gradients are useful include: Temperature fluctuations cause matter diffusion, known as Soret effects. Concentration gradients drive heat diffusion, or the Dufour effect. This effect is named after its French discoverer. These findings could be applied to many engineering and industrial contexts and have many intriguing and potentially useful effects. Joule heating unites Soret and Dufour's work. The traditional nonlinear differential approach yields enough permutations. Convergent series can be used to solve temperature, velocity, and concentration problems. These changes can occur in temperature, velocity, or concentration. The drawings clarify all about the system's most important qualities and components. A comprehensive analysis of the Nusselt and Sherwood values is also done. After graphing the Nusselt and Sherwood values, they are analyzed. We are discussing computer science. This study found that Hartman number increases reduce one's perception of radial velocity. As Prandtl and Soret molecules increase, fluid temperature decreases. In this study, we employ numerical methods to solve the micropolar fluid flow problem on a stretched and curved disk. Our methods allow us to model fluid flow in three dimensions. We focus on micropolar fluid flow. Applying the necessary transformations to a set of partial differential equations simplifies it into a set of ordinary differential equations. The equations in both sets are transformed using similarities to convert one set of partial differential equations into another set of ordinary differential equations. The gunshot method and the Runge–Kutta algorithm can solve coupled equations numerically. The nondimensional radius of curvature can quantify and characterize many physical phenomena. Strain, microrotation velocity, and fluid velocity are examples. Due to the variances between curved and flat stretched sheets, the border layer strain cannot be neglected. Due to differences in stretching sheets,     

Liquid-solid separation phenomena of two-phase turbulent flow in curved pipes

The present study is to contribute some knowledge of phase separation phenomena of liquid-solid two-phase turbulent flow in curved pipes and provide a basis for the invention and development of a new type of curved pipe separator. Firstly, the solid-liquid two-phase flows in two-dimensional (2D) curved channels were numerically simulated using a two-way coupling Euler-Lagrangian scheme. Phase distribution characteristics of 2D curved channel two-phase flow were examined under conditions of different particle size, liquid flowrate and coil curvature. Based on the numerical results, the dynamic effects and contributions to phase separation of particle-subjected forces, including centrifugal force, drag force, pressure gradient force, gravity force, buoyancy force, virtual mass force and lift force, were exposed by kinematic and dynamic analysis along particle trajectories. Secondly, measurement of particle size and concentration profiles in helically coiled tube two-phase flow was conducted using a nonintrusive Malvern 2600 particle sizer based on laser diffraction. Particle size and concentration distribution characteristics of helically coiled tube two-phase flow and the effect of secondary flow on phase separation were analyzed based on experimental data.     

Application of radially varying magnetic field on a peristaltic flow of non‐Newtonian fluid in the presence of heat and mass transfer

This article deals with the variable MHD effects on the peristaltic flow of a non‐Newtonian fluid in the presence of heat and mass transfer. The walls of annulus are maintained at different temperatures. Continuity, momentum concentration, and energy equations are utilized in the mathematical analysis. Two types of solutions, namely, the exact and numerical, are derived. These solutions are compared and discussed. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20314     

Newtonian heating effect on laminar flow of Casson fluids: Thermal analysis

In the present study, free convective, laminar flow of Casson fluid is investigated numerically over a nonlinear stretched sheet to observe the characteristics of heat transfer in the presence of Newtonian heating. Nonlinear differential equations are derived from the present flow by utilizing the appropriate transformations. Thereafter, for the linear stretching case, an exact solution is applied for the momentum equation, and for the nonlinear stretching case, a convergent numerical technique, SRM, is applied. Computations of SRM and exact solutions are displayed through graphs. For various physical parameters, variation in velocity profile is observed by means of numerical computations and presented graphically. For checking the accuracy and convergence of the proposed method, outcomes are validated with the available outcomes in the literature and compared. The outcomes demonstrate that the velocity profile is reduced for the nonlinear stretching parameter effect, and, with increasing $\mathit{Pr}$, the temperature is decreased and there is a reduction in the thickness of the thermal boundary layer.     

An analysis of the characteristics of the thermal boundary layer in power law fluid

This paper presents a theoretical analysis of the heat transfer for the boundary layer flow on a continuous moving surface in power law fluid. The expressions of the thermal boundary layer thickness with the different heat conductivity coefficients are obtained according to the theory of the dimensional analysis of fluid dynamics and heat transfer. And the numerical results of CFD agree well with the proposed expressions. The estimate formulas can be successfully applied to giving the thermal boundary layer thickness.     

Thermal dispersed homogeneous-heterogeneous reaction within MHD flow of a Jeffrey fluid in the presence of Newtonian cooling and nonlinear thermal radiation

The current study deals with the effects of Newtonian cooling, magnetic field, and nonlinear radiation on the flow of a Jeffrey fluid along with thermal dispersion and homogeneous-heterogeneous reaction towards a stagnation point. The developed governing equations are transformed into nondimensional equations employing suitable similarity transformations along with their related boundary conditions. To solve and analyze these equations, the BVP4C solver of MATLAB has been used. The various properties of the fluid flow such as velocity, temperature, and concentration are represented in their respective graphs. The values obtained for skin friction and Nusselt number are expressed in the form of a table. The important outcomes of the present study are that the velocity declines as we increase the melting parameter, magnetic parameter, and Prandtl number. The temperature profile increases with radiation parameter, heat source, and magnetic number. An inclination is seen in the concentration of the fluid with a rise in Schmidt number whereas declination is seen with a rise in the homogeneous reaction parameter. Also, a comparison Table 1 has been made with the previous work under limited conditions. The table shows that the current work justifies the previous work system under those conditions. The present model can be utilized for many industrial purposes. Large-scale industries like plastic and food processing industries can utilize these results to enhance their productivity.     

Thermophoretic particle deposition and heat generation analysis of Newtonian nanofluid flow through magnetized Riga plate

The Riga surface is composed of an electromagnetic actuator that comprises a span-wise associated array of discontinuous electrodes and an everlasting magnet mounted over a planer surface. The electro-magneto-hydrodynamic has an attractive role in thermal reactors, fluidics network flow, liquid chromatography, and micro coolers. Inspired by these applications, a laminar, two-dimensional nanofluid flow with uniform heat sink-source, thermophoretic depositions of the particles, and the Newtonian heating effect are investigated. The equations that describe the fluid motion are reduced into a system of ordinary differential equations with the help of spatial similarity variables. Numeric solutions of ordinary differential equations are executed through the Runge–Kutta–Felhberg 45 order technique via a shooting scheme. The role of various nondimensional factors on physically interesting quantities is elaborated graphically. The velocity profile rises for modified Hartmann number and decreases for porosity parameter. Thermal enhancement is high in the common wall temperature condition comparative to the case of the Newtonian heating conditions. The concentration profile is enhanced with Schmidt number, but the reverse trend is observed for the thermophoretic parameter. The rate of mass transfer is increased with Schmidt number.     

Non-Newtonian fluid flow with the influence of induced magnetic field through a curved channel under peristalsis

In this study, we investigated the influence of the induced magnetic field on the Jeffrey fluid under peristalsis through the curved channel. The governing equations, such as the continuity equation, momentum equation, and magnetic force functions, are formulated. The lengthy equations are shortened by considering the approximations of the tiny Reynolds number and the long wavelength. From the resulting reduced equations, the exact solution is determined. Graphs are used to explain the graphical results of the impact of important parameters of velocity, magnetic force function, current density, induced magnetic field, pressure rise, and stream functions.     

Conjugate heat transfer from a circular cylinder to a power‐law non‐Newtonian fluid

In this paper, conjugate heat transfer from a circular cylinder with a heat source to a non‐Newtonian power‐law fluid is studied. Numerical calculations are carried out in an unconfined computational domain for Reynolds numbers (), power‐law indices (), and Prandtl numbers () with different heat source values. The pressure coefficient, value, and position of maximum temperature inside the cylinder and the local and average Nusselt number are calculated. Also, the effects of Re, Pr, n, and heat source value on the thermal characteristics in the solid cylinder and the fluid around it are studied and discussed.     

Heat and mass transfer of magnetohydrodynamic Casson fluid flow over a wedge with thermal radiation and chemical reaction

A numerical computation to analyze the heat and mass transfer mechanism of a magnetohydrodynamic radiative Casson fluid flow over a wedge in the presence of Joule heating, viscous dissipation, and chemical reaction is carried out in this study. The flow-governing partial differential equations are transformed as ordinary differential equations by relevant similarity transformations and subsequently resolved by Runge–Kutta numerical approach with a shooting technique. The characteristics of momentum, thermal, and concentration border layers due to various influencing parameters are graphically outlined and numerically computed by MATLAB software. We present comparative solutions to construe the relative outcomes of Casson fluid versus Newtonian fluid. Computational outcomes of friction factor and Nusselt and Sherwood numbers are tabulated with suitable interpretations. An increase in skin friction values is noted due to an increment in the thermal Grashof number, whereas a decrease is observed due to the chemical reaction parameter. The Casson fluid displays a superior heat transfer mechanism than the Newtonian fluid. Obtained outcomes are in good agreement with the prevailing literature in the limiting case.     

Heat transfer analysis in a hydromagnetic Walters' B fluid with elastic deformation and Newtonian heating

In this study, a computational investigation is carried out to examine the interaction of heat generation/absorption with elastic deformation in a viscous hydromagnetic Walters’ B model past a stretching surface under the intensity of Newtonian heating. The model equations which are responsible for the motion of the fluid and heat interactions are reworked to ordinary differential equations by the appropriate similarity variables and solved via the homotopy analysis method. The parameters encountered were discussed through graphs and tables. The result reveals among others that the heat generation and Newtionian heating magnifies the temperature across the layer and makes quiescent fluid experience a thermal effect.     

Pressure transient analysis for fluid flow through horizontal fractures in shallow organic compound reservoir of hydrogen and carbon

Pure hydrogen does not occur in large quantities in nature, and it is usually locked up in energy-rich organic compound. One of the challenges to sustain the usage of hydrogen energy is to produce sufficient energy-rich organic compound from the organic compound reservoir of hydrogen and carbon, which requires understanding the fluid flow behavior through such reservoir. The horizontal fractures can be created during the hydraulic fracturing process in shallow energy-rich organic compound reservoirs due to the geo-mechanical effect. However, it lacks of a comprehensive analytical model to describe the transient flow behavior through the horizontal fractures. In this paper, an analytical model for horizontal fractures in shallow organic compound reservoirs considering the effects of wellbore storage and skin factor with constant pressure, closed and infinite boundary conditions, are presented to investigate pressure transient behavior and flow characteristics. The analytical solution is derived in Laplace domain, which may require numerical inverse transform to obtain the solution real space. To obtain the explicit form in real space, the approximate solutions for early time, middle time and late time are also presented to investigate the characteristics of type curves. Type curves are established for the transient pressure analysis to recognize the flow characteristics through horizontal fractures. Flow for horizontal fractures can be divided into five stages according to characteristics of dimensionless pseudo pressure derivative curve. The effects of parameters on pressure behavior are discussed in detail, which include wellbore storage coefficient, dimensionless formation thickness, dimensionless vertical location, and skin factor. The results indicate that horizontal fractures are more applicable in thin instead of thick reservoirs.     

Finite element analysis of non‐Newtonian magnetohemodynamic flow conveying nanoparticles through a stenosed coronary artery

The present study considers two‐dimensional mathematical modeling of non‐Newtonian nanofluid hemodynamics with heat and mass transfer in a stenosed coronary artery in the presence of a radial magnetic field. The second‐grade differential viscoelastic constitutive model is adopted for blood to mimic non‐Newtonian characteristics, and blood is considered to contain a homogenous suspension of nanoparticles. The Vogel model is employed to simulate the variation of blood viscosity as a function of temperature. The governing equations are an extension of the Navier‐Stokes equations with linear Boussinesq's approximation and Buongiorno's nanoscale model (which simulates both heat and mass transfer). The conservation equations are normalized by employing appropriate nondimensional variables. It is assumed that the maximum height of the stenosis is small in comparison with the radius of the artery, and, furthermore, that the radius of the artery and length of the stenotic region are of comparable magnitude. To study the influence of vessel geometry on blood flow and nanoparticle transport, variation in the design and size of the stenosis is considered in the domain. The transformed equations are solved numerically by means of the finite element method based on the variational approach and simulated using the FreeFEM++ code. A detailed grid‐independence study is included. Blood flow, heat, and mass transfer characteristics are examined for the effects of selected geometric, nanoscale, rheological, viscosity, and magnetic parameters, that is, stenotic diameter (d), viscoelastic parameter (), thermophoresis parameter (), Brownian motion parameter (), and magnetic body force parameter (M) at the throat of the stenosis and throughout the arterial domain. The velocity, temperature, and nanoparticle concentration fields are also visualized through instantaneous patterns of contours. An increase in magnetic and thermophoresis parameters is found to enhance the temperature, nanoparticle concentration, and skin‐friction coefficient. Increasing Brownian motion parameter is observed to accelerate the blood flow. Narrower stenosis significantly alters the temperature and nanoparticle distributions and magnitudes. The novelty of the study relates to the combination of geometric complexity, multiphysical nanoscale, and thermomagnetic behavior, and also the simultaneous presence of biorheological behavior (all of which arise in actual cardiovascular heat transfer phenomena) in a single work with extensive visualization of the flow, heat, and mass transfer characteristics. The simulations are relevant to the diffusion of nano‐drugs in magnet‐targeted treatment of stenosed arterial disease.     

MHD dissipative fluid past a stretching sheet in the presence of Soret effect with Newtonian convective heat and mass conditions

This article deliberates a theoretical study on a two‐dimensional magnetohydrodynamic free convection flow of an electrically conducting, heat generation/absorption fluid flowing past a linearly stretching sheet, placed vertical in a non‐Darcian porous medium with Soret effect. As the magnetic Reynolds number of the flow field considered very small (due to noncomparability of the induced and applied magnetic fields), the influence of the induced magnetic field is thus neglected. Again due to weak applied voltage differences at the lateral ends, the influence of the electric current is also ignored. A homotopy analysis method is developed to solve the similarity transformed equations subject to a set of convective heat and mass boundary conditions. Numerical data simulations are made on various fluid variables by using some practical/selected values of the governed parameters and illustrated through graphs and tables. It is found that the Newtonian heating parameter enhanced the velocity, temperature, and concentrations, while the solutal Newtonian heating parameter accelerates the rate of flow of heat and masses but minimizes the temperature gradient. The local Forchheimer and dissipation parameters are found to raise the temperature and concentrations, while the flow rate accelerates due to dissipation parameter but decelerates in presence of Forchheimer parameter.     

Effect of microgravity on flow boiling heat transfer of liquid hydrogen in transportation pipes

The flow boiling phenomenon of liquid hydrogen (LH2) during transportation in microgravity is very different from that under terrestrial condition. In this study, a saturated flow boiling of LH2 in a horizontal tube has been simulated under microgravity condition using coupled level-set and volume of fluid method. The validation of the developed model shows good agreement with the experimental data from the literature. The changes of heat fluxes and pressure drops under different gravitational accelerations were analyzed. And, the variation of heat fluxes with different wall superheat and contact angle were compared between microgravity (10⁻⁴g) and normal gravity (1g) condition. Also, the influence of surface tension were studied under microgravity. The numerical results indicate that the heat flux decrease with the decrement of gravitational acceleration. And the heat transfer ratio decrease with the increment of wall superheat in the nucleate boiling regime. The heat transfer slightly reduce when considering surface tension. In addition, the changes of contact angle have a more significant impact on heat transfer under microgravity condition.     

Numerical and sensitivity analysis of MHD bioconvective slip flow of nanomaterial with binary chemical reaction and Newtonian heating

The impact of Stefan blowing on the MHD bioconvective slip flow of a nanofluid towards a sheet is explored using numerical and statistical tools. The governing partial differential equations are nondimensionalized and converted to similarity equations using apposite transformations. These transformed equations are solved using the Runge–Kutta–Fehlberg method with the shooting technique. Graphical visualizations are used to scrutinize the effect of the controlling parameters on the flow profiles, skin friction coefficient, local Nusselt, and Sherwood number. Moreover, the sensitivities of the reduced Sherwood and Nusselt number to the input variables of interest are explored by adopting the response surface methodology. The outcomes of the limiting cases are emphatically in corroboration with the outcomes from preceding research. It is found that the heat transfer rate has a positive sensitivity towards the haphazard motion of the nanoparticles and a negative sensitivity towards the thermomigration. The thermal field is enhanced by the Stefan blowing aspect. Moreover, the fluid velocity can be controlled by the applied magnetic field.     

Effects of Newtonian heating and thermal radiation on micropolar ferrofluid flow past a stretching surface: Spectral quasi‐linearization method

This study article addressesthe flow and heat transfer characteristics of a magnetite Fe₃O₄ micropolar ferrofluid flow past a stretching sheet. For practical interest, thermal radiation, Newtonian heating, and a heat source or sink are considered in this investigation. A useful Tiwari‐Das nanofluid model is considered to analyze the microstructure and inertial characteristics of the water‐based nanofluids containing iron oxide. The dimensionless nonlinear ordinary differential equations are solved by employing suitable similarity variables. The resulting nonlinear system is solved by the spectral quasi‐linearization method. The effects of different nondimensional parameters on various profiles are shown graphically and explored in detail. It is found that the micropolar ferrofluid exhibits a higher energy distribution than that of a classical micropolar fluid. Compared to the classical micropolar liquid, local skin‐friction is more significant for the micropolar magnetite ferrofluid. In the presence of Newtonian heating, the thermal behavior of the micropolar nanofluid is remarkably better than that of the classical micropolar fluid.     

Mixed convection in laminar film flow of a micropolar fluid

In this paper, the steady mixed convection boundary layer in laminar film flow of a micropolar fluid is considered. The resulting nonlinear coupled ordinary differential equations are solved numerically using an efficient implicit finite-difference scheme. The numerical results obtained for the skin friction coefficient and the local Nusselt number, as well as the velocity, angular velocity or microrotation and temperature profiles are presented in tables and figures for different values of the material parameter K and the Richardson number Ri when the Prandtl number Pr = 0.7 and Pr = 1.     

Numerical exploration of thermal radiation and Biot number effects on the flow of a non‐Newtonian MHD Williamson fluid over a vertical convective surface

A theoretical and computational study of the magnetohydrodynamic flow and free convection heat transfer in an electroconductive polymer on the external surface of a vertical plate under radial magnetic field is presented. The Biot number effects are considered at the vertical plate surface via modified boundary conditions. The Williamson viscoelastic model is employed which is representative of certain industrial polymers. The nondimensional, transformed boundary layer equations for momentum and energy are solved with the second‐order accurate implicit Keller box finite difference method under appropriate boundary conditions. Validation of the numerical solutions is achieved via benchmarking with earlier published results. The influence of Weissenberg number (ratio of the relaxation time of the fluid and time scale of the flow), magnetic body force parameter, stream‐wise variable, and Prandtl number on thermo fluid characteristics are studied graphically and via tables. A weak elevation in temperature accompanies increasing Weissenberg number, whereas a significant acceleration in the flow is computed near the vertical plate surface with increasing Weissenberg number. Nusselt number is reduced with increasing Weissenberg number. Skin friction and Nusselt number are both reduced with increasing magnetic field effect. The model is relevant to the simulation of magnetic polymer materials processing.