Search

The present study investigates the entropy generation of chemically reactive micropolar hybrid nanoparticle motion with mass transfer. Magnetic oxide (Fe3O4) and copper oxide (CuO) nanoparticles were mixed in water to form a hybrid nanofluid. The governing equations for velocity, concentration, and temperature are transformed into ordinary differential equations along with the boundary conditions. In the fluid region, the heat balance is kept conservative with a source/sink that relies on the temperature. In the case of radiation, there is a differential equation along with several characteristic coefficients that transform hypergeometric and Kummer's differential equations by a new variable. Furthermore, the results of the current problem can be discussed by implementing a graphical representation with different factors, namely the Brinkman number, porosity parameter, magnetic field, micropolar parameter, thermal radiation, Schmidt number, heat source/sink parameter, and mass transpiration. The results of this study are presented through graphical representations that depict various factors influencing the flow profiles and physical characteristics. The results reveal that an increase in the magnetic field leads to a reduction in velocity and entropy production. Furthermore, temperature and entropy generation rise with a stronger radiation parameter, whereas the Nusselt number experiences a decline. This study has several industrial applications in technology and manufacturing processes, including paper production, polymer extrusion, and the development of specialized materials. [ABSTRACT FROM AUTHOR]

Nanofluids have improved thermophysical properties compared to conventional fluids, which makes them promising successors in fluid technology. The use of nanofluids enables optimal thermal efficiency to be achieved by introducing a minimal concentration of nanoparticles that are stably suspended in conventional fluids. The use of nanofluids in technology and industry is steadily increasing due to their effective implementation. The improved thermophysical properties of nanofluids have a significant impact on their effectiveness in convection phenomena. The technology is not yet complete at this point; binary and ternary nanofluids are currently being used to improve the performance of conventional fluids. Therefore, this work aims to theoretically investigate the ternary nanofluid flow of a couple stress fluid in a vertical channel. A homogeneous suspension of alumina, cuprous oxide, and titania nanoparticles is formed by dispersing trihybridized nanoparticles in a base fluid (water). The effects of pressure gradient and viscous dissipation are also considered in the analysis. The classical ternary nanofluid model with couple stress was generalized using the fractal–fractional derivative (FFD) operator. The Crank–Nicolson technique helped to discretize the generalized model, which was then solved using computer tools. To investigate the properties of the fluid flow and the distribution of thermal energy in the fluid, numerical methods were used to calculate the solution, which was then plotted as a function of various physical factors. The graphical results show that at a volume fraction of 0.04 (corresponding to 4% of the base fluid), the heat transfer rate of the ternary nanofluid flow increases significantly compared to the binary and unary nanofluid flows. [ABSTRACT FROM AUTHOR]

In this paper, a heat generator with fluid agitation is developed and experimentally studied. This heat generator can convert kinetic energy from a wind turbine directly to thermal energy through the process of viscous dissipation—a process achieved through the agitation of the working fluid inside a container. In the experimental study, an electric motor (instead of a wind turbine) was used to provide the kinetic energy input to the heat generator. The torque, rotational speed, and temperature rise in the fluid were measured. Using the measured quantities, the efficiency of kinetic energy to sensible heat conversion was calculated. Experiments were conducted to investigate the effects of different impellers, rotational speeds, and working fluids, including distilled water, ethylene glycol (EG), and their respective nanofluids, with A l 2 O 3 nanoparticles at different concentrations. The study also found that the temperature rise in fluids due to viscous dissipation was influenced by the specific heat of the fluid, suggesting that the heat generator can be optimized for energy storage with high-specific-heat fluids, such as water, or for achieving a higher temperature rise with low-specific-heat fluids, such as ethylene glycol. The experimental results indicated that the heat generator was up to 90% efficient in converting kinetic energy to thermal energy. The study revealed that, for constant power input, the heat dissipation rate depends solely on the vessel's geometry, not the fluid properties. Optimizing the impeller design and baffles within the vessel is crucial for maximizing power input. For applications, a wind turbine can power this heat generator to provide heat to a house or a commercial building. [ABSTRACT FROM AUTHOR]

The resistance loss and energy consumption when fluid flows through a tee in an HVAC system are severe. To improve energy efficiency and reduce carbon emissions, a novel tee with a U-shaped deflector is proposed, supported by experiments and numerical simulations. The resistance reduction mechanism of the U-shaped deflector was analyzed according to the viscous dissipation principle and the field synergy principle. The resistance reduction of the novel tee with different deflector angles and a traditional tee were compared. The results show that the resistance loss of the tee was mainly due to the flow separation and deformation of the fluid in the main branch. The relationship between the local resistance coefficient and the diameter ratio of the main-branch pipe was exponential, and the relationship between the local resistance coefficient and the diameter ratio of the main straight pipe was linear. The total resistance loss reduction rate of the tee with the addition of a 26° deflector was the highest, reaching 72.4%, the volume-weighted average synergy angle increased by 1°, and the viscous dissipation decreased by 21.7%. This study provides a reference for the resistance reduction design of complex local components such as tees in HVAC systems. [ABSTRACT FROM AUTHOR]

The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow. [ABSTRACT FROM AUTHOR]

In the field of heat and mass transfer applications, non-Newtonian fluids are potentially considered to play a very important role. This study examines the magnetohydrodynamic (MHD) bioconvective Eyring–Powell fluid flow on a permeable cone and plate, considering the viscous dissipation (0.3 ≤ Ec ≤0.7), the uniform heat source/sink (−0.1 ≤ Q0 ≤ 0.1), and the activation energy (−1 ≤ E1 ≤ 1). The primary focus of this study is to examine how MHD and porosity impact heat and mass transfer in a fluid with microorganisms. A similarity transformation (ST) changes the nonlinear partial differential equations (PDEs) into ordinary differential equations (ODEs). The Keller Box (KB) finite difference method solves these equations. Our findings demonstrate that adding MHD (0.5 ≤ M ≤ 0.9) and porosity (0.3 ≤ Γ ≤ 0.7) effects improves microbial diffusion, boosting the rates of mass and heat transfer. Our comparison of our findings to prior studies shows that they are reliable. [ABSTRACT FROM AUTHOR]

This work aimed to numerically investigate the dynamic and thermal behavior of a fully developed, laminar, gaseous flow in a microchannel featuring a rhombic cross-section. Due to new fabrication techniques, microducts with rhombic cross-sections have recently received more attention. The momentum and energy balance equations were solved by using a commercial CDF code and assuming the slip and the H2 boundary conditions. The temperature jump between the wall and the adjacent fluid was also taken into account. The accuracy of the numerical results was checked by using the data available in the literature in terms of velocity profiles in the slip flow regime and the Nusselt number in the continuum flow regime. To also investigate the geometry effects on the fluid behavior, several values of the side angle of the rhombus were considered. The numerical results revealed that the rarefaction degree and geometrical properties significantly affected the Nusselt number. [ABSTRACT FROM AUTHOR]

The flow and heat transfer induced by an exponentially shrinking sheet with hybrid nanoparticles are investigated comprehensively in this paper. Nanoparticles are considered due to their unusual characteristics such as extraordinary thermal conductivity, which is significant in advanced nanotechnology, heat exchangers, material sciences, and electronics. The main objective of this research is to enhance heat transportation. The flow model is first transformed and simplified to a system of ordinary differential equations utilizing non-dimensional quantities and similarity functions. Then, the desired system is solved with the help of the Runge–Kutta numerical method and the shooting technique in MATLAB script. The results show that a stronger porosity parameter raises the temperature while diminishing the velocity. Additionally, they emphasize that augmentations in the magnetic parameter, Eckert number, radiation parameter, and the volume fractions of titanium dioxide and silver nanoparticles are all proportional to the temperature profile. [ABSTRACT FROM AUTHOR]

Several primary mechanisms are less utilized in engineering and recent technologies due to unsustainable heating. The impact of viscous dissipation and Joule heating is very important to examine current density and heat rate across a magnetized cylinder. The key objective of this examination was to insulate excessive heat around the cylinder. The present effort investigated the impact of viscous dissipations, Joule heating, and magnetohydrodynamics (MHD) on the transitory motion of convective-heat transport and magnetic flux features of dissipative flows throughout a magnetized and warmed cylinder at suitable places. The suggested turbulent dynamical structure of mathematics is offered for an associated method of partial differentiation equations impacted by boundary values. The complex equations are translated via non-dimensional shapes by using relevant non-dimensional numbers. The non-dimensional representation has been improved to make it easier to conduct uniform computational calculations. The computational answers for these linked dimensionalized formulations have been achieved using the Prandtl coefficient Pr, Joule heating parameter ζ , Eckert number E c , the magneto-force number ξ , the buoyancy parameter λ , and multiple additional predefined factors. The important contribution of this work is based on non-fluctuating solutions that are utilized to examine the oscillating behavior of shearing stress, rate of fluctuating heat transport, and rate of fluctuating magnetic flux in the presence of viscous dissipation and Joule heating at prominent angles. It is shown that the velocity of a fluid increases as the buoyancy parameter increases. The maximum frequency of heat transmission is illustrated for each Eckert variable. [ABSTRACT FROM AUTHOR]

The performance of the calorimetric microflow sensor is closely related to the thermal sensing part design, including structure parameter, heater temperature, and operation environment. In this paper, several measures to enhance the performance of the calorimetric microflow sensor were proposed and further verified by numerical simulations. The results demonstrate that it is more favorable to reduce the negative impact of flow separation as the space between detectors and heater is set to be 1.6 μm so as to improve the accuracy of the sensor. With an appropriate gap, the front arranged obstacle of the upstream detector can effectively widen the measure range of the sensor, benefiting from the decrease in upstream viscous dissipation. Compared to a cantilever structure, the resonances can be effectively suppressed when the heater and detectors are designed as bridge structures. In particular, the maximum amplitude of the bridge structure is only 0.022 μm at 70 sccm, which is 53% lower than that of the cantilever structure. The optimized sensor widens the range by 14.3% and significantly increases the sensitivity at high flow rates. Moreover, the feasibility of the improved measures is also illustrated via the consistency of the trend between the simulation results and experimental ones. [ABSTRACT FROM AUTHOR]

Nanofluid lubrication and machining are challenging and significant tasks in manufacturing industries that are used to control the removal of a material from a surface by using a cutting tool. The introduction of a nanofluid to the cutting zone provides cooling, lubricating, and chip-cleaning benefits that improve machining productivity. A nanofluid is a cutting fluid that is able to remove excessive friction and heat generation. Chemical reactions and temperature-dependent density are essential in the thermal behavior of a nanofluid. The present study presents a careful inspection of the chemical reactions, temperature-dependent density, viscous dissipation, and thermophoresis during the heat and mass transfer of a nanofluid along a magnetically driven sheet. The physical attitude of viscous dissipation and the chemical reaction improvement rate in magneto-nanofluid flow is the primary focus of the present research. By applying the proper transformation, nonlinear partial differential expressions are introduced to the structure of the ordinary differential framework. The flow equations are simplified into nonlinear differential equations, and these equations are then computationally resolved via an efficient computational technique known as the Keller box technique. Flow factors like the Eckert number, reaction rate, density parameter, magnetic force parameter, thermophoretic number, buoyancy number, and Prandtl parameter governing the velocity, temperature distribution, and concentration distribution are evaluated prominently via tables and graphs. The novelty of the current study is in computing a heat transfer assessment of the magneto-nanofluid flow with chemical reactions and temperature-dependent density to remove excessive friction and heating in cutting zones. Nanofluids play significant roles in minimum quantity lubrication (MQL), enhanced oil recovery (EOR), drilling, brake oil, engine oil, water-miscible cutting fluids, cryogenic cutting fluids, controlled friction between tools and chips and tools and work, and conventional flood cooling during machining processes. [ABSTRACT FROM AUTHOR]

Numerical simulations have been performed to investigate the influence of constant volumetric heat generation and viscous dissipation on the unsteady natural convection flow of an incompressible Newtonian fluid contained in a rectangular cavity. The left vertical wall of the cavity is cooled, while the right vertical wall is heated, and the bottom and top walls are adiabatic. A numerical technique based on the implicit finite difference method (IFDM), along with an upwind finite difference scheme and an iterative successive over relaxation (SOR) technique, is employed to solve the governing equations numerically. The effect of physical parameters, namely the modified Rayleigh number ( 10 3 ≤ R a ≤ 10 7 ), aspect ratio ( 1 ≤ A ≤ 4 ), Prandtl number ( P r = 0.7 , 1.0 , 6.2 , 15), volumetric internal heat generation parameter ( Q λ = 0 , 1), and Eckert number ( 0 ≤ E c ≤ 10 − 6 ), on the streamlines and isotherms are discussed graphically. Variations of maximum stream function, as well as average and local Nusselt number, are also discussed. The results show that the increase in Eckert number from 0 to 10 − 4 causes the average heat transfer to decrease, while P r = 0.71 , R a = 10 4 , and Q λ = 0 . Additionally, the average heat transfer decreases as the cavity width increases from 1 to 4, while P r = 0.71 , R a = 5 × 10 4 , E c = 10 − 6 and Q λ = 1 . The results of the numerical model used here are in excellent accord with earlier findings. [ABSTRACT FROM AUTHOR]

This paper presents a non-isothermal, non-Newtonian Computational Fluid Dynamics (CFD) model for the mixing of a highly viscous polymer suspension in a partially filled sigma blade mixer. The model accounts for viscous heating and the free surface of the suspension. The rheological model is found by calibration with experimental temperature measurements. Subsequently, the model is exploited to study the effect of applying heat both before and during mixing on the suspension's mixing quality. Two mixing indexes are used to evaluate the mixing condition, namely, the Ica Manas-Zlaczower dispersive index and Kramer's distributive index. Some fluctuations are observed in the predictions of the dispersive mixing index, which could be associated with the free surface of the suspension, thus indicating that this index might not be ideal for partially filled mixers. The Kramer index results are stable and indicate that the particles in the suspension can be well distributed. Interestingly, the results highlight that the speed at which the suspension becomes well distributed is almost independent of applying heat both before and during the process. [ABSTRACT FROM AUTHOR]

This study addresses heat and mass transfer of electrical magnetohydrodynamics (MHD) Williamson fluid flow over the moving sheet. The mathematical model for the considered flow phenomenon is expressed in a set of partial differential equations. Later, linear and nonlinear ordinary differential equations (ODEs) are obtained. The finite element method tackles a reduced system of ODEs with boundary conditions. Galerkin weighted residuals and constructs of weak formulations constitute the basis of this method. An iterative procedure is considered for handling nonlinear terms in a given system of ODEs. Some results acquired using the finite element method are compared with those reported in previous research via the Matlab solver bvp4c in order to validate the obtained solutions of ODEs. It is seen that the velocity profile is decayed by enhancing the Wiesenberg number. The finite element method also converges to an accurate solution by increasing the number of elements, whereas Matlab solver bvp4c produces accurate results on small grid points. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures. [ABSTRACT FROM AUTHOR]

The present work has mathematically modeled the peristaltic flow in nanofluid by using thermal radiation, induced a magnetic field, double-diffusive convection, and slip boundary conditions in an asymmetric channel. Peristalsis propagates the flow in an asymmetric channel. Using the linear mathematical link, the rheological equations are translated from fixed to wave frames. Next, the rheological equations are converted to nondimensional forms with the help of dimensionless variables. Further, the flow evaluation is determined under two scientific assumptions: a finite Reynolds number and a long wavelength. Mathematica software is used to solve the numerical value of rheological equations. Lastly, the impact of prominent hydromechanical parameters on trapping, velocity, concentration, magnetic force function, nanoparticle volume fraction, temperature, pressure gradient, and pressure rise are evaluated graphically. [ABSTRACT FROM AUTHOR]

The current analysis discusses Jeffery nanofluid's thermally radiative flow with convection over a stretching wedge. It takes into account the Brownian movement and thermophoresis of the Buongiorno nanofluid model. The guiding partial differential equations (PDEs) are modified by introducing the symmetry variables, leading to non-dimensional ordinary differential equations (ODEs). To solve the generated ODEs, the MATLAB function bvp4c is implemented. Examined are the impacts of different flow variables on the rate of transmission of heat transfer (HT), temperature, mass, velocity, and nanoparticle concentration (NC). It has been noted that the velocity and mass transfer were increased by the pressure gradient factor. Additionally, the thermal boundary layer (TBL) and nanoparticle concentration are reduced by the mixed convection (MC) factor. In order to validate the present research, the derived numerical results were compared to previous findings from the literature while taking into account the specific circumstances. It was found that there was good agreement in both sets of data. [ABSTRACT FROM AUTHOR]

This study investigates magnetohydrodynamic (MHD) nanofluid flow through a stretching vertical surface influenced by Joule heating, chemical reaction, viscosity dissipation, thermal radiation, and activation energy. Such physical problems have significance in applied mathematics, engineering, and physics, and they are frequently found in symmetrical scenarios. A transformation of the similarity technique is used to reduce the difficulty of the boundary layer equations for nonlinear motion, energy, solute, and nanoparticle concentration. To identify these variations with local similarity, we employ symmetry analysis. The altered equations were solved using the shooting technique with Matlab bvp4c. It was found that raising the Schmidt number increases the impact of temperature and concentration profiles. As the Biot number and thermal radiation rise, the local Nusselt number, local Sherwood number, and skin friction increase as well. The comparative table shows good agreement with the current results. [ABSTRACT FROM AUTHOR]

This study explores the influence of an inclined magnetic field and variable viscosity on the entropy generation in steady flow of a couple stress fluid in an inclined channel. The walls of the channel are stationary and non-isothermal. The fluid flow is driven due to pressure gradient and gravitational force. Reynold's model for temperature-dependent viscosity was used. The dimensionless, non-linear coupled equations of momentum and energy was solved, and we obtained an analytical solution for the velocity and temperature fields. The entropy generation and Bejan number were evaluated. The variation of pertinent parameters on flow quantities was discussed graphically. The rate of volume flow, skin friction coefficient, and Nusselt number at the surfaces of the channel were calculated and their variations were discussed through surface graphs. From the results, it is noticed that the entropy generation rate can be minimized by increasing the magnetic field and the temperature difference parameters. The findings of the current study in some special cases are in precise agreement with the previous investigation. [ABSTRACT FROM AUTHOR]

This communication predominately discusses the rheological attributes of the Darcy–Forchheimer flow of a nanoliquid over a stretchy sheet with a magnetic impact. The present model considers the two diverse nanoparticles, such as C u and A g , and water as a base liquid. The heat equation accounts for the consequences of thermal radiation and a nonlinear heat sink/source when evaluating heat transmission phenomena. The current mechanical system is represented by higher-order PDEs, which are then remodeled into nonlinear higher-order ODEs that employ appropriate symmetry variables. The current mathematical systems are numerically computed by implementing the bvp4c technique. The characteristic attitudes of the related pertinent factors on the non-dimensional profiles are sketched via the figures, tables, and charts. The analysis predicts that the speed of the nanoliquid particles becomes slower when there is more presence of a magnetic field and injection/suction parameters. The growing amount of radiation is also pointed out, and the Eckert number corresponds to enriching the thermal profile. [ABSTRACT FROM AUTHOR]

The present exploration discusses the combined effect of non-linear thermal radiation along with viscous dissipation and magnetic field through a porous medium. A distinctive aspect of our work is the simultaneous use of porous wall and a porous material. The impact of thermal rays is essential in space technology and high temperature processes. At the point when the temperature variation is very high, the linear thermal radiation causes a noticeable error. To overcome such errors, nonlinear thermal radiation is taken into account. The coupled system of ordinary differential equations are derived from the partial differential equation. The dimensional model equations are transformed into non-dimensional forms using some appropriate non-dimensional transformation and the resulting nonlinear equations are solved numerically by executing persuasive numerical technique R-K integration procedure with the shooting method. Graphical analysis were used to assess the consequences of engineering factors for the momentum, angular velocity, concentration and temperature profiles. The skin friction values, local Sherwood and Nusselt number are the fascinating physical quantities whose numerical data are computed and validated against different parametric values. The vortex viscosity parameter and spin gradient viscosity parameter shows the reverse phenomenon on micro-rotation profile. The thermal radiation phenomena flattens the temperature and speeds up the heat transfer rate in the lower wall and a peak in the concentration is observed for the P e m > > 1 due to the inertial force. The Variational Iteration Method (VIM) and Adomian Decomposition Method (ADM) are the two analytical approach which have been incorporated here to decipher the non linear equations for showing better approximity. Comparisons with existing studies are scrutinized very closely and they are determined to be in good accord. [ABSTRACT FROM AUTHOR]

Nanoparticles have presented various hurdles to the scientific community during the past decade. The nanoparticles dispersed in diverse base fluids can alter the properties of fluid flow and heat transmission. In the current examination, a mathematical model for the 2D magnetohydrodynamic (MHD) Darcy–Forchheimer nanofluid flow across an exponentially contracting sheet is presented. In this mathematical model, the effects of viscous dissipation, joule heating, first-order velocity, and thermal slip conditions are also examined. Using similarity transformations, a system of partial differential equations (PDEs) is converted into a set of ordinary differential equations (ODEs). The problem is quantitatively solved using the three-step Lobatto-three formula. This research studied the effects of the dimensionlessness, magnetic field, ratio of rates, porosity, Eckert number, Prandtl number, and coefficient of inertia characteristics on fluid flow. Multiple solutions were observed. In the first solution, the increased magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters reduce the velocity field along the η-direction. In the second solution, the magnetic field, porosity parameter, slip effect, and volume percentage of the copper parameters increase the η-direction velocity field. For engineering purposes, the graphs show the impacts of factors on the Nusselt number and skin friction. Finally, the stability analysis was performed to determine which solution was the more stable of the two. [ABSTRACT FROM AUTHOR]

This article describes a two-dimensional steady laminar boundary layer flow and heat mass transfer caused by a non-Newtonian nanofluid due to a horizontally stretching sheet. The non-dimensional parameters take into consideration and regulate the effects of convective boundary condition, slip velocity, Brownian motion, thermophoresis and viscous dissipation. The thermal radiation, which affects the flow's thermal conductivity and the nanofluid's variable viscosity are also taken into consideration. We propose that a hot fluid could exist beneath the stretching sheet's bottom surface, which could aid in warming the surface via convection. The physical boundary conditions are non-dimensionalized, as are the governing transport set of nonlinear partial differential equations. By using the shooting approach, numerical values for dimensionless velocity, temperature and nanoparticle concentration are achieved. Distributions of velocity, temperature and concentration are plotted against a number of newly important governing factors, and the outcomes are then provided in accordance with those graphs. Additionally, the local skin-friction coefficient, the local Sherwood number and the local Nusselt number are discussed in order to further clarify and thoroughly explain the current problem. In order to validate the numerical results, comparisons are made with previously published data in the literature. There is a really good accord. Additionally, the current work has implications in the nanofluid applications. [ABSTRACT FROM AUTHOR]

This study deals with the analysis of the heat and velocity profile of the fractional-order Oldroyd-B bio-nanofluid within a bounded channel. The study has a wide range of scope in modern fields of basic science such as medicine, the food industry, electrical appliances, nuclear as well as industrial cooling systems, reducing pollutants, fluids used in the brake systems of vehicles, etc. Oldroyd-B fluid is taken as a bio-nanofluid composed of base fluid (blood) and copper as nanoparticles. Using the fractional-order Oldroyd-B parameter, the governing equation is generalized from an integer to a non-integer form. A strong approach, i.e., a finite difference scheme, is applied to discretize the model, because the fractional approach can well address the physical phenomena and memory effect of the flow regime. Therefore, a Caputo fractional differentiation operator is used for the purpose. The transformations for the channel flow are utilized to transfigure the fractional-order partial differential equations (PDEs) into non-dimension PDEs. The graphical outcomes for non-integer ordered Oldroyd-B bio-nanofluid dynamics and temperature profiles are navigated using the numerical technique. These results are obtained under some very important physical conditions applied as a magnetic field effect, variable thermal conductivity, permeable medium, and heat source/sink. The results show that the addition of (copper) nanoparticles to (blood) base fluids enhances the thermal conductivity. For a comparative study, the obtained results are compared with the built-in results using the mathematical software MAPLE 2016. [ABSTRACT FROM AUTHOR]

This article discusses the flow of a non-Newtonian Carreau nanoliquid across a stretching radiative nonlinear sheet that is exposed to a variable heat flux. Analysis is done with changing thermal conductivity since it affects how heat and mass transfer occur. Nanoparticles are modelled using the Brownian motion and the thermophoresis phenomenon. The introduction of a similar solution to our challenge, as obtained by our paper, received significant attention. To create a dimensionless system, the governing partial differential equations are subjected to the mathematical model's convenient similarity transformations after it has been developed. The numerical solution of the coupled highly nonlinear ordinary differential equations characterizing velocity, temperature and nanoparticles concentration is shown using an effective shooting approach. Additionally, all factors affecting the situation that could increase the effectiveness of cooling operations will be looked into. Results for velocity, the thermal field, the concentration of nanoparticles, the skin-friction coefficient, and the local Nusselt and Sherwood numbers are provided and explored. Tables and graphics will be used to illustrate the paper's conclusions. Results are also given in comparison to existing literature. Excellent agreement has been reached. Furthermore, it is clear that the local Sherwood number, the local Nusselt number, and the skin friction coefficient are all observed to increase as the power law index does. [ABSTRACT FROM AUTHOR]

The study of rotating-disk heat-flow problems is relevant to computer storage devices, rotating machineries, heat-storage devices, MHD rotators, lubrication, and food-processing devices. Therefore, this study investigated the effects of a Hall current and motile microorganisms on nanofluid flow generated by the spinning of a disk under multiple slip and thermal radiation conditions. The Buongiorno model of a nonhomogeneous nanofluid under Brownian diffusion and thermophoresis was applied. Using the Taylor series, the effect of Resseland radiation was linearized and included in the energy equation. By implementing the appropriate transformations, the governing partial differential equations (PDEs) were simplified into a two-point ordinary boundary value problem. The classical Runge–Kutta dependent shooting method was used to find the numerical solutions, which were validated using the data available in the literature. The velocity, motile microorganism distribution, temperature, and concentration of nanoparticles were plotted and comprehensively analyzed. Moreover, the density number, Sherwood number, shear stresses, and Nusselt number were calculated. The radial and tangential velocity declined with varying values of magnetic numbers, while the concentration of nanoparticles, motile microorganism distribution, and temperature increased. There was a significant reduction in heat transfer, velocities, and motile microorganism distribution under the multiple slip conditions. The Hall current magnified the velocities and reduced the heat transfer. Thermal radiation improved the Nusselt number, while the thermal slip conditions reduced the Nusselt number. [ABSTRACT FROM AUTHOR]

In this study, the entropy formation of an electromagnetohydrodynamic hybrid nanofluid at a stagnation point flow towards a stretched surface in the presence of melting heat transfer, second-order slip, porous medium, viscous dissipation and thermal radiation are investigated. Hybrid nanoparticles alumina (Al2O3) and copper (Cu) are considered, with the base fluid water (H2O). Similarity transformations are used to address the governing partial differential equations (PDEs) that lead to the corresponding ordinary differential equations. The resulting ODEs are solved by employing bvp4c solver numerically in the MATLAB package. The effects of temperature, transport, production of entropy and Bejan number B e are graphically exhibited. Higher radiation parameters R and an electric field E lead to an increase in fluid temperature. The velocity boundary layer is lowered by the magnetic field and porous media parameters. The opposite behaviour is observed in the electric field E. As a result, hybrid nanofluid has numerous uses in engineering cosmetics, automotive industry, home industry, for cancer treatment, food packaging, pharmaceuticals, fabrics, paper plastics, paints, ceramics, food colorants, electronics, heat exchangers, water purification, lubricants and soaps as well. [ABSTRACT FROM AUTHOR]

The main theme of the present study is to analyze numerically the effects of the magnetic field on the hybrid nanofluid flow over a flat elastic surface. The effects of the thermal and velocity slips are also analyzed in view of the hybrid nanofluid flow. It is considered a combination of titanium oxide (TiO2) and copper oxide (CuO) nanoparticles that are suspended in the incompressible and electrically conducting fluid (water). The behavior of the Brownian motion of the nanoparticles and the thermophoretic forces are contemplated in the physical and mathematical formulations. Moreover, the impact of the Joule heating and viscous dissipation are also discussed using the energy equation. The mathematical modeling is simulated with the help of similarity variables. The resulting equations are solved using the Keller–Box method with a combination of finite difference schemes (FDSs). Hybrid nanofluids provide significant advantages over the usual heat transfer fluids. Therefore, the use of nanofluids is beneficial to improve the thermophysical properties of the working fluid. All of the results are discussed for the various physical parameters involved in governing the flow. From the graphical results, it is found that the hybrid nanoparticles improve the concentration, temperature, and velocity profiles, as well as the thickness of the relevant boundary layer. The conjunction of a magnetic field and the velocity slip, strongly opposes the fluid motion. The boundary layer thickness and concentration profile are significantly reduced with the higher levels of the Schmidt number. [ABSTRACT FROM AUTHOR]

Fluid flow through a sphere has practical applications in numerous areas of technology, for instance, mineralogy, food engineering, and oilfield drilling. The goal of this paper is to look at how quadratic thermal radiation and activation energy affect the dissipative flow of hybrid nanofluids around a sphere with the heat source parameter. bvp4c (a MATLAB in-built function) is used to solve a system of nonlinear ordinary differential equations, which is the transformed version of the system of governing equations. Using multiple linear regression, the effects of relevant parameters on the mass transfer rate, the Nusselt number, and the skin friction coefficient are investigated. The key findings of this study are that increasing the radiation parameter improves the fluid temperature and increasing the activation energy parameter improves the fluid concentration. When the Eckert number and the parameter of the heat source are increased, the convective heat transmission is reduced. It appears that the magnetic field parameter reduces the shear stress near the surface. It is discovered that increasing the volume percentage of nanoparticles increases the skin friction coefficient and increasing the Schmidt number increases the mass transfer rate. Furthermore, the current results are validated against previously published data. [ABSTRACT FROM AUTHOR]

Nanofluids have gained prominence due to their superior thermo-physical properties. The current paper deals with MHD nanofluid flow over a non-linear stretchable surface of varying thickness in the presence of an electric field. We investigated the effects of nanometer-sized copper (Cu) particles in water (base fluid) as a nanofluid, as well as non-linear thermal radiation, variable fluid viscosity, Joule heating, viscous dissipation, and non-uniform heat flux. The current study's aim is influenced by the immense applications in industry and machine building. It has been observed that linear stretching sheets have been extensively used in heat transfer research. Moreover, no effort has been made yet to model a non-linear stretching sheet with variable thickness. Furthermore, the effects of electromagnetohydrodynamics (EMHD) boundary-layer flow of a nanofluid with the cumulative impact of thermal radiation, variable viscosity, viscous dissipation, Joule heating, and variable heat flux have been investigated. Sheets with variable thicknesses are practically significant in real-life applications and are being used in metallurgical engineering, appliance structures and patterns, atomic reactor mechanization and paper production. To investigate the physical features of the problem, we first examined the model and identified all the physical properties of the problem. This problem has been formulated using basic laws and governing equations. The partial differential equations (PDEs) that govern the flow are converted into a system of non-dimensional ordinary differential equations (ODE's), using appropriate transformations. The Adam–Bashforth predictor-corrector technique and Mathematica software are utilized to numerically solve the resulting non-dimensionalized system. The interaction of various developing parameters with the flow is described graphically for temperature and velocity profiles. It is concluded that the velocity of nanoparticles declines as the intensity of the magnetic field increases. However, the temperature of the nanomaterials rises, as increasing the values of the electric field also increases the velocity distribution. The radiation parameter enhances the temperature field. The temperature of the fluid increases the occurrence of space- and time-dependent parameters for heat generation and absorption and radiation parameters. [ABSTRACT FROM AUTHOR]

Partial filling of porous medium insert in a channel alleviates the tremendous pressure drop associated with a porous medium saturated channel, and enhances heat transfer at an optimum fraction of porous medium filling. This study pioneered an investigation into the viscous dissipative forced convective heat transfer in a parallel-plate channel, partially occupied with a porous medium at the core, under local thermal non-equilibrium condition. Solving the thermal energy equation along the Darcy–Brinkman equation, new exact temperature fields and Nusselt number are presented under symmetrical isoflux thermal boundary condition. Noteworthy is the heat flux bifurcation at the interface between the clear fluid and porous medium driven by viscous dissipation, in cases where the combined hydrodynamic resistance to fluid flow and thermal resistance to fluid conduction is considerable in low Darcy number porous medium insert. However, viscous dissipation does not affect the qualitative variation of the Nusselt number with the fraction of porous medium filling. By using Al2O3-Water nanofluid as the working fluid in a uniformly heated microchannel, partially filled with an optimum volume fraction of porous medium, the heat transfer coefficient improves as compared to utilizing water. The accompanied viscous dissipation however has a more adverse impact on the heat transfer coefficient of nanofluids with an increasing Reynolds number. [ABSTRACT FROM AUTHOR]

The reasons why the model of non-Newtonian nanofluids is more applicable than other models, particularly those that take the porous medium into account, are studied here. Thus, we looked at the heat and mass transfer features of a non-Newtonian Williamson nanofluid flow due to a stretched sheet under the impact of chemical reactions, slip velocity, viscous dissipation, and the magnetic field in this article. The main focus is on a situation in which the properties of Williamson nanofluid, such as viscosity and thermal conductivity, change with temperature. After utilizing the shooting technique, a numerical solution to the suggested problem is provided. As a result, several graphs have been drawn to highlight how various physical characteristics that arise in the problems affect velocity, temperature, and concentration profiles. It was discovered that the heat and mass transmission processes are affected by the viscous dissipation phenomena, the slip velocity assumption, and the magnetic field. Theoretical and numerical results show a high level of qualitative agreement. [ABSTRACT FROM AUTHOR]

The radiated flow of magnetized viscous fluid subject to the viscous dissipation phenomenon is numerically studied. The radiative phenomenon is addressed with nonlinear relations. Further, analysis is performed by using the slip effects and convective thermal flow constraints. The transformed problem is numerically evaluated using the Keller Box method. The physical parameter effects, such as the magnetic parameter for the velocity profile, Prandtl number, Brownian motion parameter and Biot number for the energy profile and Lewis number, and the thermophoresis parameter for the concentration profile are discussed. The obtained results suggest applications in enhancing the heat transfer phenomenon, thermal system, energy generation, heat transmission devices, power generation, chemical reactions, etc. [ABSTRACT FROM AUTHOR]

This paper aims to develop a review of the electrokinetic flow in microchannels. Thermal characteristics of electrokinetic phenomena in microchannels based on the Poisson–Boltzmann equation are presented rigorously by considering the Debye–Hückel approximation at a low zeta potential. Several researchers developed new mathematical models for high electrical potential with the electrical double layer (EDL). A literature survey was conducted to determine the velocity, temperature, Nusselt number, and volumetric flow rate by several analytical, numerical, and combinations along with different parameters. The momentum and energy equations govern these parameters with the influences of electric, magnetic, or both fields at various preconditions. The primary focus of this study is to summarize the literature rigorously on outcomes of electrokinetically driven flow in microchannels from the beginning to the present. The possible future scope of work highlights developing new mathematical analyses. This study also discusses the heat transport behavior of the electroosmotically driven flow in microchannels in view of no-slip, first-order slip, and second-order slip at the boundaries for the velocity distribution and no-jump, first-order thermal-slip, and second-order thermal-slip for the thermal response under maintaining a uniform wall-heat flux. Appropriate conditions are conferred elaborately to determine the velocity, temperature, and heat transport in the microchannel flow with the imposition of the pressure, electric, and magnetic forces. The effects of heat transfer on viscous dissipation, Joule heating, and thermal radiation envisage an advanced study for the fluid flow in microchannels. Finally, analytical steps highlighting different design aspects would help better understand the microchannel flow's essential fundamentals in a single document. They enhance the knowledge of forthcoming developmental issues to promote the needed study area. [ABSTRACT FROM AUTHOR]

Engineers and researchers are interested in the study of nonlinear convection, viscous dissipation, and Joule heating in various flow configurations due to their various applications in engineering processes. That is why the present study deals with the influence of nonlinear convection, viscous, and Joule dissipation of the temperature and velocity profile of incompressible fluid over a flat plate. In this study, the magnetic field acts perpendicular to the fluid flow and is supposed to be of uniform magnitude. Further, the Newtonian fluid, which is electrically conducting, passes over an infinite vertical flat plate under an oscillatory motion. The term representing the influence of the nonlinear convection phenomenon is integrated into the Navier–Stokes equation. The governing equations of the mentioned study were modeled in the form of non-linear PDEs and modified as non-dimensional equations via appropriate scaling analyses, which resulted in coupled and non-linear PDEs. For the numerical solution of the transformed non-linear PDEs, the finite difference method was applied. Finally, we present the effects of various flow parameters via graphical illustrations. [ABSTRACT FROM AUTHOR]

Heat and mass transfer study of hybrid nanomaterial Casson fluid with time-dependent flow over a vertical Riga sheet was deliberated under the stagnation region. In the presence of the Riga sheet in fluid flow models, this formulation was utilized to introduce Lorentz forces into the system. We considered the three models of hybrid nanomaterial fluid flow: namely, Yamada Ota, Tiwari Das, and Xue models. Two different nanoparticles, namely, SWCNT and MWCNT under base fluid (water) were studied. Under the flow suppositions, a mathematical model was settled using boundary layer approximations in terms of PDEs (partial differential equations). The system of PDEs (partial differential equations) was reduced into ODEs (ordinary differential equations) after applying suitable transformations. The reduced system, in terms of ODEs (ordinary differential equations), was solved by a numerical scheme, namely, the bvp4c method. The inspiration of the physical parameters is presented through graphs and tables. The curves of the velocity function deteriorated due to higher values of M. The Hartmann number is a ratio of electric force to viscous force. The electric forces increased due to higher values of the modified Hartmann number, ultimately declining the velocity function. The skin friction was reduced due to an incremental in ϖ , while the Nusselt number raised with higher values of ϖ. Physically, the Eckert number increased, which improved kinetic energy and, as a result, skin friction declined. The heat transfer rate increased as kinetic energy increased, and the Eckert number increased. The skin friction reduced due to physical enhancement of β 1 , the shear thinning was enhanced which reduced the skin friction. [ABSTRACT FROM AUTHOR]

Here, our main aim is to examine the impacts of Dufour and Soret in a radiative Darcy–Forchheimer flow. Ohmic heating and the dissipative features are outlined. The characteristics of the thermo-diffusion and diffusion-thermo effects are addressed. A binary chemical reaction is deliberated. To examine the thermodynamical system performance, we discuss entropy generation. A non-linear differential system is computed by the finite difference technique. Variations in the velocity, concentration, thermal field and entropy rate for the emerging parameters are scrutinized. A decay in velocity is observed for the Forchheimer number. Higher estimation of the magnetic number has the opposite influence for the velocity and temperature. The velocity, concentration and thermal field have a similar effect on the suction variable. The temperature against the Dufour number is augmented. A decay in the concentration is found against the Soret number. A similar trend holds for the entropy rate through the radiation and diffusion variables. An augmentation in the entropy rate is observed for the diffusion variable. [ABSTRACT FROM AUTHOR]

The nature of this prevailing inquisition is to scrutinize the repercussion of MHD mixed convective flow of CNTs/ A l 2 O 3 nanofluid in water past a heated stretchy plate with injection/suction, heat consumption and radiation. The Joule heating and viscous dissipation are included in our investigation. The Navier–Stokes equations are implemented to frame the governing flow expressions. These flow expressions are non-dimensioned by employing suitable transformations. The converted flow expressions are computed numerically by applying the MATLAB bvp4c procedure and analytically by the HAM scheme. The impacts of relevant flow factors on fluid velocity, fluid temperature, skin friction coefficient, and local Nusselt number are illustrated via graphs, tables and charts. It is unequivocally shown that the fluid speed declines when escalating the size of the magnetic field parameter; however, it is enhanced by strengthening the Richardson number. The fluid warmness shows a rising pattern when enriching the Biot number and heat consumption/generation parameter. The findings conclusively demonstrate that the surface drag force improves for a larger scale of Richardson number and is suppressed when heightening the unsteady parameter. In addition, it is evident from the outcomes that the heat transfer gradient decreases to increase the quantity of the Eckert number in the convective heating case; however, the opposite nature is obtained in the convective cooling case. Our numerical results are novel, unique and applied in microfluid devices such as micro-instruments, sleeve electrodes, nerve growth electrodes, etc. [ABSTRACT FROM AUTHOR]

The present analysis has interesting applications in physiology, industry, engineering and medicine. Peristaltic pumps acquire an elliptical cross-section during motion. Peristaltic pumps, roller pumps and finger pumps also have highly useful applications. Transportation through these pumps provides an effective fluid movement and the substance remains separate from the duct walls. Convection and diffusion analyses were executed with accentuated viscous dissipation for the non-Newtonian flow that occurs inside a duct. The viscous effects are reviewed with an integrated convection and diffusion analysis that elucidates in-depth heat flux. Viscous dissipation appears to be the primary cause of increased heat generation. The Cartesian coordinate system is availed to develop this problem under consideration. A dimensionless set of coupled partial differential equations is attained by utilizing the relevant transformations that eventually simplify this complex problem. These coupled equations are solved step by step with a consideration of a polynomial solution method for coupled equations. The unfolded graphical outcomes of velocity, temperature and concentration reveal an axial symmetric flow. A higher rate of convection is observed due to viscous effects. Both the velocity and temperature profiles have an increasing function of Q. [ABSTRACT FROM AUTHOR]

Nanofluids are extremely useful to investigators due to their greater heat transfer rates, which have significant applications in multiple industries. The primary objective of this article is to look into the effect of viscous dissipation in Sisko nano liquid flow with gold Au nanoparticles on a porous stenosis artery. Heat transfer properties were explored. Blood was utilized as a base fluid for nanoparticles. To renovate the governing nonlinear PDEs into nonlinear ODEs, appropriate transformations were used. The bvp4c-based shooting method, via MATLAB, was used to determine the numerical results of the nonlinear ODEs. Furthermore, flow forecasts for each physical quantity were explored. To demonstrate the physical influences of flow constraints versus presumed flow fields, physical explanations were used. The findings demonstrated that the velocity contour improved as the volume fraction, curvature, power law index, and material parameter upsurged. For the Prandtl number, the volume fraction of nanoparticles, the index of the power law, and the temperature profile of the nanofluid declined. Furthermore, the drag force and transfer of the heat were also investigated as explanations for influences on blood flow. Further, the Nusselt number reduced and the drag force enhanced as the curvature parameter values increased. The modeling and numerical solutions play an impressive role in predicting the cause of atherosclerosis. [ABSTRACT FROM AUTHOR]

The stagnation point flow of unsteady compressible Casson hybrid nanofluid flow over a vertical stretching sheet was analyzed. The comparative study of Yamada Ota, Tiwari Das, and Xue hybrid nanofluid models was performed. The Lorentz force was applied normal to flow directions. The effect of nonlinear radiation was studied. We considered the SWCNT (signal wall carbon nanotube) and MWCNT (multi-wall carbon nanotube) with base liquid (water). Under the flow suppositions, a mathematical model was settled by means of boundary layer approximations in terms of partial differential equations. The suitable transformation was developed by using the lie symmetry method. Partial differential equations were transformed into ordinary differential equations by suitable transformations. The dimensionless system was elucidated through a numerical technique named bvp4c. The impacts of pertinent flow parameters on skin friction, Nusselt number, and temperature and velocity distributions were depicted through tabular form as well as graphical form. In this study, the Yamada Ota model achieved a higher heat transfer rate compared to the Tiwari Das and Xue hybrid nanofluid models. The skin friction ( C fx Re − 1 / 2 ) increased and temperature gradient ( Nu x Re − 1 / 2 ) declined due to the increment of solid nanoparticle concentration ( ϕ 2 ). Physically, skin friction increased because the higher values of the solid nanoparticles increased resistance to the fluid motion. [ABSTRACT FROM AUTHOR]

A numerical analysis of an unsteady radiative and viscous dissipative fluid flow across a semi-infinite oscillating vertical plate with a constant temperature and mass diffusion is examined here. The fluid under consideration is optically thin gray, emitting, heat-retaining, and non-dispersing. A finite-difference approach known as the Crank−Nicolson strategy was applied to find the solution to the limitless governing equations. Applications of such engineering problems can be found in fields such as aerospace, solar power, the cooling of nuclear reactors, and chemical and mechanical engineering. Based on the computational solutions, the impacts of distinct physical parameters, such as velocity, concentration, temperature, skin friction, Nusselt number, and Sherwood number profiles, are portrayed pictorially and imparted. The numerical solution of the velocity profile developed in this study fits extremely well with what was previously published and validated. Furthermore, we discovered that plate oscillation, radiation, and viscous dissipation parameters surprisingly influence the flow pattern. [ABSTRACT FROM AUTHOR]

The behaviour of magnetic impact on the unsteady separated stagnation-point flow of hybrid nanofluid with the influence of viscous dissipation and Joule heating is investigated numerically in this study. A new mathematical hybrid nanofluid model is developed, and similarity solutions are obtained in the form of ordinary differential equations (ODEs). The bvp4c approach in MATLAB is used to determine the reduced ODEs' estimated solutions. The influence of various physical parameters is scrutinised. The findings revealed that the skin friction coefficient increases with the increment of the nanoparticle volume fraction and the unsteadiness parameter. This observation is also applied to the heat transfer rate of the fluid. Additionally, the presence of the magnetic and acceleration parameter provides a significant result in the heat transfer performance. The addition of the Eckert number increased the temperature profile distribution, thereby spontaneously decreasing the heat transfer rate. The first solution is declared stable by the analysis of solution stability. [ABSTRACT FROM AUTHOR]

Droplet impact may rupture a liquid film on a non-wettable surface. The formation of a stable dry spot has only been studied in the inviscid case. Here, we examine the break-up of viscous films, and demonstrate the importance and role of the viscous dissipation in both film and droplet. A new model was therefore proposed to predict the necessary droplet energy to create a dry spot. It also showed that the dissipation contribution in film dominates when the ratio of the thicknesses to drop diameter is larger than 7/4. [ABSTRACT FROM AUTHOR]

The present study is carried out to examine the behavior of magnetohydrodynamic Williamson nanofluid flow and heat transfer over a non-linear stretching sheet embedded in a porous medium. In the current work, the influence of heat generation and viscous dissipation has been taken into account. The considered phenomenon in the form of partial differential equations is transformed into ordinary differential equations by utilizing an appropriate similarity transformation. The reduced form is solved by using rigorous MATLAB built-in solver bvp4c. The numerical solutions for the velocity field, temperature field, and mass concentration along with the skin friction coefficient, Nusselt number, and Sherwood number are computed. The obtained solutions are shown in graphs and are discussed with physical reasoning. It is noted that by increasing Williamson fluid parameter W, the velocity decreases and concentration profile increases. It is deduced that increasing Eckert number Ec leads to a rise in temperature and mass concentration. It has been viewed that with the increment in heat generation parameter Q, the temperature field increases and concentration decreases. The results show that an increasing magnetic field parameter M leaves a decreasing trend in the velocity field and an increasing trend in the temperature field and concentration profile. The present results are compared with the existing solution which shows good agreement and endorses the validation of current solutions. [ABSTRACT FROM AUTHOR]

A novel computational approach is developed to investigate the mixed convection, boundary layer flow over a nonlinear elastic (stretching or shrinking) surface. The viscous fluid is electrically conducting, incompressible, and propagating through a porous medium. The consequences of viscous dissipation, Joule heating, and heat sink/source of the volumetric rate of heat generation are also included in the energy balance equation. In order to formulate the mathematical modeling, a similarity analysis is performed. The numerical solution of nonlinear differential equations is accomplished through the use of a robust computational approach, which is identified as the Spectral Local Linearization Method (SLLM). The computational findings reported in this study show that, in addition to being simple to establish and numerically implement, the proposed method is very reliable in that it converges rapidly to achieve a specified goal and is more effective in resolving very complex models of nonlinear boundary value problems. In order to ensure the convergence of the proposed SLLM method, the Gauss–Seidel approach is used. The SLLM's reliability and numerical stability can be optimized even more using Gauss–Seidel approach. The computational results for different emerging parameters are computed to show the behavior of velocity profile, skin friction coefficient, temperature profile, and Nusselt number. To evaluate the accuracy and the convergence of the obtained results, a comparison between the proposed approach and the bvp4c (built-in command in Matlab) method is presented. The Matlab software, which is used to generate machine time for executing the SLLM code, is also displayed in a table. [ABSTRACT FROM AUTHOR]

The conditions defining a stationary fluid flow may lead to a multiplicity of solutions. This circumstance is widely documented in the literature when mixed convection in a vertical channel or duct is accompanied by an important effect of viscous dissipation. Usually, there are double stationary solutions with a parallel velocity field which satisfy given temperature boundary conditions and with a prescribed mass flow rate. However, in a vertical internal flow, the dual solutions can be determined only numerically as they do not have a closed analytical form. This study shows that, in a horizontal channel, stationary mixed convection with viscous dissipation shows up dual flow branches whose mathematical expressions can be determined analytically. The features of these dual flows are discussed. [ABSTRACT FROM AUTHOR]

The current investigations are carried out to study the influence of the Darcy–Forchheimer relation on third-grade fluid flow and heat transfer over an angled exponentially stretching sheet embedded in a porous medium. In the current study, the applied magnetic field, Joule heating, thermaldiffusion, viscous dissipation, and diffusion-thermo effects are incorporated. The proposed model in terms of partial differential equations is transformed into ordinary differential equations using suitable similarity transformation. The reduced model is then solved numerically with the help of MATLAB built-in function bvp4c.The numerical solutions for velocity profile, temperature profile, and mass concentration under the effects of pertinent parameters involved in the model are determined and portrayed in graphical form. The graphical effects of the skin friction coefficient, the Nusselt number, and the Sherwood number are also shown. From the displayed results, we conclude that when the Joule heating parameter is enlarged, the velocity and the temperature of the fluid are increased. We observed that while enhancing the viscous dissipation parameter (Eckert number) the fluid's velocity and temperature increase but decreases the mass concentration. By increasing the values of the thermal-diffusion parameter, the velocity distribution, the temperature field, and the mass concentration increase. When the diffusion–thermo parameter rises, the velocity field and the temperature distribution increase, and the reverse scenario is seen in the mass concentration. The results of the current study are compared with already published results, and a good agreement is noted to validate the current study. [ABSTRACT FROM AUTHOR]

In the current study, since nanofluids have a high thermal resistance, and because non-Newtonian (Ree-Eyring) fluid movement on a stretching sheet by means of suspended nanoparticles A A 7072 - A A 7075 is used, the proposed mathematical model takes into account the influence of magnetic dipoles and the Koo-Kleinstreuer model. The Cattaneo-Christov model is used to calculate heat transfer in a two-dimensional flow of Ree-Eyring nanofluid across a stretching sheet, and viscous dissipation is taken into account. The base liquid water with suspended nanoparticles A A 7072 - A A 7075 is considered in this study. The PDEs are converted into ODEs by exhausting similarity transformations. The numerical solution of the altered equations is then performed utilising the HAM. To examine the performance of velocity, temperature profiles, concentration profiles, skin friction, the Nusselt number, and the Sherwood number, a graphical analysis is carried out for various parameters. The new model's key conclusions are that the A A 7075 alloy outperforms the A A 7072 alloy in terms of thermal performance as the volume fraction and ferro-magnetic interaction constraint rise. Additionally, the rate of heat transmission and the skin friction coefficient improve as the volume fraction rises. [ABSTRACT FROM AUTHOR]

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

Numerical investigation of the effects of magnetic field strength, thermal radiation, Joule heating, and viscous heating on a forced convective flow of a non-Newtonian, incompressible power-law fluid in an axisymmetric stretching sheet with variable temperature wall is accomplished. The power-law shear-thinning viscosity-shear rate model for the anisotropic solutions and the Rosseland approximation for the thermal radiation through a highly absorbing medium is considered. The temperature-dependent heat sources, Joule heating, and viscous heating are considered to be the source terms in the energy balance. The non-dimensional boundary-layer equations are solved numerically in terms of similarity variable. A parameter study on the boundary value of chemical reaction and Nusselt number is performed as a function of thermal radiation parameter, Brinkman number, Prandtl number, Hartmann number, power-law index, heat source coefficient, Brownian parameter, thermophoresis parameter, and the chemical reaction parameter. The results show that the chemical reaction parameter has an increasing effect on the chemical reaction boundary while the magnetic, thermophoresis, and Brownian effects decrease the rate of the chemical reaction at the boundary. [ABSTRACT FROM AUTHOR]