Brinkman Number Research Articles

Investigation of entropy generation in the existence of heat generation and nanoparticle clustering on porous Riga plate during nanofluid flow

The objective of this research is to examine the impact of many parameters, including entropy production resulting from nanoparticle aggregation, viscous dissipation, heat source, and buoyancy, on the flow behavior of nanoliquids through a vertical Riga plate made of porous media at the two-dimensional stagnation point. By combining elements of the original Krieger-Dougherty model with the Maxwell-Bruggeman model, a new correlation for the aggregation process may be reached. The PDEs that control the boundary layer area of this problem are changed into a group of nonlinear PDEs using the right non-similarity transformations. The issue may be solved by using the BVP4c MATLAB program, which implements the local non-similarity approach and includes an extra degree of truncation. It was also found that the skin friction coefficient increased by 3.35% to 7.18% for both the aiding and opposing flow zones with the incorporation of a 1% nanoparticle volume fraction. Incorporating the Eckert number resulted in a consistent drop in heat transfer efficiency, from 7.27% to 10.24%. Aggregation of nanoparticles increases the magnitude of velocity and the temperature distribution, as shown by the model of aggregation. The augmentation of the A values is widely acknowledged as a strategy to prolong the initiation of entropy; however, on the contrary, the elevation of the Bejan number helps to expedite it. It has been empirically shown that increasing the ϕ value has a beneficial effect on both the entropy inception field and the Bejan number. An increase in the Brinkman number leads to an acceleration in the rate of entropy generation, concomitantly resulting in a decrease in the Bejan number. The suggested numerical model is validated by comparing it to existing findings that have been made public.

Numerical investigation on heat transfer characteristics of the viscoelastic fluid flow during wire coating process

Due to the high-quality data required in some major industrial fields, transferring those data seem to be an inevitable task. Wires and fibers used for data transmission are needed coating process to be safe from possible damage. This paper first conducted the mathematical Non-linear differential equations for a pressure-type die on wire coating process. Then it was found that the Least Square Method used to predict the thermal behavior of the operating fluid is reasonably accurate. At the end, some critical values such as permeability, magnetic, and third-grade parameters were changed to evaluate their effects on the fluid behavior. It found the temperature pattern rises around 21% by enhancing magnetic parameters. Moreover, the velocity pattern decreases by enlarging the magnetic field, and the temperature profile increases by rising Brinkman number.

HARK formulation for entropy optimized convective flow beyond constant thermophysical properties

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

Entropy generation analysis of a ternary hybrid nanofluid (Au-CuO-GO/blood) containing gyrotactic microorganisms in bifurcated artery

PurposeThe purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.Design/methodology/approachThe governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.FindingsThe investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.Originality/valueThis study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

Entropy analysis of double diffusion in a Darcy medium with tangent hyperbolic fluid and slip factors over a stretching sheet: Role of viscous dissipation

This study aims to numerically investigate entropy optimization for a time-independent tangent hyperbolic fluid flowing past a porous sheet that is stretching linearly. The fluid motion is generated by stretching surfaces and buoyancy forces. The analysis includes momentum, energy, and mass transport associated with mixed convection, thermal radiation, velocity, thermal, and concentration slip factors. Heat dissipation is also considered in energy transport through the viscous dissipation effect. The mathematical formulation leads to a set of non-linearly coupled partial differential equations. To obtain a similarity solution, similarity variables are introduced. The numerical solution of the leading differential equations is obtained using the fourth-order Runge-Kutta method with the shooting technique. The graphical results are presented to show the physical significance of the relevant parameters. The main objective of entropy optimization is achieved by increasing the magnitude of the Darcy dissipation parameter. Entropy generation is directly proportional to the Brinkmann number, Reynolds number, and radiation parameter. The second law of thermodynamics is fulfilled by introducing slip conditions over the porous medium. The use of a tangent hyperbolic fluid over a porous medium has practical applications in various porous geometries, such as oil/gas reservoir simulation, enhanced oil recovery, carbon dioxide sequestration, and water soil infiltration. Therefore, optimizing entropy generation in these mechanical systems is crucial.

Electroosmotic flow and heat transfer characteristics of a class of biofluids in microchannels at high Zeta potential

Peristalsis is an important dynamic phenomenon in the field of biomedical research, and has great application prospects in microscale fluids. In recent years, this biomimetic (peristaltic) phenomenon has gained widespread attention due to its large-scale applications in various medical and industrial fields, such as radiation therapy, peristaltic blood pumps, and drug delivery systems. In this study, the electroosmotic flow and heat transfer characteristics are investigated under high wall Zeta potential and slip boundary conditions for a certain type of biological fluid that satisfies the Newtonian fluid model. Fluid flows under the joint action of external electric field, magnetic field, and Joule heating. Firstly, without using the Debye-Hückel linear approximation, the numerical solutions are given by using the Chebyshev spectral method for the nonlinear Poisson-Boltzmann equation, the fourth-order differential equation satisfied by the stream function, and the thermal energy equation. The results are compared with those obtained by using the Debye-Hückel linear approximation to demonstrate the effectiveness of the numerical method used in this study. Secondly, the effects of wall Zeta potential, Hartmann number <inline-formula><tex-math id="M11">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M11.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M11.png"/></alternatives></inline-formula>, electroosmotic parameter <inline-formula><tex-math id="M12">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M12.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M12.png"/></alternatives></inline-formula>, slip parameter <inline-formula><tex-math id="M13">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M13.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M13.png"/></alternatives></inline-formula> are discussed on the flow characteristics, peristaltic pumping, and trapping phenomena under electromagnetic environments, and the influence of Joule heating parameter <inline-formula><tex-math id="M14">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M14.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M14.png"/></alternatives></inline-formula> and Brinkman number <inline-formula><tex-math id="M15">\begin{document}$Br$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M15.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M15.png"/></alternatives></inline-formula> is explored on heat transfer characteristics. The results show that 1) wall Zeta potential plays an important role in controlling the velocity of fluid peristaltic flow; 2) the increase of electroosmotic parameter <inline-formula><tex-math id="M16">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M16.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M16.png"/></alternatives></inline-formula> and slip parameter <inline-formula><tex-math id="M17">\begin{document}$\beta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M17.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M17.png"/></alternatives></inline-formula> increases the flow velocity in the central region of the channel, while the increase of Hartmann number <inline-formula><tex-math id="M18">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M18.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M18.png"/></alternatives></inline-formula> hinders the flow of fluid; 3) these flow behaviors exhibit opposite trends near the channel walls; 4) the number of streamlines captured by peristaltic transport decreases with Hartmann number <inline-formula><tex-math id="M19">\begin{document}$H$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M19.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M19.png"/></alternatives></inline-formula> and electroosmotic parameter <inline-formula><tex-math id="M20">\begin{document}$m$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M20.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M20.png"/></alternatives></inline-formula> increasing; 5) the increase of Joule heating parameter <inline-formula><tex-math id="M21">\begin{document}$\gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M21.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M21.png"/></alternatives></inline-formula> and Brinkman number <inline-formula><tex-math id="M22">\begin{document}$Br$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M22.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="6-20231685_M22.png"/></alternatives></inline-formula> leads temperature to rise.

HIEMENZ STAGNATION POINT FLOW OF A TERNARY NANOFLUID AND HEAT TRANSFER DUE TO POROUS STRETCHING/SHRINKING SHEET WITH BRINKMAN MODEL

The role of the Brinkman model is analyzed in the current work by taking the flow of ternary hybrid nanofluids with heat transfer in the presence of radiation and mass transpiration. The ordinary differential equations (ODEs) are yielded from the partial differential equations (PDEs) by using similarity variables. This flow is used in many real life significances viz., glass blowing, petroleum products, polymer extrusion, and so on. The role of the Brinkman model and radiation is used in velocity and heat equations. These equations are solved exactly to get a solution domain and confluent hypergeometric equation. Three types of nanoparticles, namely Al<sub>2</sub>O<sub>3</sub>, single wall carbon nanotubes, and graphene are inserted in the flow to enhance thermal efficiency. Additionally, dual behavior is seen in the instance of the shrinking sheet. Also, a unique solution is observed at the stretching sheet case. The novelty of the current analysis explains the stagnation point flow by considering the effect of the Brinkman model in the presence of ternary nanoparticles. By using these nanoparticles, the main goal of the current work is achieved. It includes the effect of the Brinkman model on ternary nanofluids, and the comparison between three nanoparticles can be achieved. The results of various parameters viz., solid volume fractions, mass transpiration, radiation, Brinkman number, porous medium parameter, and heat source/sink parameter can be examined with the help of graphical arrangements. At the end, we conclude the important outcomes as the solution domain value decays on rising values of porous medium parameter and mass transpiration values rise on increaing values of the solution domain.

Heat Transfer in Couette–Poiseuille Flow through Porous Medium

Analytical solutions were derived to investigate the effect of viscous dissipation on the temperature distribution and heat transfer characteristics of Couette-Poiseuille flow in a saturated porous medium between two parallel plates with simultaneous pressure gradient. The fluid is steady, laminar and both hydro-dynamically and thermally fully developed, while the thermal boundary conditions considered are both plates being kept at asymmetric heat fluxes. For Couette-Poiseuille flow, the temperature distribution and the Nusselt number were affected greatly by Brinkman number Br, Darcy number Da and velocity of the moving plate

Numerical analysis on thermal control and irreversibility for 3D Casson hybrid nanofluid flow within two permeable stretching surfaces with interfacial nanolayer thickness and slip velocities

During the preparation of nanoparticles, the nanolayer thickness plays a vital role in further controlling the flow and thermal–physical features of the fluid. Features are observed to be more prominent in the presence of hybrid nanomaterials. In the present problem, the concomitant effects of the interfacial nanolayer of nanomaterials MWCNT and Fe 3 O 4 during a 3D Casson hybrid nanofluid flow between two parallel plates have been investigated. An appropriate transition is applied to rationalize the substantially paired and nonlinear governing equations. Equations after similarity transformation are processed by concerning the finite element method. Impressions of different governing parameters on the governing systems in conjunction with entropy and the Bejan number are displayed through graphs and tables. Graphs are drawn with an evaluation of general and hybrid nanofluids and different nanolayer thicknesses of nanoparticles. Three-dimensional features were observed for skin friction and the rate of heat transfer. The thermal impact is very significant in the presence of nonlinear thermal radiation and a heat source. After simulation, it is indicated that heat transfer rate disrupts with Biot number while it upgrades with heat generation. The entropy of the system is restricted with an increase in the magnetic and Brinkman numbers, while the Bejan number shows the opposite behavior with respect to those parameters. With an increase in the interfacial nanolayer thickness, the entropy of the system slows down.

Anisotropic Darcy–Brinkman Magnetic Fluid Convection under the Influence of a Time-Dependent Sinusoidal Magnetic Field

The impact of the sinusoidal mode of a magnetic field involving time fluctuations on the threshold of the ferromagnetic smart liquid convection in a saturated permeable medium is investigated using the regular perturbation technique. The Darcy–Brinkman model with anisotropic permeability is used to describe the flow through porous media. The thermal anisotropy is implemented in the energy equation. The problem might be useful in thermal engineering applications such as dynamic loudspeakers and computer hard discs and in medical applications like the treatment of tumor cells and the cell separation, to name a few. The regular perturbation technique is based on the minimum amplitude of a magnetic field modulation, and the onset criterion is dealt with in terms of a correction in the critical Rayleigh number and wavenumber. The thermal Rayleigh number correction depends on the magnetic field modulation frequency, magnetic force, anisotropies, porosity, and Prandtl number. At moderate values of the magnetic field modulation frequency, the impact of various physical factors is perceived to be noteworthy. The influences of the magnetic mechanism, Prandtl number, porosity parameter, and Brinkman number are shown to augment the destabilizing effect of the magnetic field modulation for moderate values of the frequency of a modulation. However, the destabilizing effect of the magnetic field modulation is diminished due to an increase in the values of the mechanical anisotropy parameter and thermal anisotropy parameter. The study reveals that the effect of the magnetic field modulation could be exploited to control the convective instability in an anisotropic porous medium saturated by a ferromagnetic fluid.

The onset of anisotropic Darcy–Brinkman penetrative convection with local thermal nonequilibrium due to heat generation and extraction

AbstractAn anisotropic, fluid‐saturated porous medium with local thermal nonequilibrium is the subject of this paper's analysis of the stability of the commencement of convection caused by internal heat generation. The classical Darcy's momentum equation is applied with the Brinkman model. To observe the thermal instabilities in the fluid layer, it is assumed that there is steady heat extraction through the bottom boundary and constant heat generation inside the fluid layer. The critical internal Darcy Rayleigh and associated wave numbers are computed using linear instability and energy approaches using the Chebyshev pseudospectral method to determine the existence of instability or otherwise. The fluid layer becomes unstratified as a result of heat generation inside the fluid, which encourages the occurrence of any subcritical instability. The critical Darcy–Rayleigh number has been found to be significantly influenced by a number of parameters, including the anisotropy parameter, internal heat parameter, porosity‐modified conductivity ratio, inter‐phase heat transfer parameter, and Darcy–Brinkman number.

Impact of magnetic field on heat transfer with viscous dissipation at the conduction limit in a channel with a centred porous layer: constant wall temperature

This paper investigates the impact of a magnetic field on heat transfer within a duct containing a centrally located porous layer. The duct comprises both fluid and porous regions, with the porous material occupying the central section. The channel walls are maintained at constant temperatures. In the fluid region, the flow field is governed by the Poiseuille flow equation, while in the porous region, the non-Darcy Brinkman equation is employed to model the flow. It is assumed that the flow field is fully developed. To account for viscous dissipation, two dissipation models, namely the clear fluid compatible (CFC) model and the form drag (FD) model, are implemented in the porous region. The study delves into the detailed effects of these dissipation models on heat transfer. The system is characterized by several well-established properties, including the porous fraction (δp), Darcy number (Da), Brinkman number (Br), and Hartmann number (M). Analytical expressions for the limiting Nusselt number (LNN) and the limiting temperature profiles (LTP) are derived at the conduction limit, taking into consideration the presence of the magnetic field. For high Hartmann numbers, the CFC model is deemed appropriate for the viscous dissipation model.

Entropy optimized flow subject to variable fluid characteristics and convective conditions

Background and objectiveNanofluids possess significant enhancement in nanomaterial properties such as convective heat transfer coefficient, thermal conductivity (which increases volumetric fraction of nanoparticles) and diffusivity at reasonable nanoparticle concentration. Nanofluids provide interesting new opportunities to develop nanotechnology-based operative coolants for different kinds of innovative applications. Hydromagnetic radiative flow of nanomaterial by curved stretched sheet is addressed in presence of Darcy-Forchheimer relation. Heat generation and dissipation are deliberated. Variable mass diffusivity and thermal conductivity behaviors are under consideration. Convective conditions are taken into account. Random diffusion and thermophoresis behaviors are considered. Dufour and Soret behaviors are taken. Binary chemical reaction and thermal radiation are explored. Entropy rate is taken into consideration. MethodologyNonlinear formulation is reduced to ordinary differential system. Convergent solutions for nonlinear ordinary systems are developed invoking Optimal homotopy analysis method (OHAM). ResultsImpacts for influential parameters regarding fluid flow, pressure, thermal distribution, entropy and concentration are discussed. Larger magnetic variable has reverse behavior on entropy rate and pressure. Higher magnetic field intensifies thermal distribution whereas reverse effect noted for liquid flow. Thermal distribution has increasing trend for Dufour number and variable thermal conductivity. Concentration reduces for random motion and Schmidt number. Concentration has increasing behavior for Soret number and variable mass diffusivity parameter. Larger estimation of thermal Biot number has same impact on thermal distribution and entropy. Increasing behaviors of entropy rate and concentration for solutal Biot number are observed. Bejan number reduces against Brinkman number whereas opposite trend holds for radiation parameter.

Impacts of entropy generation in second-grade fuzzy hybrid nanofluids on exponentially permeable stretching/shrinking surface

The present investigation aims to use entropy analysis to analyze the unsteady Magnetohydrodynamic (MHD) flow in a second-grade fuzzy hybrid Al2O3-Cu/SA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( {{\ ext{Al}}_{{2}} {\ ext{O}}_{{3}} - {\ ext{Cu/SA}}} \\right)$$\\end{document} nanofluid over an exponentially shrinking/stretching surface. The model for hybridization of the mixture of alumina Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left( {{\ ext{Al}}_{{2}} {\ ext{O}}_{{3}} } \\right)$$\\end{document} and copper (Cu) nanoparticles in the sodium alginate (SA) base fluid under heat source/sink, nonlinear thermal radiation, and viscous dissipation. The fundamental partial differential equations (PDEs) are simplified using an appropriate similarity conversion to generate the ordinary differential equations (ODEs). The analytical computation occurs in the MATHEMATICA program implementing the homotopy analysis method (HAM). In terms of code validity, our results are preferable to previous findings. The features of several parameters against the velocity, surface friction coefficient, entropy, temperature, and Nusselt number are described through graphs. According to our findings, the rise in the Brinkman and Reynolds numbers enhanced the total entropy of the system. Furthermore, the nanoparticle volume fraction and viscus dissipation magnifies the fluid temperature while retards the flow profile throughout the domain. Fluid velocity declined due to the Lorentz force using magnetic impact applications. The imprecision of nanofluid and hybrid nanofluid volume fractions was modelled as a triangular fuzzy number (TFN) [0%, 1%, 2%] for comparison. The double parametric approach was applied to deal with the fuzziness of the associated fuzzy parameters. The nonlinear ODEs convert into fuzzy differential equations (FDEs) and use HAM for the fuzzy solution. From our observation, the hybrid nanofluid displays the maximum heat transfer compared to nanofluids. This important contribution will support industrial growth, particularly in the processing and manufacturing sectors. The percentage increase in skin friction factor is 18.3 and 15.0 when α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} take input in the ranges of 0 ≤ α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha$$\\end{document} ≤ 0.8 and 0 ≤ β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document} ≤ 1, respectively.

Radiative and dissipative MHD Eyring–Powell nanofluid bioconvective flow through peristaltic waves in the presence of bilateral chemical reaction with Arrhenius activation energy: Entropy optimization

The novel characteristics of nanofluids made them potentially important in the heat transfer mechanisms happening in industrial and medical processes, such as electronic devices, pharmacological techniques, hybrid combustion engines, thermal management of cars, refrigerator, chiller, temperature of gases reduction, and so on. In comparison to base fluid, these procedures have a propensity to improve thermal conductivity and convective transference of heat. This distinctive aspect has recently generated interest in nanofluids through various fluid flow models. The issue at hand involves the peristaltic flow of magnetohydrodynamics Eyring–Powell nanofluids through a microchannel containing oxytactic bacteria and nanoparticles. For a thorough analysis of irreversibility optimization, the analysis of entropy is additionally taken into consideration. To comprehend the flow physics associated with bolus formation and the effect of reflux on the micro vessel, a 3-D computational fluid dynamic analysis is performed. The effects of bilateral chemical interaction with nonlinear mixed convection and Arrhenius activation energy are considered in the present analysis. The complexity of the system was achieved through a numerical approach based on the concepts of small Reynolds number and large wavelength. The resulting nonlinear coupled differential equation system is solved numerically using the built-in command in MATHEMATICA (Parametric ND Solve Function). To perform a thorough comparative examination for various values of the considered sections of the channel, graphs have been used. Some of the investigation’s findings are the entropy profile has been improved for incremental values of Hartmann number and Brinkmann number whereas the axial velocity shows a downward trend for the highest values of the Hartmann number and the material fluid parameter.

Numerical and analytical study of heat transfer in the wire coating process using Carreau–Yasuda fluid model

In this article, we present a non-isothermal study of the wire coating process using the Carreau–Yasuda fluid model. Our aim is to explore how the Carreau–Yasuda fluid model parameters are linked to key operational factors in the wire coating process. These factors encompass the radius of the coated wire, the volumetric flow rate, and the force needed to pull the wire. The equations that depict the flow and heat transfer within the die are solved: (a) analytically using the perturbation method to get the analytical expression for velocity, temperature distribution, and relevant engineering quantities; (b) numerically using shooting method with the “Runge–Kutta–Fehlberg algorithm.” The physical effects of the Weissenberg number (We), power law index (n), pressure gradient (A), and Brinkman number (Br) on the velocity profile, temperature distribution, and engineering quantities are discussed with the help of different graphs. Our findings reveal that, in the case of shear thinning (n < 1) with a constant pressure gradient, as compared to the Newtonian scenario, both the thickness of the coated wire and the force required to pull the wire decrease with an increase in the Weissenberg number (We). Moreover, the force required to pull the wire also decreases with an increase in the values of the pressure gradient parameter.

Analysis of Joule heating and viscous dissipation on electromagnetohydrodynamic flow with electroosmotic effect in a porous microchannel: A heat transfer miniature enhancement

AbstractThis work investigates the effect of Joule heating and viscous dissipation due to electric double layer (EDL) and electroosmotic effect on steady fully developed electromagnetohydrodynamic flow in a porous microchannel. Dimensionless formulations of the Poisson–Boltzmann, momentum, and energy equations are derived for the electric potential, velocity profile, and temperature distribution in the microchannel. Exact solutions for the temperature distributions and velocity profiles were obtained using the method of undetermined coefficients. The Debye–Hückel linearization is used to get an exact solution for the electric potential. The results showed that the Brinkmann number , Joule heating parameter , Debye–Hückel parameter , Hartmann number , electric field , and suction/injection parameter have a substantial impact on flow formation and heat transfer. Using MATLAB software, graphical simulations are provided to deliver a greater understanding of the influence of relevant parameters on the results achieved.

Entropy generation in magneto couple stress bionanofluid flow containing gyrotactic microorganisms towards a stagnation point on a stretching/shrinking sheet

The study focuses on the behavior of an electrically conducting non-Newtonian fluid with couple stress properties, using water-based bionanofluid. The fluid is analyzed as it flows across a porous stretching/shrinking sheet within its own plane. This Study also explores the Bejan Number and Entropy Generation. To facilitate this investigation, the governing nonlinear partial differential equations undergo a transformation, wherein they are converted into nonlinear ordinary differential equations through a suitable similarity transformation. An ideal strategy has been employed to achieve the desired results from the modeled challenge. The Homotopy Analysis Method is applied to determine the solution of the system of differential equations. The convergence of the applied method and their comparison with the numerical method are described through graphs and tables. The main features of the different profiles are briefly described. Graphs are used to analyze the impact of the Bejan number, concentration, temperature, velocity profile, and entropy production rate. Tables present the characteristics of skin friction, Nusselt, and Sherwood numbers for various limitations. The stretching and ambient fluid velocities should fluctuate linearly as the distance from the stagnation point increases. A rise in the magnetic and porosity parameters is accompanied by an increase in the velocity profile. While the velocity profile falls off as a Couple of fluid parameters are increased. The phenomenon of temperature boost is observed to be positively correlated with the increase in Brownian motion parameter while exhibiting no significant dependence on other parameters such as Brinkman number, Prandtl number Lewis number and Thermophoresis parameter. Entropy generation increases with the Brinkman number while decreasing with the radiation parameter and diffusion parameter as is plainly demonstrated.

Computation of non-Newtonian quadratic convection in electro-magneto-hydrodynamic (EMHD) duct flow with temperature-dependent viscosity

Motivated by novel developments in smart non-Newtonian thermal duct systems, a theoretical study has been presented in this article for electro-magneto-hydrodynamic (EMHD) buoyancy-driven flow of a fourth-grade viscoelastic fluid in a vertical duct with quadratic convection. The viscosity of the fourth-grade fluid model is assumed to be temperature-dependent, and the Reynolds exponential model is deployed. Viscous heating and Joule dissipation effects are included. The duct comprises a pair of parallel electrically insulated vertical flat plates located a finite distance apart. Via suitable scaling transformations, a nonlinear boundary value problem is derived for the momentum and heat transport. A homotopy perturbation method (HPM) solution is obtained coded in Mathematica symbolic software. There is a considerable enhancement in wall skin friction with an increment in fourth-grade fluid parameter, Brinkman number, electrical field parameter, thermal buoyancy parameter, and quadratic thermal convection parameter. However, skin friction is strongly reduced with a rise in variable viscosity parameter, Hartmann (magnetic) number, and electromagnetic heat generation to conduction ratio. Nusselt number magnitudes are elevated with increase in variable viscosity parameter, thermal buoyancy parameter, and quadratic thermal convection parameter, whereas they are significantly suppressed with increment in fourth-grade fluid parameter, Brinkman number, and Hartmann magnetic number.

Entropy Generation Optimization in an Unsteady Hybrid Nanofluid Flow Over a Flat Plate with Variable Viscosity: A Cattaneo-Christov Heat Flux Model

Nanofluids are a novel and intriguing class of heat transmission fluids that can be used in place of more conventional options. They have several applications, including fuel cells, heat exchangers, and the pharmaceutical industry. When it comes to heat transport, hybrid nanofluids much outperform their mono-fluid counterparts. These are being put to use in a wide variety of areas, from solar power to air conditioning. Unsteady flow characteristics of a hybrid nanofluid (Ethylene Glycol + ZnO + TiO2) over a flat plate at varied Lorentz forces, volume fraction of nanoparticles, and thermal radiation are unknown when variable viscosity is taken into account. Paper’s novelty is addressing this gap, which is to examine the impact of variable viscosity on the hybrid nanofluid flow by a flat plate under convective boundary condition when thermal radiation and magnetic field are significant. Cattaneo and Christov’s heat flux model is used to analyse the phenomenon of heat transfer. This paper also includes an analysis of irreversibility. The equations required to represent the problem have been turned into a system, and this system has been solved using the bvp4c solver. Validated the results (of engineering parameters including friction coefficient) obtained using the bar graphs by using Multiple linear regression. It has been observed that the thermal relaxation parameter (Γ) and the unsteady parameters (S) both have similar effects on the heat transmission rate. It is found that there is an increment of 0.001278 (when 0 ≤ Γ ≤ 0.6) and 0.103865 (when 0.4 ≤ S ≤ 1) in the Nusselt number. It is clear from a closer inspection that as magnetic field parameter (Mg) and viscosity parameters (δ) are raised, the friction factor declines. It is observed that, at 0 ≤ Mg ≤ 1.8, friction factor declines at a proportion of 0.08974. It is detected that higher Brinkman number values lead to a greater rate of entropy generation and an upsurge in the (temperature-dependent) viscosity parameter contributes to a decline in the same. As the viscosity parameter is amplified, it is also seen that the fluid’s velocity declines.