Brinkman Number Research Articles

Case study of entropy optimization with the flow of Non-Newtonian nanofluid past converging conduit with slip mechanism: An application of geothermal engineering

Magneto hydrodynamic flow over a wedge-shaped channel is often seen in geothermal applications, microelectronic, energy systems, and pumping systems. The slip condition is a normally recognized condition for the fluid flow occurs along lubricated, coated, wall channels. The best examples of such flows are the blood flow in arteries with plaque layer arteries. Flow configuration within channel is anticipated by using Carreau nanofluid injection at inlet. The intersecting wall of channel is inclined with respect to horizontal plane to make convergent angle of −α and divergent angle of α. The mathematical equations for energy and nanofluid concentration are established using well-known Navier–Stokes Equation with conservation equations invoking modified Buongiorno model. The temperature differences between the wall and core region leads to entropy. By using distinguishing amendments, system of equations are remodeled into system of ordinary differential equations (ODE's), which are numerically solved by Bvp4c technique of MATLAB for realistic conditions of under discussed phenomena. Simple shear close to the wall admit compression in local flow topology in zones of channel (divergent). The temperature field increases along thermal radiation, Brinkman number, nanoscale effects and heat source. Entropy is minimal and can be minimized with optimal angle and slip velocity.

The computational model of nanofluid considering heat transfer and entropy generation across a curved and flat surface

The entropy generation analysis for the nanofluid flowing over a stretching/shrinking curved region is performed in the existence of the cross-diffusion effect. The surface is also subjected to second-order velocity slip under the effect of mixed convection. The Joule heating that contributes significantly to the heat transfer properties of nanofluid is incorporated along with the heat source/sink. Furthermore, the flow is assumed to be governed by an exterior magnetic field that aids in gaining control over the flow speed. With these frameworks, the mathematical model that describes the flow with such characteristics and assumptions is framed using partial differential equations (PDEs). The bvp4c solver is used to numerically solve the system of non-linear ordinary differential equations (ODEs) that are created from these equations. The solutions of obtained through this technique are verified with the available articles and the comparison is tabulated. Meanwhile, the interpretation of the results of this study is delivered through graphs. The findings showed that the Bejan number was decreased by increasing Brinkman number values whereas it enhanced the entropy generation. Also, as the curvature parameter goes higher, the speed of the nanofluid flow diminishes. Furthermore, the increase in the Soret and Dufour effects have enhanced the thermal conduction and the mass transfer of the nanofluid.

Entropy generation analysis on Darcy-Forchheimer Maxwell nanofluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model and Joule heating

This research paper inspects the flow characteristics of a magnetohydrodynamic (MHD) Maxwell nanofluid in the presence of a Darcy-Forchheimer (DF) model applied to a stretching sheet. Additionally, numerical analysis is performed to evaluate the findings, utilizing a nanofluid composed of copper (Cu) suspended in water. The energy equation in this study incorporates thermal radiation, viscous dissipation, the Cattaneo-Christov heat flux model, and joule heating. The entropy generation is then determined based on the obtained solutions for temperature and velocity, in compliance with the flow constraints. By applying suitable similarity transformations, the conservative equations of energy and momentum are transformed into nonlinear ordinary differential equations (ODEs). To solve these equations, a bvp4c method implemented through Matlab software is employed. By taking into account pertinent characteristics like the relaxation Prandtl number, magnetic parameter, time parameter, radiation parameter, and others, one can analyse the normalized shear stress at the wall, temperature profile, and rate of heat flux. For practical purposes, the local Nusselt and number of skin frictions are determined for various modified values of the physical constraints. This provides vital insights about the system's behavior under various settings. The graphical results indicate that the velocity profile exhibits a decrease as the volume fraction, magnetic parameter, Maxwell fluid parameter, and inertia coefficient parameter increase. The entropy generation demonstrates an increase with growing values of the Brinkman number and magnetic parameter. On the other hand, entropy generation declines with increasing values of the temperature ratio parameter. The Bejan number exhibits the opposite behavior of the entropy generation. Specifically, as the Bejan number increases, the entropy generation decreases, and vice versa.

Theoretical modeling of squeezing flow in porous media under arbitrary boundary velocity

Squeezing flow within a thin porous gap driven by a moving boundary is a fundamental phenomenon in industrial and biological systems but lacks accurate theoretical models. This study fills the gap by introducing a comprehensive solution using Fourier transforms, considering porous media effects, and handling arbitrary moving boundaries. The model explores the impact of Womersley and Brinkman numbers on velocity and pressure, providing a robust framework for various applications. By harmonizing the considerations of arbitrary moving boundaries with porous characteristics, this work not only deepens our theoretical understanding but also sets the stage for innovative research and development in the field of squeezing flow dynamics.

Entropy production in unsteady MHD double diffusive and chemically reactive nanofluid flow past a rotating permeable plate using overlapping grid spectral collocation technique

The entropy production phenomenon due to the applied external magnetic fields, thermal dissipation, chemical reaction and the impact of rotating pervious plate on heat transfer, nanofluid friction and mass transfer has been numerically explored. The nanofluid flow is presumed to be unsteady, smooth, hydro-dynamically and electrically conducting. The well known Navier–Stokes time-dependent equations in cartesian coordinates for velocity, temperature and concentration are modelled and scaled down to a system of ODEs by applying suitable similarity transformations with unsteady dimensionless parameters. A new numerical scheme known as the overlapping grids spectral collocation method (OGSCM) is applied in finding the approximate solutions to the highly nonlinear ODEs. The results obtained are then used for solving the entropy equation and the rate of irreversibility is represented graphically. Several engineering variables, such as the coefficient of heat transfer, Nusselt number and Sherwood number, are also thoroughly examined. The OGSCM proved to be accurate, computationally efficient, time efficient and converges fast. We discovered that increased applied magnetic field, chemical reaction parameter, rotation parameter, and Schmidt parameter insert more energy into the system which reduces the thermal boundary layer and hence reducing the rate of entropy generation. Furthermore, the entropy generation rate is increased by increasing the Grashof number, Brinkman number, permeability, Prandtl number, and thermal radiation parameter.

Non-similar analysis of MHD bioconvective nanofluid flow on a stretching surface with temperature-dependent viscosity

In this research, we explore the potential of magnetohydrodynamic (MHD) bioconvective nanofluids with varying viscosity through non-similarity analysis, aiming to enhance the thermal performance of biological and industrial systems. Recent years have witnessed significant advancements in energy applications, motivating our investigation. To enhance heat transfer, we employ propylene glycol as the base liquid, incorporating silicon dioxide and molybdenum disulfide nanomaterials. This unique configuration enables efficient heat dissipation and accommodates inner heat sources or sinks. Our model relies on partial differentials, and we derive a non-similar dimensionless representation of the governing system using appropriate transformations. We utilize ordinary differential equations (ODEs), approximating local non-similarity (LNS), to estimate transformed non-similar partial differential equations (PDEs). Numerical simulations are performed using the bvp4c algorithm. Throughout our analysis, we present various physical parameters, demonstrating their importance in fluid flow and thermal transport through graphical and tabular representations. Our findings show that alterations in the magnetic parameter lead to changes in fluid velocity and temperature profiles. Similarly, adjustments in the viscosity parameter affect fluid velocity, and variations in the temperature-dependent viscosity parameter influence velocity profiles, with temperature profiles responding to changes in the Brinkman number and heat source parameter. Additionally, we observe concentration profile adjustments with shifts in the Schmidt number and enhanced migration of particles or components within the nanofluid with rising Soret numbers, impacting the concentration profile. Furthermore, an increased Peclet number positively influences microorganism profiles, while the Lewis number exhibits contrasting behavior. To further validate our approach, we present comparative analyses of skin friction coefficients and Nusselt numbers in tabular form. Our primary objective in this study is to formulate non-similar transformations tailored to the specific problem under consideration. These transformations aim to produce accurate and efficient results, providing valuable insights for future research endeavors in the field of nanofluid flows.

Numerical assessment of irreversibility in radiated Sutterby nanofluid flow with activation energy and Darcy Forchheimer

Entropy generation is a concept that is primarily associated with thermodynamics and engineering, and it plays a crucial role in understanding and optimizing various processes and systems. Applications of entropy generation can be seen in turbo machinery, reactors, chillers, desert coolers, vehicle engines, air conditioners, heat transfer devices and combustion. Due to industrial applications entropy generation has gained attention of researchers. Owing such applications, current communication aims to model and analyzed the irreversibility in Sutterby nanoliquid flow by stretched cylinder. Momentum equation is reported by considering porosity, Darcy Forchheimer and magnetic field. While in energy equation radiation and Joule heating effects are accounted. Activation energy impact is accounted in the modeling of concentration equation. Thermodynamics second law is utilized for physical description of irreversibility analysis. Through similarity transformations dimensional equations representing flow are transformed to dimensionless ones. Numerical solution for ordinary system is obtained via Runge–Kutta-Fehlberg scheme in Mathematica platform through NDsolve code. Influence of prominent variables on velocity, entropy, temperature, Bejan number and concentration are graphically analyzed. Coefficient of skin friction, gradient of temperature and Sherwood number are numerically analyzed. The obtained results show that velocity field decreases through higher porosity and Forchheimer variables. Velocity and temperature curves shows an opposite trend versus magnetic parameter. A decay in concentration distribution is noticed through larger Schmidt number. Entropy generation amplifies against magnetic parameter and Brinkman number.

Consequences of variable wall permeability and magnetic field on non-isothermal flow in converging/diverging tubes

The current article is devoted to the development of a theoretical model investigating heat transfer analysis of MHD blood flow through renal tubules. For this purpose, we consider the transport of Newtonian fluid inside a non-uniform tube whose lateral surface is kept at constant temperature. The walls of tube are considered to admit the variable permeation and the flow is actuated by an externally applied magnetic field. The solution of the problem is formulated analytically in terms of axial and radial velocities and temperature distribution under the presumption of lubrication approximation in the inertia free flow field. Implication of Darcy’s law for fluid seepage across the tubular membrane results in an ordinary differential equation having variable coefficients for the unknown pressure, which is successfully computed numerically using RK45 routine. Performance of velocity, pressure and temperature distributions has been investigated for various values of the physical parameters involving in the model. Moreover, flow rate behavior, fluid reabsorption and the leakage flux has been analyzed through graphs and tables. The characteristics of heat transfer in the flow field is also evaluated for various values of Brinkman number. A significant discovery reported in the results of present model reveals that the axial flow exhaustion and radial flow reversal are significantly influenced by the tube converging/diverging parameter and the Hartmann number as well. By employing a strong magnetic field, exhaustion and reversal phenomena in the flow field can be restrained up to a certain limit. Moreover, with an increasing wall permeability, there is a significant exhaustion of axial flow in a divergent tube and a prominent assistance takes place in the radial flow reversal for convergent tube. It is hoped that the present model will bear the potential to study flow in renal tubules and in hemodialyzer.

Influence of various shape factors on a hybrid nanofluid flow over a convectively heated exponential stretching sheet with exponential heat source and activation energy: An irreversibility analysis

Understanding and controlling the shape factors of nanoparticles in fluid flow problems is crucial for optimizing heat transfer, fluid dynamics, and various applications such as nanofluids, drug delivery systems, catalysis, and nanocomposites. By tailoring the shape of nanoparticles, researchers can manipulate their behavior, dispersion, and interaction with the fluid, thereby optimizing the desired outcomes in various fluid flow problems. In this work, we investigated how thermal radiation, exponential heat source, and activation energy parameters affect the laminar flow properties of a hybrid nanofluid (Water + Graphene + Multi-Walled (MW) Carbon Nanotubes (CNTs)) over an exponentially expanding sheet. This article also includes an analysis of irreversibility. The equations required to represent the problem have been turned into a system of nonlinear ordinary differential equations, and this system has been unraveled by means of the bvp4c solver. Outcomes are presented for three instances, i.e. platelet, cylinder, and spherical shape factors. It is observed that there is an increase in the formation of entropy associated with the upsurge in the values of the Brinkman number, but there is an inverse proportional relation between activation energy () and entropy generation. It is clear from a closer inspection that as the friction factor declines with the escalation in the magnetic field parameter () and volume fraction of graphene (). At the skin friction coefficient is seen to drop at a rate of 0.69807 (in all cases). It is discovered that, when (Prandtl number), the Nusselt number declines by 0.009161 (platelet shape), 0.009397 (cylinder shape), and 0.009997 (spherical shape). It is remarked that the transmission rate of mass declines with the rise in At the Sherwood number is seen to drop at a rate of 0.30723 (platelet shape), 0.30718 (cylinder shape), and 0.30708 (spherical shape).

Effect of viscous dissipative fluid in a slit micro-channel with heated super-hydrophobic surface

The analytical solution of heat transfer and hydro magnetic flow for an incompressible, electrically-conducting, and viscous dissipative fluid traveling vertically through an isothermally heated parallel plate in a slit micro-channel is performed. One channel surface was super-hydrophobic slip and temperature jump, whereas the other did not. This study also examined the effects of super-hydrophobic slip and a temperature jump on characteristic flow of magneto-hydrodynamics (MHD) free convection flow with viscous dissipative fluid. The perturbation technique was used to solve the coupled nonlinear and coupled equations analytically. With the aid of illustrative graphs, the results were presented, and the effects of the relevant controlling parameters namely Brinkman number, magnetic field, velocity slip condition and temperature jump effects were analysed for temperature, velocity, skin friction and Nusselt number distributions when either wall is heated by constant wall temperature. The result demonstrated that the activities of Brinkman number, Br, substantially increase fluid velocity, whereas growing levels of magnetic field effect was seen to slow down the flow movement. In addition, the fluid velocity is higher for greater values of temperature jump and velocity slip effects respectively. Furthermore, this research can prove very useful for designers in improving the performances of mechanical systems when viscous dissipation is involved, as well as heat transfer in micro-channels, as it is in combustion.

Analysis of heat transfer in [formula omitted]-immiscible layers of a horizontal Jeffrey fluid film flow

This paper deals with theoretical analysis of heat transfer in n-immiscible layers of a horizontal Jeffrey fluid film, driven by a heated plate and surface tension gradient. The formulation of the horizontal n-immiscible layers is based on mass, momentum, and energy conservation laws. The resulting systems of coupled linear ordinary differential equations are solved to obtain exact solutions for velocity, temperature, volume flow rate, shear stress, and rate of heat transfer. The effects of flow control parameters of interest, such as the inverse capillary number C, thermal conductivity of fluid χ, and Brinkmann number Br, on the velocity and temperature of the 5-immiscible layers, are investigated through graphical analysis. It is observed that increasing C leads to an increase in the velocity of all 5-immiscible layers. The temperature of all 5-immiscible layers also rises with increasing values of C, χ, and Br. The analysis of these 5-immiscible layers provides significant knowledge and understanding that may be applied to systems with a higher or lower number of immiscible layers utilizing the expressions derived for n-immiscible layers of a fluid film. Moreover, a comparison between immiscible layers of Newtonian fluid and Jeffrey fluid films is made in terms of velocity and temperature.

Impact of rotation on thermal instability of Darcy–Brinkman porous layer filled with a Jeffrey nanofluid

The novelty of this research lies in its investigation of the initiation of thermal instability within a Darcy–Brinkman porous layer containing a Jeffrey nanofluid under the influence of rotation. While non-Newtonian fluids complex flow patterns and heat transfer enhancements due to thermal gradients are known, this study addresses a specific and previously unexplored aspect, the impact of rotation on Darcy–Brinkman porous layer containing a Jeffrey nanofluid. When a fluid is subjected to rotation, it can induce additional forces and flow patterns within the fluid. The linear stability theory and normal mode analysis method are used to analyze the stability of the system analytically and are computed numerically using the software Mathematica version 11.3. The investigation focuses on understanding the influence of various factors, namely, the Taylor number, the Lewis number, the Jeffrey parameter, the modified diffusivity ratio, nanoparticles Rayleigh number, the Darcy–Brinkman number, and medium porosity on the onset of thermal instability in the physical system. This novel perspective can contribute to a deeper understanding of heat transfer processes in non-Newtonian fluids and has potential applications in improving the efficiency of industrial systems, such as cooling systems, heat exchangers, and microfluidic devices where efficient heat transfer is crucial for performance improvement.

Irreversibility analysis of Magnetohydrodynamic (MHD) mixed convection flow of viscoelastic hybrid nanofluid flow in a channel

This manuscript delves into the analysis of irreversibility in Magnetohydrodynamic (MHD) mixed convection flow of a viscoelastic hybrid nanofluid within a vertical channel. The study adopts a parallel plate configuration and employs Aluminum oxide (Al2O3) and Titanium oxide (TiO2) nanoparticles dispersed in a Carboxymethyl cellulose (CMC)-water base fluid. Utilizing similarity transformations, the governing partial differential equations (PDEs) are converted into a set of ordinary differential equations (ODEs), streamlining the mathematical model. These ODEs are then solved using the homotopy analysis method via Mathematica software for various governing parameter values. Key parameters including the Brinkman number, volume fractions of nanoparticles, magnetic effects, and wall temperature parameter are systematically investigated. Noteworthy insights include that volume fraction and magnetic parameter augments velocity at the left wall and slows down it toward the right wall; Brinkman number and wall temperature parameters significant in elevating temperature; Entropy and Bejan number respond differently to variations in the Brinkman number. Entropy escalates with increasing magnetic parameter, while the Bejan number declines. Illustrated through graphs, these findings enrich the comprehension of MHD mixed convection flow and heat transfer in viscoelastic hybrid nanofluids, elucidating irreversibility aspects tied to such systems.

Water-based nanofluid flow and heat transfer in thin film over an unsteady stretching sheet: An entropy analysis

The transfer of thermal energy is intrinsically associated with the generation of entropy. Here, we investigate the entropy generation number in nanofluid thin film flow over a radiated stretching sheet subject to different shapes of titanium oxide and copper nanoparticles in base fluid water. In addition, the impact of the magnetic field, viscous dissipation, and Joule heating were also considered. Using a suitable similarity transformation, the momentum and energy equations that describe the flow are converted into ordinary differential equations. These equations are then solved numerically using bvp4c in MATLAB. Graphs and explanations show how different physical parameters affect the velocity profile, temperature distribution, Nusselt number, skin friction coefficient, entropy generation number, and Bejan number. As the Brinkman number went up, fluid friction and Joule loss caused more entropy generation, but the Bejan number showed the opposite trend. In a certain situation, it is also important to note that as the value of the radiation parameter goes up, the irreversibility of heat transfer becomes more important. In addition, spherically shaped nanoparticles have the lowest entropy among all other forms. Hence, nanoparticles have the ability to reduce the amount of energy lost in any physical process and increase the overall productivity of systems. Understanding the flow and heat transmission within a thin film has many practical applications in industry, including aerodynamic lamination of plastic sheets, wire and fiber coating, food processing, annealing and thinning of copper wires, reactor fluidization, and many more.

Dynamics of thermal radiation and Lorentz force on the hybrid nanofluid (Ethylene Glycol + Graphene + Copper) flow via an exponentially stretching sheet with chemical reaction: An irreversibility analysis

AbstractAn exciting new class of heat transmission fluids, nanofluids, has been developed as an alternative to traditional fluids in manufacturing. Fuel cells, heat exchangers and pharmaceutical processes are just a few of the many uses for them. When compared to monofluids, the heat transmission properties of hybrid fluids are superior. These are findings used in an extensive diversity of fields, from solar energy to air conditioning. The objective of this paper is to examine how Lorentz force and chemical reaction parameters affect the characteristics of a couple stress hybrid nanofluid (Ethylene Glycol + Graphene + Copper) flow via an exponentially stretching surface. The heat transport phenomenon is studied using viscous dissipation, exponential heat source and thermal radiation parameters. Furthermore, irreversibility analysis is provided in this paper. Governing equations are transformed into a set of nonlinear ordinary differential equations using suitable similarity transformations. The bvp4c solver in MATLAB is used to solve the transformed system. Engineering parameters of interest, including skin friction coefficient, are described using bar diagrams. It has been noted that the magnetic field and volume fraction of graphene nanoparticles (ϕ1) reduce the skin friction coefficient. At , the skin friction coefficient decreases at a rate of 4.68187. It is observed that there is an increment in the fluid temperature with the rise in the exponential heat source parameter, and the velocity profile increases with the increase in the mixed convection parameter. It is detected that, while Eckert number () was set to , Nusselt number was reduced by 6.29239. It is noticed that, while the chemical reaction () is set to , the mass transfer rate rises at a Rate of 0.349644. It has been observed that as the Brinkmann number and magnetic field parameters increase, so does the rate of entropy production. It is also detected that as the porosity parameter increases, the fluid momentum decreases. Furthermore, increasing the couple stress parameter decreases the fluid velocity.

Thermo-solutal Marangoni convective Darcy-Forchheimer bio-hybrid nanofluid flow over a permeable disk with activation energy: Analysis of interfacial nanolayer thickness

Abstract The Marangoni convective phenomena have a unique impact on industries and medical tools. These phenomena are more prominent in the presence of dual nanoparticles (NPs) over base fluids such as blood that are surrounded by a thin interfacial nanolayer, an important feature to control the physical and thermal properties of the NP. In this problem, we have analysed the thermo-solutal Marangoni convective Darcy-Forchheimer flow of nanomaterials with the impact of the interfacial nanolayer. The results of the system of an exponential heat source, non-linear radiation, joule heating, and activation energy are discussed. An appropriate transition is applied to rationalise the substantially paired and nonlinear governing equations and then processed by the Galerkin finite element method (G-FEM). The impression of different governing parameters on the governing systems in conjunction with entropy and Bejan number is demonstrated through graphical and tabular form. Graphs are drawn with an evaluation of general and hybrid nanofluids (HNFs) and different nanolayer thicknesses of NPs. Activation energy and chemical reaction parameters restrict the Sherwood number, and the same is observed for the Nusselt number with an increase in the Brinkman and Eckert numbers. The thickness of the interfacial nanolayer of the NPs restricts the entropy generation of the system, while the entropy is higher for the HNF than the nanofluid. An opposite feature was observed for the Bejan number.

Irreversibility analysis and thermal radiative of Williamson (ZnO+MOS 2/C 3 H 8 O 2) hybrid nanofluid over a porous surface with a suction effect

The current approach considered the unsteady 2D laminar second law analysis on Williamson hybrid nanoliquid in a porous medium under the effect of the thermal radiative flow towards a convectively heated stretching sheet. Propylene glycol () is employed as the base liquid in this study, and the nanoparticles are Molybdenum disulfide and Zinc Oxide The purpose of the current study is to maximize the energy and mass transfer rate for industrial and engineering applications. The primary contribution of this study is to discuss heat transmission via thermal radiation, suction, and the porous parameter on the flow of a William hybrid nanoliquid. The constitutive Maxwell flow model, heat transport, and entropy generation can be reduced to ordinary differential equations by similarity transformations. The Bvp4c technique is used on these generating ODEs for the numerical technique in the methodology section. Fluid friction, heat transmission, and Joule heating are used to calculate the entropy generation number. Graphs and tables are used to investigate the effects of dimensionless parameters on flow variables and entropy generation. The primary results suggest that hybrid Maxwell nanofluid is a more efficient heat conductor than regular nanofluid. A significant drop in the velocity field is supported by the Williamson Unsteady and porosity factors The temperature profile is significantly raised by the Biot number thermal radiation and suction factor Moreover, it has been found that entropy increases with radiation but reduces in Brinkman number against the Bejan number profile. Our results for a few specific situations were compared with previously published data to establish the validity of the current study, and it was discovered that they were in strong agreement.

Investigation of dissipative heat transfer and peristaltic pumping on MHD Casson fluid flow in an inclined channel filled with porous medium

A theoretical investigation is performed for free convective peristaltic pumping of a Casson fluid through an inclined porous wavy channel. The flow is subjected to uniform magnetic field in the transverse direction. In addition, the energy equation contains porous and viscous dissipation effects. The governing flow problem is modeled for Casson fluid with the help of conservation laws of mass, momentum, and energy under the long wavelength assumption. Using a regular perturbation method, we obtained the analytical expressions for the axial velocity, temperature, pressure rise per one wavelength, and heat transfer rate. The consequences of various effects on the flow quantities are demonstrated in the form of graphical representations and discussed in detail. The findings reveal that the rise in the thermal Grashof number and permeability parameter leads to an increment in the velocity and thermal fields. The heat transfer rate strengthened when the Casson parameter and magnetic parameter were increased. The pressure rise exhibits an enhancing trend for the Brinkmann number and permeability parameter. Further, we observed a decreasing behavior on streamlines for increasing magnetic field strength. Moreover, the obtained findings are applicable to a variety of fields in the bioengineering and medical sciences, such as targeted drug delivery, heart-lung machines, MRI, cancer therapy, power conversion devices, and micromanufacturing processes.

Partial Slip and Cross-Diffusion Effects on Magnetohydrodynamic Mixed Bioconvection Flow in a Channel with Chemical Reaction

The main objective of the paper is to explore the effects of Soret and Dufour on MHD mixed bioconvection of nanofluid in a flat channel with chemical reaction, radiation, Joule heating and partial (velocity) slip. The related ordinary differential equations are comprised of velocity, energy, nanoparticle concentration, solutal concentration and microorganisms density are solved analytically subject to physically appropriate boundary conditions using homotopy analysis method (HAM). The dimensionless skin friction, heat and mass transport are discussed through plots by varying different physical parameters. The transport of heat enhances with Brinkman number but it increases gradually with thermal radiation. The fluid velocity reduces by the velocity slip, while it increases by raising the Hartmann number. The temperature of the fluid lowered due to the surplus thermal radiation. The dufour number and velocity slip create opposite effect in solutal concentration.

On Entropy Generation and Heat Transfer Due to Magneto-Marangoni Convective γ Al2O3-H2O/C2H6O2 Nanofluid Flow Over a Porous Surface

A numerical analysis is carried out for water/Ethylene Glycol based γ Al2O3 nanofluid movement over a horizontal permeable sheet placed within a porous medium using MATLAB package Bvp4c solver. Other flow controlling conditions like Non-linear thermal radiation and uniform Magnetic field are also considered for this study. The present study is novel in terms of entropy generation and heat transfer rate investigation for mentioned fluid system in the existence of dissipation (an irreversible process) and heat generation/absorption impact. First, a mathematical pattern is prepared in the form of partial differential equations to represent the Marangoni convection flow and temperature, considering suitable boundary conditions. Using similarity parameters, we convert our mathematical model in dimensionless form and then solved it. Accuracy of obtained data is also cross-checked with another numerical technique “Runge-Kutta fourth order” along with shooting process. Using velocity and temperature fields, entropy is measured for present system. From the plots, it is noted that entropy as well as Bejan number is qualitatively changed for parameters namely, volume fraction parameter, radiation parameter, Brinkmann number and heat generation/absorption parameter. It is noticed that heat transfer rate and entropy generation number is higher for γ Al2O3-C2H6O2 nano fluid then γ Al2O3-H2O nano fluid.