KHA model comprising MoS4 and CoFe2O3 in engine oil invoking non-similar Darcy-Forchheimer flow with entropy and Cattaneo-Christov heat flux.

Objective: Nanoliquid flows are widely utilized in industrial, petroleum, engineering, and pharmaceutical applications including electric cooling, drug delivery, nuclear reactor cooling, solar collectors, heat exchangers, magnetohydrodynamic power generators, aerospace, porous media, thermal storage systems, and many others. Darcy-Forchheimer magnetized hybrid nanoliquid subjected to a stretchable cylinder was addressed, and the Cattaneo-Christov heat flux analysis was considered. Herein, disulfido (dithioxo) molybdenum (MoS4) and cobalt ferrite (CoFe2O4) were considered as nanoparticles, and engine oil as a conventional liquid. The thermal relationship of heat generation and radiation was discussed, and the influence of the entropy rate was addressed. Methodology: Governing expressions were transformed into dimensionless forms. Simulation by the ND-solve technique was implemented. Conclusions: Features for the entropy rate, liquid flow, and temperature against emerging variables for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were explored. The numerical results of the coefficient of skin friction and thermal transport rate for nanoliquid (MoS4/engine oil) and hybrid nanoliquid (MoS4 + CoFe2O4/engine oil) were examined. Reduction in velocity clearly occurred through a magnetic field, whereas the reverse impact held for the entropy rate. The thermal field and entropy rate against the curvature parameter were enhanced. A decrease in liquid flow occurred for higher porosity variables. An enhancement in the entropy rate was witnessed for radiation and porosity parameters. Higher radiation and thermal relaxation time variables resulted in enhancement of the thermal transport rate.

A numerical study on the flow of water-based ternary hybrid nanomaterials on a stretchable curved sheet.

Nanomaterials are quite promising in electronic cooling systems, heat exchangers, engine lubricants, brake liquids, shock absorbers, radiators, etc. Therefore, the study of heat transfer characteristics on the flow of trihybrid nanofluids on an exponentially stretched curved surface is developed. Purpose: In this study, trihybrid nanofluid is taken into consideration, which is composed of Fe3O4, Ag and Cu as nanoparticles and water as the basefluid. Heat generation and magnetic field impacts are addressed. Based on these assumptions, the governing partial differential equations were reduced to a favorable set of ordinary differential equations using adequate transformations. Formulation: The highly nonlinear coupled system of equations was numerically solved using the shooting method with the Runge-Kutta-Fehlberg technique. Findings: Trihybrid nanofluids improve the thermal performance of fluid when compared with other fluids such as hybrid nanofluids, nanofluids, and basefluids. The trihybrid nanofluid is efficient in heat transfer phenomenon and has a significant impact on the overall performance of a system, including cooling systems, heat exchangers, electronics, and many industrial processes. Graphical representation for the physical variables of the fluid velocity and temperature is discussed. The local Nusselt number and skin friction coefficient are computed and analyzed. A magnetic field decreases the velocity but escalates the temperature. The Nusselt number decreases for larger solid volume fractions. Novelty: The Tiwari and Das model for hybrid nanofluid extended for trihybrid nanoparticles has not been investigated previously. Heat transfer examination on the flow of trihybrid nanomaterials on exponentially curved stretching sheets considering magnetism force and heat generation consequence has not yet been studied.

Entropy generation in bioconvection hydromagnetic flow with gyrotactic motile microorganisms.

Here, the magnetohydrodynamic bioconvective flow of a non-Newtonian nanomaterial over a stretched sheet is scrutinized. The characteristics of convective conditions are analyzed. Irreversibility analysis in the presence of gyrotactic micro-organisms is discussed. Energy expression is assisted with thermal radiation, heat generation and ohmic heating. Buongiorno's model is employed to discuss the characteristics of the nanoliquid through thermophoresis and random diffusions. Nonlinear expressions of the given model are transformed through adequate transformations. The obtained expressions have been computed by the Newton built in-shooting technique. Results of influential variables for velocity, concentration, microorganism field, temperature and entropy rate are graphically studied. Clearly, velocity reduction is witnessed for the bioconvection Rayleigh number and magnetic variable. A higher heat generation variable leads to augmentation of temperature. An increase in the magnetic variable results in entropy and temperature enhancement. A higher Peclet number results in microorganism field reduction. Temperature distribution rises for radiation and the thermal Biot number. A higher solutal Biot number intensifies the concentration. The entropy rate for radiation and diffusion variables is enhanced.

Unsteady nanofluid flow over a cone featuring mixed convection and variable viscosity.

This article addresses unsteady nanofluid flow over a cone with MHD and mixed convection effects. Effects of variable viscosity and viscous dissipation are also considered. The resulting system of equations is tackled through the Homotopy Analysis Method (HAM). The impact of different influential variables on skin friction coefficient, heat and mass flux are discovered through numerical tables and graphs. It is noted that the surface drag force in x and y directions increases against the buoyancy force parameter. Also, it is observed that the tangential and azimuthal velocity decrease against the variable viscosity parameter. Furthermore, the temperature of fluid is observed to decay against the unsteady parameter but it increases against the Eckert number.

Thermodynamic irreversibility effects with Marangoni convection for third grade nanofluid flow.

In this study, an analysis was performed to investigate the thermal and mass transport of radiative flow of a third-grade nanofluid with magnetohydrodynamic. The analysis concerns two-dimensional flow around an infinite disk. Heat transport is studied via heat generation/absorption, thermal radiation and Joule heating. Chemical reaction with activation energy is also considered. The nanofluid characteristics, including Brownian motion and thermophoretic diffusion, are explored via the Buongiorno model. Entropy analysis is also conducted. Moreover, the surface tension is assumed to be a linear function of concentration and temperature. Through adequate dimensionless variables, governed PDEs are non-dimensionlized and then tackled by ND-solve (a numerical method in Mathematica) for solutions purposes. Entropy generation, concentration, velocity, Bejan number and temperature are plotted as functions of the involved physical parameters. It is noticed that higher Marangoni number intensify velocity however it causes a decrease in the temperature. Entropy rate and Bejan number boost for large value of diffusion parameter.

Impacts of entropy generation in radiative peristaltic flow of variable viscosity nanomaterial.

Current analysis highlights the aspects of different nanoparticles in peristalsis with entropy generation. Mathematical equations of considered problem are modelled via conservation laws for mass, momentum and energy. Such equations contain variable viscosity, nonlinear thermal radiation, viscous dissipation, heat generation/absorption and mixed convection aspects. Boundary conditions comprise the second order velocity and first order thermal slip effects. Entropy expression is obtained by utilization thermodynamics. Simplified and dimensionless forms of the considered conservative laws are obtained through lubrication technique. Resulting system of equations subject to the considered boundary conditions is solved numerically via built-in shooting procedure in Mathematica. Such numerical procedure is very suitable to obtain numerical results directly and fastly in the form of graphs. Further all the considered flow quantities are discussed graphically for the significant parameters of interest in detail. Both velocity and temperature are decreasing against large volume fraction parameter. Increasing temperature dependent viscosity effects decrease the entropy and enhance the Bejan number.

Analytical evaluation of Oldroyd-B nanoliquid under thermo-solutal Robin conditions and stratifications.

Chilling systems are important in the improved technological thermal mechanisms which are considered continuously in passive along with active heat-transference improvement procedures. Engineers recommended several approaches to upsurge heat transference of thermal structures. The pulsating flow, corrugated tube, magnetic field aspect and nanoliquids are the heat-transference improvement procedures delved continuously. In present research work, we addressed the heat-transference characteristics of non-Newtonian (Oldroyd-B) liquid towards heated stratified surface. Thermally radiative laminar flow is modeled. In addition, we accounted Buongiorno's nanoliquid model which includes Brownian along with thermophoretic diffusions. Modeling is further based on heat source, magnetohydrodynamics, dual stratification, thermal radiation and convective conditions. Mathematical system is simplified through boundary-layer idea. Similarity variables are reported with the aim to simplify complex mathematical system. Homotopy algorithm yields convergent results of non-dimensional expressions. Our study unveils diminution of thermal along with solutal fields when stratification factors are increased.

Cattaneo-Christov heat flux (CC model) in mixed convective stagnation point flow towards a Riga plate.

This research article proposes an improved Fourier law of heat conduction (Cattaneo-Christov) in presence of heat source/sink. The heat transport characteristics are modeled for mixed convective stagnation point flow by a Riga plate. Flow is generated due to linear stretching velocity. The partial differential system is changed to ordinary differential system through implementing appropriate transformations. Series solutions are developed through semi-analytical method called as homotopy analysis method. Present research article is related to the improved Fourier law of heat conduction (Cattaneo-Christov) over a linear stretchable surface of Riga plate when fluid saturates porous space. The main outcomes of present communication are summarized as: (i) velocity of material particles decreases subject to larger inverse Darcy-number while it enhances via velocity ratio and magnetic parameters (ii) temperature distribution as well as layer thickness enhance for higher estimations of Eckert number and heat source parameter while it decays against Prandtl number (iii) skin friction coefficient decreases through higher values of inverse Darcy number and mixed convection parameter.

Corrigendum to "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer methods and programs in biomedicine 184 (2020) 105,086].

In this published paper, a mathematical modeling has been conducted for the peristaltic transport in flow of hybrid nanofluid between rotating channel in the presence of nonlinear thermal radiation, slip effects and entropy generation. This corrigendum correct the flow geometry, figures captions and plots "Transport of hybrid type nanomaterials in peristaltic activity of viscous fluid considering nonlinear radiation, entropy optimization and slip effects" [Computer Methods and Programs in Biomedicine 184 (2020) 105,086] where these mistake are occurred during production process and therefore, some captions are shuffled. The difference in the captions and plots however does not affect the authenticity and mathematical validity of the problem in purpose of this published research article is to investigate the peristaltic transport in flow of hybrid nanofluid between rotating channel subject to nonlinear thermal radiation, slip effects and entropy generation. However, the flow geometry and the captions and plots should be arranged.

Diabetic peripheral neuropathy in people with type 2 diabetes: too little too late.

Diabetic peripheral neuropathy in people with type 2 diabetes is poorly managed because of its insidious onset, delayed diagnosis and more complex aetiology resulting from the contribution of not only hyperglycaemia, but also ageing, hyperlipidaemia, hypertension and obesity. Because there is no US Food and Drug Adminstration-approved disease-modifying therapy for diabetic peripheral neuropathy, the key to ameliorating it in type 2 diabetes has to be through earlier diagnosis and timely multi-factorial risk factor reduction. The management of painful diabetic peripheral neuropathy also requires a detailed appraisal of the choice of therapy, taking into account efficacy, patient wishes, comorbidities, side effect profile and potential for abuse.

Modeling and numerical simulation of micropolar fluid over a curved surface: Keller box method.

BACKGROUND: This paper examines the flow behavior of micropolar liquid over a curved surface. MHD fluid is considered. The surface inducing the fluid motion has a prescribed temperature different from the ambient fluid moreover the heat transfer mechanism is investigated. Curvilinear coordinates are used for the mathematical formulation of the flow equation. Similarity variables are derived and are utilized to alter the governing expressions for the flow of momentum and heat transfer characteristic. METHOD: The resulting non-linear ODEs are resolved systematically by two numerically approaches namely; the Keller box method and the shooting method. RESULTS: The numerical results for the temperature and velocity fields has been presented through tables and graphs against the independent parameters and non-dimensional numbers i.e., material parameter, power law index, radius of curvature, magnetic parameter, Prandtl and Eckert numbers, skin friction (drag force) and Nusselt number. Physical explanation of the graph presented is given to understand the performance of fluid flow and heat transport phenomena in different emerging situation. CONCLUSION: The main outcomes in the presence of various flow variables on the skin friction velocity, Nusselt number, temperature are highlighted via graphical sketch and Tables. Velocity field displays a decreasing trend with magnetic parameter, power law index and radius of curvature of the stretching velocity whereas, opposite behavior observed for the material parameter. Near the surface curvature and magnetic parameter shows an enhancement in microrotation profile whereas, it shows reverse behavior when it is far away. Material parameter increases for large values of microrotation profile on the other hand power-law index decreases for large values. For higher values magnetic parameter, radius of curvature and Eckert number temperature profile increases. But temperature reduces subject to material parameter and Prandtl number.

On the numerical simulation of stagnation point flow of non-Newtonian fluid (Carreau fluid) with Cattaneo-Christov heat flux.

BACKGROUND: This research article is devoted to evaluating the impact of Cattaneo-Christov heat in MHD stagnation point flow over a stretched and shrinking surface of the cylinder. MHD liquid of Carreau fluid is considered. Flow is generated due to stretching and shrinking aspects. The energy equation is developed in the presence of Cattaneo-Christov heat flux, where thermal relaxation time plays an important role in the heat transport. METHOD: The appropriate transformations are employed to solve a differential system via shooting method (bvp4c). RESULTS: The velocity, skin friction coefficient, temperature and Nusselt number are discussed versus different pertinent flow variable graphically. Over results indicate that the velocity distribution decreases against larger magnetic power law index and Weissenberg number. Temperature field diminishes via Prandtl number and thermal relaxation variable. Engineering quantities are discussed graphically. Magnitude of skin friction or velocity gradient upsurges versus magnetic parameter. Moreover, temperature gradient or Nusselt number shows the increasing impact via Prandtl number. Main observations of the considered flow problem are listed as concluding remarks.

Development of thixotropic nanomaterial in fluid flow with gyrotactic microorganisms, activation energy, mixed convection.

BACKGROUND: In this article, impact of gyrotactic microorganisms on nonlinear mixed convective MHD flow of thixotropic nanoliquids is addressed. Effects of Brownian motion and thermophoresis diffusion are considered. Characteristics of heat and mass transfer are analyzed with activation energy, Joule heating and binary chemical reaction. Nonlinear PDE's are reduced to ordinary equation by using suitable transformations. METHOD: For convergent series solution the given system is solved by the implementation of the homotopic analysis technique (HAM). RESULTS: Influences of different flow controlling variables on the velocity, microorganisms, concentration and temperature are examined through graphs. Surface drag force, density number, Sherwood number and gradient of temperature are examined versus different flow parameters through graphs. For larger thixotropic fluid parameters the velocity field boosts up. For rising values of Hartmann number the velocity and temperature have opposite behaviors.

Darcy-Forchheimer hybrid (MoS2, SiO2) nanofluid flow with entropy generation.

BACKGROUND: The aim of this articles is to investigate the entropy optimization in Darcy-Forchheimer hybrid nanofluids flow towards a stretchable surface. The flow is caused due to stretching of surface. Energy equation is discussed through heat generation/absorption, viscous dissipation and heat flux. Here molybdenum disulfide and silicon dioxide are considered as a nanoparticles and water as continuous phase fluid. Furthermore we examined the comparative analysis of molybdenum disulfide (MoS2) and silicon dioxide (SiO2) suspended in water (H2O). Entropy optimization rate is calculated through implementation of second law of thermodynamics. METHOD: Nonlinear partial differential equations are reduced to ordinary system through adequate transformation. Here we have employed numerical built in ND solve method to develop numerical outcomes for obtained nonlinear flow expression. RESULTS: Characteristics of various engineering parameters on entropy optimization, velocity, Bejan number and temperature are graphically examined for both molybdenum disulfide and silicon dioxide. Skin friction coefficient and Nusselt number are numerically computed for various interesting parameters for both nanoparticles (SiO2 and MoS2). From obtained results it is noted that entropy optimization enhances against larger estimation of radiation and porosity parameters. Temperature and velocity have opposite behaviors for porosity parameter. Comparative study of present and with previous published literature are examined in tabulated form and found good agreement.

Entropy generation minimization (EGM) in magneto peristalsis with variable properties.

OBJECTIVE AND BACKGROUND: This article featuring the peristaltic transport of viscous material with variable properties (i.e. temperature dependent viscosity and thermal conductivity) through curved configuration. Fluid saturating through porous channel walls of uniform space. Entropy generation consideration here is to analyze irreversibility aspects. Channel boundaries retain the velocity and thermal slip conditions. METHOD: Wave frame of reference is attained with the utilization of long wavelength and small Reynolds number approach. Solution of the simplified coupled system of dimensionless constraints is obtained numerically. Detailed analysis of important quantities of interest has been presented in discussion portion. RESULTS: Entropy generation variation near center is very small whereas in the vicinity of the channel wall is larger. Bejan number has reverse variation as observed for entropy generation. CONCLUSION: Variable characteristics of viscosity has opposite impact on velocity and temperature is observed. It is also noticed small irreversibility effects are obtained for higher varying viscosity and thermal conductivity near the vicinity of the channel walls.

Electro-magneto flow of nanomaterial with irreversibility.

Here we discuss the analysis of irreversibility in electrical magnetohydrodynamic convective flow of nanomaterials over a stretchable surface. Energy equation deliberated through Joule heating, dissipation and heat source/sink. Furthermore features chemical reaction is also considered. Total entropy optimization is calculated. Salient features of thermophoresis effect and random motion of particles are studied. Nonlinear couple equations are converted to ordinary system by using the transformation. The obtained system are elucidated through ND solve technique. Salient features of pertinent variables on entropy optimization, velocity, Bejan number, concentration and temperature are discussed. Nusselt number, gradient of concentration and surface drag force are computationally calculated. Velocity and temperature show opposite behaviors via magnetic parameter. Electric and magnetic field parameters on entropy optimization have opposite results.

Theoretical and numerical investigation of Carreau-Yasuda fluid flow subject to Soret and Dufour effects.

BACKGROUND: Newtonian fluids can be categorized by a single coefficient of viscosity for specific temperature. This viscosity will change with temperature; it doesn't change with strain rate. Just a small group of liquids show such steady consistency. A fluid whose viscosity changes subject to relative flow velocity is called non-Newtonian liquids. Here we have summarized a result for the flow of Carreau-Yasuda fluid over a porous stretchable surface. Mixed convection is considered. Modeling of energy expression is performed subject to Soret and Dufour effects. METHOD: The nonlinear PDE's are changed to ODE's through suitable transformations and then solved for numerical solutions via Built-in shooting method (bvp4c). RESULTS: Variation of important variables is studied on the concentration, temperature and velocity fields. Tabular representation for study of skin friction and heat transfer rate is presented for important variables. Our results show that velocity decreases versus higher estimations of Weissenberg number, porosity parameter, buoyancy ratio and mixed convection parameter. Temperature decays via Weissenberg number and porosity parameter. Increase in concentration is noticed through higher Soret number and porosity parameter. Skin friction and heat transfer rate (Nusselt number) boosts versus larger porosity parameter and Prandtl number respectively while it decays against Weissenberg number and Dufour and Eckert number.

Irreversibility characterization and investigation of mixed convective reactive flow over a rotating cone.

BACKGROUND: Here we investigate the mixed convective unsteady magnetohydrodynamics chemically reactive flow of viscous liquid over a rotating cone. Energy attribution are deliberated in the presence of heat generation/absorption, viscous dissipation and Joule heating. Furthermore Irreversibility analysis with thermo-diffusion (Soret) effect and binary chemical reaction are also considered. Entropy optimization rate is computed with the help of thermodynamics second law. METHOD: The partial differential expression are reduced to ordinary system by using the suitable transformation. Here we have employed Newton built in shooting technique to get computational results for proposed nonlinear system. RESULTS: Influences of different interesting parameters on entropy optimization, velocity, Bejan number, concentration and temperature are discussed through graphs. The computational results of skin friction coefficient, gradient of temperature and Sherwood number are examined against different flow parameters through tables. From obtained outcome it is noticed that velocity and temperature have opposite behaviors for magnetic parameter and unsteadiness parameter. Concentration shows the opposite effect for Soret number and unsteadiness parameter. Bejan number and entropy generation rate hold opposite via larger Brinkman number, while have similar impact of temperature difference parameters. The assertion of recent work is established by comparison with previous published literature are discussed in tabulated form and found an excellent agreement.

Evaluation of entropy generation in cubic autocatalytic unsteady squeezing flow of nanofluid between two parallel plates.

BACKGROUND: Nanomaterials have advanced behaviors that make them possibly beneficial in various applications in mass and heat transports such as engine cooling, pharmaceutical processes, fuel cells, engine cooling and domestic refrigerator etc. Therefore here we deliberated the entropy generation in unsteady magnetohydrodynamic squeezing flow of viscous nanomaterials between two parallel plates. The upper plate is squeezing towards lower plate. The lower plate exhibits porous character. Energy attributes are discussed through heat flux, dissipation and Joule heating. Furthermore the irreversibility analysis with cubic autocatalysis chemical reaction is also accounted. METHODS: Nonlinear differential systems are converted to ordinary differential system by transformations. For convergent series solution the given system are solved by homotopy analysis method (HAM). RESULTS: Characteristics of various interesting variables on velocity, Bejan number, concentration, entropy optimization and temperature are deliberated through graphs. Gradient of velocity (Cfx) and Nusselt number (Nux) are numerically computed against various physical variables. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter. For larger squeezing parameter the velocity and temperature field are increased. CONCLUSIONS: The obtained results show that for larger squeezing parameter the velocity field boosts up. Velocity have opposite impact For larger magnetic and porosity parameters. Temperature is decreased for higher values of radiation parameter and Prandtl number. Temperature and concentration have same outcome for thermophoresis parameter. Entropy generation and Bejan number both quantitatively enhance versus radiation parameter, while reverse is hold for Brinkman number.

Numerical solution of MHD flow of power law fluid subject to convective boundary conditions and entropy generation.

BACKGROUND: The application of entropy optimization has consistently incorporated in traditional and industrial fields. The system is permanently sustainable, usually a final ideal structure may not exist in general, as common evolution shows trends in a long time. The measurement of the entropy generation related to heat transport can be proportional to temperature difference. The minimization of entropy generation through various parameters is our main purpose in this research article. Therefore, here we have discussed 2D flow of non-Newtonian liquid over a stretched surface with entropy optimization. Convective boundary conditions of temperature are implemented in the current flow phenomenon. Furthermore, viscous dissipation has been taken into account. METHOD: The involved nonlinear differential system has been tackled through ND solve numerical technique (Shooting method). RESULTS: The key observations are summarized as follows: (i) Velocity grows for larger estimations of power law index of fluid. (ii) Temperature θ˜(ξ) increases for Ec. (iii) Surface drag enhances for higher values of Ha. (iv) The temperature gradient NuxRe-1n+1 is inversely proportional to Ec and Ha. (v) Entropy NG(ξ) is larger for higher Ec and Ha while the opposite impact is examined for M. (vi) Bejan number Be decreases with Prand M, while it upsurges with Ha and Ec.