Thermophoresis Diffusion Research Articles

Thermal transport analysis in stagnation-point flow of Casson nanofluid over a shrinking surface with viscous dissipation

In arteries blood flow is the usual example for a Casson fluid flow among the other vital utilizations of this fluid model. Thus, it would be helpful to study the Brownian motion diffusion and thermophoresis diffusion in Casson fluid for biomedical applications. In this analysis, the electrically conducting Casson nanofluid, with suction and convective boundary condition, has been addressed in a shrinking surface. The mechanism of convective heat transfer has been elaborated with Ohmic heating and viscous dissipation effects. The numerical solutions to the governing equations have been obtained by applying the similarity transformation to the nonlinear partial differential equations. The present model is employed to examine the viscoplastic characteristics in the porous regime. This dimensionless ruling problem, along with physical boundary conditions, is handled numerically by using a Runge–Kutta Fehlberg scheme. The outcomes of the present study show that the rate of heat and mass transfer at the surface of the shrinking sheet enhances with the growth in Casson fluid parameter and magnetic parameter. Furthermore, it is observed that the shear stress at the wall rises with the increment in magnetic parameter. Moreover, unsteadiness parameter is the decreasing function of heat and mass transfer rates.

On the Radiative, Diffusion and Chemical Effects of Soot Formation in a Nonsmoking Laminar Ethylene Diffusion Flame

ABSTRACT As one of the important by-products of incomplete combustion due to a high local equivalence ratio, soot particles can affect the flame structure and species distributions through their radiative, diffusion, and chemical effects based on the conservation equation of energy. In this work, a fully step-by-step decoupling method was employed to numerically isolate the various effects of soot formation on flame properties and soot evolution in a laminar nonsmoking ethylene diffusion flame. The combustion process was solved by a detailed kinetic model coupled with a sectional soot model. Results show that, the peak temperature of the flame increases when the radiative effect of the particles is neglected; however, it decreases when the chemical effect is excluded due to the absence of particle oxidation. The flame height, which depends on OH concentration, increases under both the radiative and chemical effects of soot particles. When soot radiation is not considered, the peak concentration of CO increases because of a lower conversion of CO to CO2 under higher local temperature, and a further increase is observed when soot reactions are removed, since the formation of CO is the only pathway of carbon conversion under this condition. When the radiation of soot particles is not considered, soot volume fraction (SVF) is reduced owing to a lower hydrogen-abstraction-carbon-addition (HACA) rate caused by a shorter residence time. In addition, soot particles move inside the flame where both SVF and temperature are lower due to their thermophoresis diffusion. The inception and coagulation rates increase without the radiative effect of soot, therefore, the average diameters of primary particles are smaller and the aggregate characteristics are higher.

Irreversibility analysis for axisymmetric nanomaterial flow towards a stretched surface

• Hydromagnetic axisymmetric flow of nanomaterial by a nonlinear stretched sheet is addressed. • Dissipation and radiation effects are scrutinized in heat equation. • Thermophoresis and Brownian motion are scrutinized. • Irreversibility analysis is scrutinized. Magnetohydrodynamic axisymmetric flow of viscous nanoliquid towards a variable stretching sheet is scrutinized. Flow is generated due to nonlinear stretching. Joule heating, heat flux and dissipation are analyzed in heat expression. Random and thermophoresis diffusions are considered. Physical description of entropy generation is also accounted. Entropy generation and heat transfer analysis are scrutinized through thermodynamics laws. Furthermore chemical reaction along with Arrhenius activation energy is addressed. Ordinary differential system is obtained through suitable variables. Homotopic convergent solutions for nonlinear system is developed. Influence of flow variables on entropy rate, velocity, Bejan number, concentration and temperature are analyzed. Further velocity gradient and heat and mass transfer rates are discussed. Reduction in velocity is noticed for magnetic variable. Thermal field has an enhancing trend for magnetic and Eckert number. Larger thermophoresis variable rises the temperature. An increment in entropy rate is observed for magnetic parameter. An increment in drag force is seen for magnetic variable.

Dissipative effects in hydromagnetic nanomaterial flow with variable fluid characteristics: Modern diffusion analysis

Low thermal conductivity is the major issue in heat transfer problems. It can be increased through the saturation of nanoparticles into base liquid. They have wide applications in engineering, electronics as well as in biomedicines. For cancer treatment magnetic nanoparticles are very effective. Nanofluids are excessively used as coolants in industries for example in automobiles, radiators, heat exchangers, cooling of microchips, nanocryosurgery and in cryopreservation etc. This attempt addresses the flow behavior of MHD fluid considering of nanoparticles. Here, the stretchable surface is responsible for fluid flow. Energy equation is formulated under the impacts of Joule heating and viscous dissipation. Varying thermal conductivity alongside with varying mass diffusivity are also incorporated. Flow analysis is exhibited by Thermophoresis and Brownian diffusion. Movement of heat and mass are addressed by using improved diffusive theory. It is noted that Brownian and thermophoresis diffusions will appear under the theory of modified fluxes. Behavior of unlike parameters in nanofluid velocity, fluid temperature and particles concentration are disclosed graphically. Skin friction co-efficient (drag force) is plotted. Both temperature and concentration profiles raises with enlarged thermal conductivity parameter and mass diffusivity parameter. Also local inertia coefficient parameter and Darcy porosity parameter diminishes the drag force.

Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces, diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick’s law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis, Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon, heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.

Bioconvection transport of magnetized micropolar nanofluid by a Riga plate with non-uniform heat sink/source

The purpose of this work is to discuss the 2D bioconvective micropolar nanoliquid transport with thermal radiation and non-uniform heat sink/source through the Riga plate. Novel features of activation energy are considered. In addition, the Buongiorno nanoliquid transport model is incorporated, which includes Brownian and thermophoresis diffusions aspects. By using effective transformations, nonlinear expressions in the present flow model are transformed into higher-order ODEs. The obtained ODEs are then computed by utilizing an innovative bvp4c solver (shooting scheme) in MATLAB tool. The outcomes of velocity, temperature, concentration, and microorganisms are discussed. Velocity is reduced for growing magnitudes of magnetic and bioconvective Rayleigh numbers. Velocity field boosts up for improvement in Marangoni ratio parameter. The micro rotation profile diminishes for magnetic parameter, and it enhances for micro rotation parameter. The presented findings show that upgraded thermal conductivity of nanoliquid is very useful in medication delivery, medication, food manufacturing, safer cooling surgery, cooling reactors, oil and gas, nanotechnology, biological engineering, heat storage systems, magnetic cell isolation, biosensors, biotechnology, pharmaceutical, and military fields.

Effects of Brownian motions and thermophoresis diffusions on the hematocrit and LDL concentration/diameter of pulsatile non-Newtonian blood in abdominal aortic aneurysm

LDL concentration is believed to be responsible for plaque formation that leads to atherosclerotic cardiovascular disease. We conducted this study to investigate the effects of hematocrits and LDL diameters on LDL concentration on the wall of an abdominal aortic aneurysm (AAA). The blood flow was considered to be a pulsatile and non-Newtonian flow whose viscosity was a function of hematocrits and strain rate. Lumen, Brownian, and thermophoresis diffusions were analyzed in LDL concentration. The results demonstrated that adding thermophoresis diffusion increases LDL concentration. Moreover, among three types of LDLs, including small LDLs, intermediate LDLs, and large LDLs, small LDLs were the ones with the highest concentration at the wall of the aneurysm. Furthermore, the effects of vorticity on diffusions were examined; it could be noted that the maximum Brownian diffusion appeared in vorticity places. Our results indicated that Brownian diffusion declines as hematocrit reaches 45% whereas thermophoresis diffusion increases. The current simulation investigated the effects of hematocrits, vorticity, Brownian, and thermophoresis diffusions on LDL concentration on the wall. Three types of LDL were taken into account for investigation of the effects of the diameter and reference concentration on LDL concentration. The outcomes of this study could be summarized as the following: the maximum amount of the wall shear stress appeared at 0.2T and at the upstream end of the AAA; moreover, thermophoresis diffusion increased small LDL concentration by 26% on the wall for hematocrit 45%.

Effectiveness of Magnetized Flow on Nanofluid Containing Gyrotactic Micro-Organisms over an Inclined Stretching Sheet with Viscous Dissipation and Constant Heat Flux

The bioconvection phenomenon, through the utilization of nanomaterials, has recently encountered significant technical and manufacturing applications. Bioconvection has various applications in bio-micro-systems due to the improvement it brings in mixing and mass transformation, which are crucial problems in several micro-systems. The present investigation aims to explore the bioconvection phenomenon in magneto-nanofluid flow via free convection along an inclined stretching sheet with useful characteristics of viscous dissipation, constant heat flux, solutal, and motile micro-organisms boundary conditions. The flow analysis is addressed based on the Buongiorno model with the integration of Brownian motion and thermophoresis diffusion effects. The governing flow equations are changed into ordinary differential equations by means of appropriate transformation; they were solved numerically using the Runge–Kutta–Fehlberg integration scheme shooting technique. The influence of all the sundry parameters is discussed for local skin friction coefficient, local Nusselt number, local Sherwood number, and local density of the motile micro-organisms number.

Numerical simulation for bioconvectional flow of burger nanofluid with effects of activation energy and exponential heat source/sink over an inclined wall under the swimming microorganisms

Nanofluids has broad applications such as emulsions, nuclear fuel slurries, molten plastics, extrusion of polymeric fluids, food stuffs, personal care products, shampoos, pharmaceutical industries, soaps, condensed milk, molten plastics. A nanofluid is a combination of a normal liquid component and tiny-solid particles, in which the nanomaterials are immersed in the liquid. The dispersion of solid particles into yet another host fluid will extremely increase the heat capacity of the nanoliquid, and an increase of heat efficiency can play a significant role in boosting the rate of heat transfer of the host liquid. The current article discloses the impact of Arrhenius activation energy in the bioconvective flow of Burger nanofluid by an inclined wall. The heat transfer mechanism of Burger nanofluid is analyzed through the nonlinear thermal radiation effect. The Brownian dispersion and thermophoresis diffusions effects are also scrutinized. A system of partial differential equations are converted into ordinary differential equation ODEs by using similarity transformation. The multi order ordinary differential equations are reduced to first order differential equations by applying well known shooting algorithm then numerical results of ordinary equations are computed with the help of bvp4c built-in function Matlab. Trends with significant parameters via the flow of fluid, thermal, and solutal fields of species and the area of microorganisms are controlled. The numerical results for the current analysis are seen in the tables. The temperature distribution increases by rising the temperature ratio parameter while diminishes for a higher magnitude of Prandtl number. Furthermore temperature-dependent heat source parameter increases the temperature of fluid. Concentration of nanoparticles is an decreasing function of Lewis number. The microorganisms profile decay by an augmentation in the approximation of both parameter Peclet number and bioconvection Lewis number.

Bioconvection mechanism using third-grade nanofluid flow with Cattaneo–Christov heat flux model and Arrhenius kinetics

This paper aims to study the effects of activation energy and thermal radiation in the bioconvection flow of nanofluid (third-grade nanofluid) containing swimming microorganisms in the presence of a heat source-sink past a stretching sheet. Brownian movement and thermophoresis diffusion are used in mathematical modeling. The given flow phenomenon is modeled in the form of governing partial differential equations. Furthermore, appropriate dimensionless transformation is used to transfer the governing system of PDEs into an ordinary one. The remodeled systems of ODEs are tackled numerically by bvp4c on Matlab with a shooting scheme in computational tool MATLAB. The bearing of prominently involved parameters on the numerical solution of velocity, temperature distribution, nanoparticles concentration and concentration of microorganisms is comprehensively discussed and elaborated through figures. It is established that velocity can be improved with a mixed convection aspect. Furthermore, the temperature and concentration of nanoparticles reduce against Prandtl number, also, large Peclet number declines the microorganisms field. The work contained in this paper has applications in nanotechnology, electrical and mechanical engineering, biomedicine, biotechnology, drug delivery, cancer treatment, food processing and various industries. No such work is yet reported, and it is good for the research in applied sciences.

Thermal convection in a layer of micropolar nanofluid

AbstractThe theoretical investigation of thermal convection in a horizontal layer of micropolar nanofluid is examined within the rule of linear stability hypothesis. The model applied for nanofluid integrates the impact of Brownian and thermophoresis diffusions. The flux of the volumetric fraction of nanoparticles is considered to be nil on the boundaries. The critical eigenvalues are achieved using the Galerkin approach, and the results are discussed and illustrated graphically. The results show that the Lewis number, the modified diffusivity ratio, the nanoparticle Rayleigh number, and the coefficient of coupling amid spin and heat flux accelerate the onset of convective motion, whereas the micropolar parameter and the coefficient of coupling amid vorticity and spin delay the onset of convective motion in the system.

Combined heat source and zero mass flux features on magnetized nanofluid flow by radial disk with the applications of Coriolis force and activation energy

The nanomaterials are more efficient in different areas like in pharmacy industry, cooling of compressors, engines, heating materials, damage cells destruction and brain tumors etc. The foremost aim of the this communication is to scrutinize the effects of activation energy on the nanofluid flow of an infinite, rotating and stretchable disk in radial direction with thermal heat source (THS) and the exponential space heart source (ESHS). Brownian and thermophoresis diffusions are countered to study the nanofluid. The Coriolis force and effects of radial magnetism are deployed. Nonlinear Boungiorno model is utilized. The modeled PDEs are converted to system of ODEs via proper variables. The obtained system is approximated through NDSolve technique. Features of various variables on flow profiles are examined and outcomes are declared via curves and tables. It is investigated that ESHS is highly influential than THS on fluid temperature. Furthermore it is found that activation energy enhances the concentration.

Numerical performance of thermal conductivity in Bioconvection flow of cross nanofluid containing swimming microorganisms over a cylinder with melting phenomenon

This study investigates the effects of melting phenomena and non-linear thermal radiation in Cross nanofluid bioconvection flow with motile microorganisms with a convective boundary over a cylinder. Brownian motion and thermophoresis diffusion are also taken into account in this mathematical model. A governing partial differential equation is used to represent the given flow phenomena. The proper dimensionless transformation is then employed to convert the PDE controlling system into an ordinary one. Bvp4c numerically solves redesigned ODE problems using a shooting strategy in the computational tool MATLAB. Figures versus velocity, temperature distribution, nanoparticle concentration, and microbe concentration profiles are used to analyze and expound on the notably involved aspects thoroughly. It has been demonstrated that increasing the estimates of a mixed convection parameter can enhance velocity. By increasing the Prandtl number, the temperature and concentration of nanoparticles decrease. A high Peclet value lowers the microorganism's profile.

FDM analysis for nonlinear mixed convective nanofluid flow with entropy generation

This analysis is concerned with unsteady Darcy-Forchheimer flow of nanomaterial by a stretching sheet. Heat transfer is carried out in presence of nonlinear mixed convection. Brownian motion and thermophoresis diffusion describe nanomaterial characteristics. Further magnetic field and viscous dissipation impacts are considered. By choosing suitable variables problem related expressions (PDEs) are transformed into dimensionless PDEs. These PDEs are then tackled through finite difference scheme. Entropy generation, skin friction, mass transfer rate and heat transfer rate are elaborated for involved parameters. Velocity enhances with increment in buoyancy variable and time while it reduces via higher Forchheimer number and porosity parameter. Temperature of the fluid decays with larger time while it boosts with an increment in Eckert number and nonlinear convection parameter. Higher values of Schmidt number lead to decay in concentration while it intensifies against higher thermophoretic diffusion parameter and time. Entropy production rate boosts against Prandtl and Eckert numbers while it is controlled via higher temperature ratio and volume ratio parameters.

Thermo diffusion and diffusion thermo impacts on bioconvection Walter-B nanomaterial involving gyrotactic microorganisms

Here magnetohydrodynamic (MHD) bioconvection Walter-B nanofluid flow due to stretched sheet is considered. Significance of motile gyrotactic microorganisms and melting phenomena are scrutinized. Energy equation is assisted with Brownian motion, thermal radiation, Joule heating and thermophoresis diffusion. Diffusion-thermo and thermo diffusion impacts are also considered. Suitable transforms are used to reduce related expressions into ordinary differential systems. Non-linear ODEs are tackled through homotopy analysis method (HAM). Convergent series solutions are obtained. Impacts of melting parameter, Dufour number, bioconvection Lewis number, radiation parameter, Soret number, Brownian motion parameter, magnetic parameter, Prandtl number and Peclet number are addressed. Velocity intensifies with increase in melting and viscoelastic parameters while it decay against magnetic parameter. Decay in temperature in noted against melting and radiation parameters while it enhances for higher Brownian motion parameter and Prandtl number. Concentration increases against Brownian motion parameter while it decays against higher melting parameter. Microorganism field increases with Peclet number while it decays with bioconvection Lewis number.

Thermo-bioconvection transport of nanofluid over an inclined stretching cylinder with Cattaneo–Christov double-diffusion

In this paper, Newtonian nanofluid flow is observed under the effects of the magnetic field, activation energy and motile microorganisms over an inclined stretchable cylinder. The magnificent aspects of nanoliquid are demonstrated by enduring the Brownian motion and thermophoresis diffusion features. Nonlinear higher order partial differential equations are transformed into first-order ordinary differential equations with suitable similarity variables. The attained sets of governing equations are then cracked by bvp4c procedure in MATLAB mathematical software. The numerical and graphical outcomes of controlling parameters such as Prandtl number, mixed convection, activation energy, thermophoresis, Brownian parameter, Biot number, Lewis number, Peclet number and motile concentration parameter against the velocity, temperature, volumetric concentration and motile concentration of nanoparticles of the fluid are discussed. The velocity is enhanced with the growth valuation in mixed convection and decay by rising variation of buoyancy ratio parameter, magnetic parameter and bio-convective Rayleigh parameter. The evolution in motile microorganisms is due to the increasing values of microorganisms Biot number. The presented data can be helpful in enhancement of manufacturing processes, biomolecules, extrusion systems applications and energy production improvement.

Nonlinear thermally radiative heat transport for brinkman type micropolar nano-material over an inclined surface with motile microorganisms and exponential heat source

The novel aim of current analysis is to identify the characteristics of Arrhenius activation energy and nonlinear thermal radiation in bio-convective brinkman type micropolar nanofluid flow with gyrotactic motile microorganisms and melting phenomena through a stretched surface. The temperature dependent heat source/sink and exponential space-based thermal source are considered. Further, concentration of nano-materials and thermal fields are considered in the occurrence of Brownian motion and thermophoresis diffusion. The narrating boundary layer flow equations of brinkman type micropolar fluid model are reframed on the form of ordinary ones with the help of appropriate similarity transformation. The bvp4c collocation technique is used in the transformed model with shooting scheme to obtain a numerical solution of the original problem. The numerical data for the velocity, thermal and solutal fields, and microorganism's field is graphically designed and impacts of the prominent parameters are described in detail. It is notice from the current study velocity of fluid has diverse nature against magnetic parameter. Growing behavior of velocity field is depicted for higher estimation of mixed convection parameter. The microorganism field is boosted up by increasing melting parameter. The current model is applicable in nanotechnology, biotechnology, drug delivery, protein chips, DNA chips, food processing, cancer treatment, smart sensors and in many more fields

Numerical simulation for bio-convective flow of Sutterby nanofluid by a rotating disk

Nanofluids play a vital role in the improvement of our practical life. The potential usage of nanomaterials in different applications such as oil recovery, refrigeration systems, a freeze of electrical components in computers, development of liquid displays, cooling spirals, mechanical engineering, electrical engineering, heat storage devices and biotechnology. Swimming microorganisms have a crucial role in various areas of life, such as medicines, bioengineering, biofuels and food processing. Microorganisms are used as antibiotics in medicine and help to create a vaccine. Keeping in mind these applications, the current research provides a mathematical model for bioconvection Sutterby nanofluid flowing past the rotating stretching disk with magnetic field, motile microorganisms, chemical reactions and heat generation. The Brownian movement and thermophoresis diffusions are also considered. The governing equation structures are simplified by suitable transformations. A popular bvp4c solver in MATLAB computational software is employed to achieve numerical results for the non-linear model. The flow evaluation for the effects of several prominent numbers on temperature, velocities, concentration and motile microorganism profiles is executed graphically and numerically. The volumetric concentration of nanomaterial rises for thermophoresis number while shows opposite nature for Prandtl and Lewis parameters. The boosting values of bioconvection Lewis number, Peclet number and bioconvection Rayleigh number decay the motile microorganisms’ concentration.

Development of bioconvection flow of nanomaterial with melting effects

Here magnetohydrodynamic (MHD) bio-convective flow of nanomaterial due to stretched sheet is examined. Melting effects in the presence of motile gyrotactic microorganisms are addressed. Further effects of nonlinear radiation, Brownian motion, Joule heating and thermophoresis diffusion are considered in energy equation. Related expressions are transmitted into dimensionless differential system through appropriate variables. Homotopy analysis method is employed for solutions of nonlinear system. Convergence region of solutions are examined. Entropy optimization, Bejan number and other engineering quantities like Nusselt number, surface drag force, Sherwood and microorganism density numbers are elaborated. Graphical results showing the influence of various emerging parameters on microorganism concentration, fluid velocity, concentration and on temperature distribution are presented. Velocity intensifies with increasing in melting while it decays against magnetic parameter. An enhancement in temperature is noted against higher Brownian motion and Prandtl number while it decays for higher radiation and melting variables. Concentration decays against higher melting parameter while it enhances against higher Brownian motion parameter. Microorganism field increases with Peclet number while it decays against higher melting and bio-convection Lewis number.

Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.