Runge Kutta Fehlberg Research Articles

Global approximate solution of SIR epidemic model with constant vaccination strategy

Providing a global semi-analytical method has the advantage of offering a global and accurate solution to the epidemic model, which can help in studying and controlling the spread of the disease. Unlike numerical methods such as the Runge–Kutta–Fehlberg method, global semi-analytical methods can provide an explicit expression of the solution over the entire time period, including obtaining the peak time, which is crucial information for understanding disease spread. In this paper, a global semi-analytical method based on the two-point Padé approximants for solving the SIR epidemic model of childhood diseases is presented. The objective of this study is to examine the temporal dynamics of a childhood disease when a preventive vaccine is present. For this purpose, we have first derived the solution of the SIR model of childhood diseases in terms of series expansions for small and large values. Then, the theory of two-point Padé approximations is used to provide the global approximate solution. The peak time related to this model is also obtained via these global approximants. Furthermore, in order to show the efficiency of our study, some graphs have been given to compare our results with those obtained using the classical Padé approximations and the numerical Runge–Kutta–Fehlberg method.

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

AbstractMagnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self‐similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth‐order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.

Three Dimensional Modelling of Magnetohydrodynamic Bio-Convective Casson Nanofluid Flow with Buoyancy Effects Over Exponential Stretching Sheet Along with Heat Source & Gyrotactic Micro-Organisms

In current analysis, influence of buoyancy forces in MHD bioconvective non-Newtonian nanofluids over three dimensional exponential sheet has been studied numerically. Additionally, impact of heat source parameter along with convective conditions has been incorporated. Moreover, nanofluid flow with gyrotactic microorganisms has been analyzed in presence of chemical reaction. Initially similarity variables are used for the conversion of partial differential equations into highly non-linear differential equations. Thusly, non-linear behavior of equations makes typical solutions which are not solved analytically. So, computational MATLAB software is used to calculate results and graphs by following shooting algorithm with Runge Kutta Fehlberg technique using ODE45 solver. Present modeling investigates the influence of crucial fluid parameters especially; magnetic M (0.1 ≤ M ≤ 0.9), Casson parameter β (0.09 ≤ β ≤ 0.13), permeability parameter Bθ, Brownian motion Nb (0.5 ≤ Nb ≤ 5.0), thermophoresis Nt (0.2 ≤ Nt ≤ 2.0), thermal Biot number Bt (0.3 ≤ Bt ≤ 0.7), heat generation parameter Q (0.1 ≤ Q ≤ 0.5), Prandtl number Pr (0.1 ≤ Pr ≤ 0.9), concentration Biot number Bc (0.1 ≤ Bc ≤ 0.9), Lewis number Le (1 ≤ Le ≤ 5), chemical reaction parameter Ch (0.1 ≤ Ch ≤ 0.9), bioconvective Lewis number Lb (0.1 ≤ Lb ≤ 2), Peclet number Pe (0.1 ≤ Pe ≤ 5), gyrotactic Biot number Bn (0.1 ≤ Bn ≤ 0.5), stretching ratio parameter c (0.1 ≤ c ≤ 0.3) and microorganism concentration difference parameter Ω (0.1 ≤ Ω ≤ 5.0). Final results are compared for Prandtl number and stretching ratio parameter along with residual errors. It is inferred that motile concentration declines for larger bioconvective Lewis number whereas rises for motile gyrotactic microorganism Biot number.

Squeezing flow of aqueous CNTs-Fe3O4 hybrid nanofluid through mass-based approach: Effect of heat source/sink, nanoparticle shape, and an oblique magnetic field

Here, the squeezing unsteady 2-dimensional incompressible hybrid nanofluid flow between two collateral sheets has been investigated numerically, considering the influences of magnetic field and the mutable thermal conductivity. The solid-particles are the magnetite (Fe3O4) and the carbon nanotubes (CNTs) inserted in the base liquid (water). To give a complete development investigation of the present problem, the influences of a heat source/sink have also been analyzed. The technique used is pursuant to the Tiwari-Das nanofluid method which nanoparticle weights are considered instead of the volumetric concentration of the solid-particles. At first, the controlling dimensional PDEs, including continuity, momentum conservation, and energy conservation, are changed to a non-dimensional ODEs system applying adequate similarity reduction. The Runge–Kutta–Fehlberg (RK4) approach and shooting procedure is utilized to solve nonlinear ODEs system numerically. The impression of the controlling parameters on the temperature and velocity of working fluid as well as the Nusselt number, and the skin friction has been studied and analyzed. The mass-based manner gives trustable results for the flow and heat transfer analysis in the presence heat generation source and also an oblique magnetic ground. The results demonstrate that the entity of temperature-dependent thermal conductivity and the oblique magnetic ground reduces heat transfer. Furthermore, the greatest temperature distribution was related to spherical solid-particles in the presence of a horizontal magnetic ground.

Electro-magnetic radiative flowing of Williamson-dusty nanofluid along elongating sheet: Nanotechnology application

The flowing of nanomolecules in Williamson nanoliquids via a stretched sheet has a significant influence, and its demand in the manufacturing, therapeutic disciplines, medication, and cooking supplies is enormous and frequently reported. However, 2-dimensional (2-D) combined convective flowing of Williamson-dusty nanofluid (WDNF) via a stretchable sheet in the presence of a magneto force and the porous medium remains unidentified. Hence, this report inspects the combined influence of Brownian and thermophoretic diffusion preserved in magneto WDNF modeling in the occurrence of radiative flowing. The Runge-Kutta Fehlberg approach (RKFA) is used to numerically study the problem of an ordinary differential system employing shooting techniques. The table also addresses the frictional force factor, heat, and mass transmission rate, as well as validates the current findings with earlier available results in the scheduled manner. The acquired outcomes demonstrate that a larger magnetic field decreases the rapidity and thickening of the impetus boundary layer of nanofluids. The momentum dust parameter and the fluid interaction parameter are shown to enhance the heat transmission rate. The rapidity and temperature fields of the liquid and dusty phases improved as the radiation parameter was raised on the contrary of magnetism force which causes dwindling in two phases. Consequently, the examined model's heat transference is reduced in the opposite direction of the Weissenberg number by the magnetic force. Additionally, it is found that higher thermophoresis parameters show an increasing trend in temperature for both phases.

Irreversibility analysis of tangent hyperbolic fluid flow in a microchannel: a hybrid nanoparticles aspects

The tangent hyperbolic fluid model is an interesting model in all the non-Newtonian fluid models, which is developed for particular applications in chemical engineering systems such as polymer solution, ceramic processing, fluid beds, and oil recovery. Hence the intent of the present study is to explore the flow and thermal behavior of tangent hyperbolic fluid flowing through an upright microchannel. In the analysis, water and ethylene glycol are the base fluid with titanium and copper nanoparticles considered. The combined impact of nonlinear thermal radiation, no slip, buoyancy force, and Newton boundary condition on the thermal performance are studied, and further, the skin friction and Nusselt number are examined. The thermal dependent heat source effect was also taken into account. The governing equations were solved numerically by employing Runge–Kutta Fehlberg’s fourth-fifth order. The impact of the pertinent constraint on the Nusselt number, thermal field, flow field, skin friction, Bejan number, and entropy generation are depicted graphically and examined. Entropy generation rises by 15% when ethylene glycol is a base fluid and 12% when the water is a base fluid, with an enhancement of the Brinkman number by 200%. The outturn entrenched that the heat transfer rate in water-based hybrid nanofluid is more remarkable when compared with the heat transfer rate of EG-based hybrid nanofluid. It is noted that the significant increment in the Nusselt number has been attained through a rise in the Weissenberg number and power law index.

Analysis of heat transfer phenomenon in hydromagnetic micropolar nanoliquid over a vertical stretching material featuring convective and isothermal heating conditions

This article evaluates the heat transfer mechanism in an incompressible hydromagnetic micropolar nanofluid enclosed in a two-dimensional vertically stretchable material surface in a porous device. In the current study, the developed model features the significant contributions of nonlinear radiative flux, viscous dissipation, Brownian movement together with thermophoresis effects in the transport region. An approach of similarity transformations is employed to transmute the transport equations from partial into ordinary differential equations. The translated equations are then integrated numerically via Runge–Kutta Fehlberg scheme plus shooting technique. From the analysis, it is found that there is an improvement in the mechanism of heat transfer for large magnitude of temperature ratio and radiation parameters due to the application of Convective Heating Condition (CHC) whereas the case of Isothermal Wall Condition (IWC) reveals an opposite direction for these parameters. Besides, an improvement in the magnitudes of the material micropolar term, Eckert number together with thermophoresis and Brownian movement parameters creates a decline in the surface heat transfer for both heating conditions.

Effect of thermophoretic particle deposition on the three-dimensional flow of nanofluid induced by a nonlinear stretched surface

The current investigation is carried out to study a heat source/sink in a porous medium generated by a nonlinear stretched surface with the impact of thermophoretic particle deposition (TPD) on three-dimensional (3D) nanofluid flow due to the vast range of industrial applications like a condensation of aerosol particles on walls, extraction of oil, coated steel cooling, and radial reflectors. The mathematical model was subjected to a boundary layer approximation, which resulted in the development of partial differential equations (PDEs) then converting these equations to ordinary differential equations (ODEs) the similarity variable is used. The system of reduced ODEs is solved with Runge–Kutta-Fehlberg fourth fifth-order (RKF-45) and shooting techniques with the help of MATLAB software. Discussions are made with the help of graphs obtained for various dimensionless constraints. The results show that nanoparticle addition will improve the thermal profile, but contrary behavior is seen in the velocity and concentration profiles. Three-dimensional figures are drawn to show the behavior of different constraints over Nusselt, Sherwood, and Skin friction factors along with the numerical tabulation presented.

Chemically radiative and mixed convection solute transfer in boundary‐layer flow of Jeffrey nanofluid along an inclined stretching cylinder with joule heating and double stratification impacts

AbstractAn endeavor is consummate to study the steady mixed convection solute transfer in two‐dimensional viscous fluid. A joule heating incompressible flow along an inclined stretching cylinder and double stratification impact on Jeffrey Nanofluid is scrutinized. Acquired nanomaterial pattern comprises the phenomena of thermophoresis and Brownian motion. By applying rule of approximation transformation, the nonlinear PDEs converted into ODEs. Shooting via Newton Raphson technique is used to solve the ODE'S with boundary conditions into initial conditions, also applying Runge–Kutta–Fehlberg technique of fourth order for numerical purpose. Computation for skin friction, () for Nusselt, and for Sherwood number are fetched in table format by using mathematical software Matlab. The results reveal that M (0, 0.3, 0.6, 0.9), γ (0.1, 0.3, 0.7, 1.3), and α will increase upto 7.51, 8.55, and 10.27%, respectively. The behavior of on and falling off upto 11.20 and 28.38%, respectively with the increase of , but in shows opposite reaction on Sherwood number. It is culminated that for velocity augments with the value of Deborah number of four different sizes (0.8, 1.1, 1.4, and 1.7) upto 14.28, 16.6, and 20% while situation is reversed in case of magnetic factor (0, 0.3, 0.6, 0.9) upto 20, 28.12, and 39.13%. Effect of for temperature enhanced with the value of Brownian motion on (0.0, 0.2, 0.4, and 0.6), about 16.66, 20, and 25%, respectively. The maximum effect percentage with radiation factor on is 39 and minimum percentage is 25.71. Eckert number on ( − 4, 0, 4, 8) and thermophoresis on diminished with pile‐up Prandtl number on (1.2, 1.5, 1.8, and 2.1). Impact of for concentration and local Sherwood number showed reverse situation on Schmidt number.

A comparative analysis on magnetically triggered non-Newtonian nanofluid flow over a melting disk

ABSTRACT The prediction of melting-solidification rate and thermal distribution is very significant in some modern technologies. Recently, heat transfer accompanied with melting phenomenon has gained considerable research attention owing to a large number of applications, including purification of materials, glass industry, castings of metals, and material processing . In view of this, the theoretical analysis is performed to report a comparative analysis on the flow of Casson nanofluid over a disk. Here, we analyse the impact of melting effect on Casson nanofluid flow by taking into account of Arrhenius activation energy and melting effects along with 50% ethylene glycol as base fluid, which is novel in the present work. Considering suitable similarity variables , the framed equations are reduced into ordinary differential equations (ODEs) and numerical results are obtained using the Runge-Kutta Fehlberg’s fourth-fifth order (RKF-45) method along with shooting technique. Further velocity, thermal and concentration profiles for several physical parameters are examined briefly and illustrated graphically. The outcome reveals that increasing values of magnetic parameter declines velocity profile and boosts up values of melting parameter decays thermal profile. Increasing values of activation energy parameter enhance the concentration profile but for higher values of chemical reaction parameter concentration profile decays.

Thermal Performance on Radiative and Ohmic Dissipative Magneto-Nanoliquid Over Moving Flat Porous Plate Suspended by Single Wall Carbon Nanotubes and Multi Wall Carbon Nanotubes

This investigation examines heat transport in the flow of magnetized Blasius flow suspended by carbon nanotubes (CNTs) on an accelerated by moving flat porous plate that contains water and ethylene glycol as base fluids. The transfer of heat has been contemplated in the company of suspended CNTs above a plane plate. The flow simulations are carried by utilizing the impact of magnetic field and uniform porous medium. The transport of thermal is controlled by the significant influence of thermal radiation, heat source, heat and Joule dissipation. Utilizing scaling analysis flow governing problem is converted into a set of higher order nonlinear ordinary differential equations which afterwards are tackled numerically by employing Runge-Kutta Fehlberg 45 method with shooting quadrature. Quantities of flow physical significance are portrayed through graphically. Verification of attained numerical results with available literature under certain limitations are presented and found excellent agreement. With elevation in convective term flow profiles of SWCNTs and MWCNTs are reduced. A reduction of flow characteristic dimensions is observed with increasing magnetic field and porosity terms. Finally, SWCNTs and MWCNTs are positively influenced by Joule dissipation and negatively by thermal radiation.

Application of the Small Punch Creep-Recovery Test (SPCRT) for the Estimation of Large-Amplitude Viscoelastic Properties of Polymers.

The Small Punch Creep-Recovery Test (SPCRT) is a novel miniature test used to estimate the viscoelastic properties of polymers and biomaterials. The current investigation related to the SPCRT is limited to Finite Element Method (FEM) simulations and experimental tests on PVC. The aim of this investigation was focused on: (i) extending the experimental tests to other polymers with dissimilar viscoelastic properties; (ii) deepening the influence of non-linear viscoelastic properties in the estimation capabilities of the SPCRT; and (iii) developing a numerical methodology to estimate and take into account the viscoelastic recovery produced during the unloading step of compressive creep-recovery tests (CCRT) and SPCRTs. The experimental tests (CCRTs and SPCRTs) were done on polyethylene PE 500, polyoxymethylene POM C, nylon PA 6, and polytetrafluoroethylene (PTFE), with a range of creep loads, in the case of CCRTs, in the whole elastic regime and the surroundings of the yield strength of each material. The experimental results confirmed that the SPCRT was an accurate and reliable testing method for linear viscoelastic polymers. For a non-linear viscoelastic behavior, SPCRT estimated the viscoelastic properties obtained from CCRTs for creep loads near the yield strength of the polymer, which corresponded with large-amplitude viscoelastic properties in dynamic creep testing. In order to consider the viscoelastic recovery generated in the unloading step of CCRTs and SPCRTs, a Maxwell-Wiechert model with two branches was used, simulating the different steps of the experimental tests, and solving numerically the differential equation of the Maxwell-Wiechert model with the Runge-Kutta-Fehlberg (RKF) numerical method. The coefficients of the elements of the Maxwell-Wiechert model were estimated approaching the straining curve of the recovery step of the simulation with the same curve registered on each experimental test. Experimental CCRTs with different unloading times demonstrated that the use of this procedure derived in no influence of the unloading step time in the viscoelastic properties estimation.

Crosswise Stream of Cu-H2O Nanofluid with Micro Rotation Effects: Heat Transfer Analysis.

The present study focuses on a crosswise stream of liquid-holding nano-sized particles over an elongating (stretching) surface. Tiny particles of copper are added into base liquid (water). The influence of the micro rotation phenomenon is also considered. By means of appropriate transformations non-linear coupled ordinary differential equations are attained that govern the flow problem. The Runge-Kutta-Fehlberg scheme, together with the shooting method, is engaged to acquire results numerically. Micropolar coupling parameter, microelements concentration and nanoparticles volume fraction effects are examined over the profiles of velocity, temperature and micro-rotation. Moreover, heat flux and shear stress are computed against pertinent parameters and presented through bar graphs. Outcomes revealed that material constant has increasing effects on normal components of flow velocity; however, it decreasingly influences the tangential velocity, micro-rotation components and temperature profile. Temperature profile appeared to be higher for weak concentration of microelements. It is further noticed that normal velocity profile is higher in magnitude for the case of strong concentration (n = 0) of microelements, whereas tangential velocity profile is higher near the surface for the case of weak concentration (n = 0.5) of microelements. An increase of 3.74% in heat flux is observed when the volume fraction of nanoparticles is increased from 1 to 5%.

Numerical simulation of MHD two‐dimensional flow incorporated with joule heating and nonlinear thermal radiation

AbstractThe current investigation presents a numerical simulation of boundary layer flow with heat transfer. The study primarily emphasizes heat generation due to the influence of nonlinear thermal radiation. Moreover, the simultaneous effects of Joule heating and viscous dissipation have been incorporated for the thermal enhancement of the magnetohydrodynamics (MHD) on the convective boundary layer flow over a flat plate. Dimensional analysis is brought into use to determine the hydro and thermal boundary layer thickness for the two‐dimensional flow. Subsequently, the application of the suitable similarity transformation yields a nonlinear coupled flow problem with is solved numerically with the help of the Runge–Kutta Fehlberg (RKF) method incorporated with the Shooting technique. Moreover, this theoretical study highlights the immense mechanical and aeronautical applications of thermal radiation. In view of computational findings and simulating results, linear and nonlinear thermal radiation effects can also be investigated on fluids passing through a cylinder and channels. Finally, computational data tabulated against some pertinent parameters and parametric study reveal that non‐linear thermal radiation is more effective for highly viscous fluids.

Application of Manifold Corrections in Tidal Evolution of Exoplanetary Systems

The discovery of numerous close-in planets has updated our knowledge of planet formation. The tidal interaction between planets and host stars has a significant impact on the orbital and rotational evolution of the close planets. Tidal evolution usually takes a long time and requires reliable numerical methods. The manifold correction method, which strictly satisfies the integrals dissipative quasiintegrals of the system, exhibits good numerical accuracy and stability in the quasi-Kepler problem. Different manifold correction methods adopt different integrals or integral invariant relations to correct the numerical solutions. We apply the uncorrected five- and six-order Runge–Kutta–Fehlberg algorithm [RKF5(6)], as well as corrected by the velocity scaling method and Fukushima’s linear transformation method to solve the tidal evolution of exoplanet systems. The results show that Fukushima’s linear transformation method exhibits the best performance in the accuracy of the semimajor axis and eccentricity. In addition, we predict the tidal timescale of several current close exoplanetary systems by using this method.

Dusty Casson Fluid Flow containing Single-Wall Carbon Nanotubes with Aligned Magnetic Field Effect over a Stretching Sheet

Two-phase flow is the mutual interaction between solid and fluid phases which encountered in real life applications, such as sedimentation, blood flow, water pollution, fluidized bed and to name a few. In the theoretical study, this binary mixture is represented by partial differential equations that denotes its physical properties of all phases. Therefore, the interaction between three important elements over a stretching sheet is examined in this study where the focus is on Casson fluid, single-wall carbon nanotubes (SWCNTs) and dust particles. Moreover, the aligned magnetic field effect and Newtonian heating (NH) are associate together to influence the flow region. In order to generate the results, the equations that governed the current model must therefore employ the similarity variables to produce the ordinary differential equations. Formulation of the problem is then continued by solving the resulting equations using Runge-Kutta Fehlberg (RKF45) method. Significant outputs for considered parameters are presented through graph. It is found that, the growing effect of fluid-particle interaction particle decreases the fluid phase distribution which contributes to the opposite trend in dust phase.

How Fluid Particle Interaction Affects the Flow of Dusty Williamson Fluid

A model of two-phase flow involving non-Newtonian fluid is described to be more reliable to present the fluid that involves industrial applications due to the special characteristics in its behavior. Many models of non-Newtonian fluid were discovered in the last few decades but the model that captured the most attention is the Williamson model. The consideration of the existing particles in the Williamson flow (two-phase Williamson fluid) will make the model more interesting to investigate. Hence, this paper is aimed to explore the flow of two-phase Williamson fluid model in the presence of MHD and thermal radiation circumstances. The obtained ordinary differential equations after the transformations are solved using the Runge-Kutta Fehlberg (RKF45) method. The flow is considered asymmetric since it moves over a vertical stretching sheet with external stimuli. The result displays variation in dust phases compared to the fluid phase under distribution of velocity and temperature. It can be concluded that the fluid–particle interaction (FPI) parameter lessening the motion of fluid and heating characteristics. In addition, the upsurges on skin friction and heat transfer are resulting from the rising FPI. Furthermore, the presence of Williamson parameter increases the skin friction while causing degenerations on heat transfer of flow.

Magnetohydrodynamic flow and Hall current effects on a boundary layer flow and heat transfer over a three-dimensional stretching surface

The current investigation is being carried out to investigate the impacts of magnetohydrodynamic flow and hall current effects on boundary layer flow across a three-dimensional stretching surface. The governing equations are framed with reasonable assumptions, and appropriate similarity transformations are applied to convert a set of partial differential equations into ordinary differential equations. To solve the reduced equations, the Runge Kutta Fehlberg 4th 5th order technique is utilised. The results reveal that primary and secondary velocity improves with the velocity parameter and Eckert number decrease for the magnetic parameter. The improvement in the Grashof number will improve the primary velocity but a reverse trend is seen in the case of secondary velocity. The thermal profile improves with the magnetic parameter, the velocity parameter, and the Eckert number, but it degrades with the Grashof number. The rate of heat transmission increases with the magnetic parameter and the Eckert number, whereas it decreases with the remaining factors.

Analysis of buoyancy assisting and opposing flows of colloidal mixture of titanium oxide, silver, and aluminium oxide nanoparticles with water due to exponentially stretchable surface

Energy is essential for a nation's economic growth. Energy is recognized in contemporary society as being crucial to the development of quality of life and sustainability. The environment transforms/absorbs heat and sunlight in a variety of ways. Some of these transitions lead to the flow of renewable energy sources like wind and biomass. Solar energy has become one of the promising alternative energy sources in the future because to the improvements made to enhance its performance. In this context, the impact of solar radiation on modified nanofluid flowover an exponential stretching sheet is examined. Using the proper similarity transformations, the governing equations for the flow assumptions are reduced to ordinary differential equations. The numerical simulation of these simplified equations is then performed using the Runge-Kutta Fehlberg method and the shooting methodology. With the aid of graphs and tables, the effects of numerous parameters on the involved fields are described. Results reveal that the modified nano liquid shows increased heat transport for opposing flow situation than the assisting flow situation for incremented values of porosity parameter and volume fraction. The modified nanoliquid shows increased heat transport for opposing flow situation with respect to augmented values of radiation parameter.

Mixed convective flow of Casson nanofluid in the microchannel with the effect of couple stresses: irreversibility analysis

ABSTRACT The current cutting-edge modelling involves mixed convection and couple stress influences on the velocity and thermal distribution of the flow of Casson nanomaterial in possession of microchannel. This study elucidates the mass and heat transport of Casson nanomaterial in the upright microchannel in the existence with non-linear thermal radiation, Brownian motion and thermophoresis. Along with the flow, the particle size effects are also taken into consideration. The channel walls facilitate the sucking/injecting the fluid into the microchannel. Viscous dissipation and buoyant forces are deliberated in the study. Slip regime and convective conditions are taken at the boundaries. By making use of velocity and thermal profile, the entropy produced and dominance of heat or fluid friction irreversibilities are analyzed. The obtained equations are non-dimensionalized using non-dimensional entities and further solved using Runge-Kutta Fehlberg 4–5th order procedure together with shooting technique. Illustrations of the graph exemplify the outcomes of the work. The impact of couple stress parameter depicts the depletion of velocity profile as the couple stress takes into consideration the size effect of the particle, which enhances viscosity and hence declines velocity of the flow. The irreversibility in the channel can be achieved to be least when the thermal and solutal Grashof number is kept low.