Thermal Convective Boundary Conditions Research Articles

Thermodynamic analysis of MHD Prandtl-Eyring fluid flow through a microchannel: A spectral quasi-linearization approach

In designing efficient micro devices, particularly microchannels used in cooling electronic components and biomedical microfluidic systems, The foremost application explored is the design and optimization of microchannels employed in the electronic device cooling systems. To possess these microchannels from overheating and damaging their gentle electronic components, exact fluid flow and heat transmission regulation are required. To better design cooling systems, engineers can use mathematical models of Prandtl-Eyring fluid flows to antedate temperature and velocity profiles. The entropy generation also helps in optimizing the design for better fluid transport efficiency. Therefore, the present aim is to characterize the impact of dissipative heat along with magnetization in Prandtl-Eyring non-Newtonian fluid via microchannel. The novelty of the study is the assumption of convective thermal boundary conditions that show efficient heat transport phenomena. A set of similarity rules is adopted for the transformation of the governing equations, and a spectral quasi-linearization technique is then utilized for the solution of the designed miniature. One of the special attractions of the proposed study is the analysis of entropy, which is obtained due to the irreversibility processes within the system. However, irreversibility occurs because of heat transfer, diffusion processes, viscous dissipation, etc. The physical behavior of the pertinent factors is deployed graphically, whereas the validation of the result in a particular case is displayed in tabular form. We use a second law analysis to determine the origins of irreversibility in the thermal system. It is evident that an increase in fluid parameters results in a reduction in entropy generation. An augmentation in the Biot number substantially intensifies the Bejan number. The findings suggest that the magnetic parameter and fluid parameter α have a diminishing effect on velocity.

Thermal analysis of AIN-Al2O3 Casson hybrid nano fluid flow through porous media with inclusion of slip impact

A mathematical analysis of magnetized Casson hybrid nanofluid flow over a stretching permeable sheet with porosity effects and being exposed to thermal convective boundary conditions with slip in velocity and concentration have been presented numerically. The attained steady-state partial differential equations are highly coupled and nonlinear in nature and are not agreeable to any of the direct techniques. Hence, they are being reduced to coupled-nonlinear ordinary differential equations by means of appropriate similarity transformations. A MATLAB-based, bvp4c scheme has been employed to obtain numerical solutions. Suitable graphs have been plotted which demonstrates the fluid flow velocity, temperature, concentration and micro-organism distribution fields in the boundary layer regime. Magnifying Casson fluid parameter and porosity leads to a decline in the velocity field. Amplifying the concentration slip decays the concentration profile. A comparative analysis was conducted to confirm the findings from previous research, demonstrating strong consistency with the results previously documented. Enhancing heat transfer in microelectromechanical systems (MEMS), optimizing medical drug delivery techniques, and boosting the efficiency of cooling systems in industrial processes are all potential applications of this study.

Comparative investigation of activation energy and biot number on quadratic convective flow of a radiating micropolar fluid

In this study, we evaluate the significance of activation energy for initiating a chemical reaction in a two-dimensional laminar flow of a micropolar fluid over a semi-infinite inclined plate. The internal heat transfer mechanism of fluid is modeled with considerations of radiation and convective thermal boundary conditions. The momentum equation uses quadratic density relations in the concentration and temperature differences in buoyancy. In addition, flow through a porous medium surrounded by an inclined plate is modeled by the Darcy-Forchheimer model. Using a spectral successive linearization approach achieves the numerical results for the dimensionless equations. Basic characteristics of flow are examined for a range of dimensionless physical parameters. Quadratic convection is observed to have a stronger impact on the physical components of the flow than linear convection. In addition, compared to the linear illustration, the quadratic convection scenario results in a 14 % − 19 % increase in surface drag and heat transmission rate and a 5 % − 9 % decrease in mass transfer rate. Further, a higher activation energy corresponds with a higher concentration of micropolar fluid. Furthermore, as the radiation and Biot number rise, the velocity and rate of heat transfer correspondingly increase. We believe that the obtained results apply to aerosol technologies and polymeric mixtures used under extreme temperatures and concentrations.

Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip Conditions: A Model-Based study

This research looks at the stagnation point flow of MHD Al2O3-Cu/H2O hybrid nanofluid against a permeable, vertically extending surface that uses thermal radiation and how different models of thermal conductivity affect it. This study is unique because it looks at how changes in thermal conductivity, mixed convection, and the slip velocity of hybrid nanofluids affect the stretching surface. It also looks at how changes in temperature, skin-friction coefficient, Nusselt number, and velocity affect convective thermal boundary conditions. With the use of boundary layer approximations, the complicated system of PDEs is simplified. The dimensionality of these PDEs and the boundary conditions they include are eliminated by applying certain modifications. Combining a local non-similarity approach up to the second truncation level with MATLAB's built-in finite difference code (bvp4c), one can obtain the results of the updated model. The research demonstrates and analyzes the impact of different factors on fluid flow and heat transfer characteristics in the studied flow situations. This is done by comparing the computed data with available literature and presenting the findings in graphical form. Tables are generated to present the numerical fluctuations of the drag coefficient and Nusselt number. This study shows how important thermal conductivity is in the mixed convection of hybrid nanofluids and looks into what happens when the thermal conductivity parameter is changed. Significantly, an augmentation in this parameter results in an elevation in the temperature distribution of the hybrid nanofluid while simultaneously reducing the rate of heat transfer across various models. Furthermore, increasing the nanoparticle volume fraction parameter leads to higher temperature and Nusselt number profiles while reducing skin friction. The mixed convection parameter has a notable impact on increasing the friction coefficient on the stretched vertical surface. However, because these elements function as regulating variables, it decreases when the magnetic, mass suction, and velocity slip parameters are present. The results also demonstrate notable discrepancies in the mean Nusselt values generated by various thermal conductivity models. According to the analysis, the Hamilton-Crosser model has the lowest average Nusselt numbers, followed by the Yamada-Ota model and the Xue model, in that order.

Thermal characterization of an interior permanent magnet electric motor

An engineering approach for thermal characterization of an interior permanent magnet electric motor (EM) with a specific aim to identify the interdependency between its mean coil temperature and the maximum component temperatures at the conditions with constant and variable loads/speeds is proposed. For specifying the convective thermal boundary condition between stator and rotor that spins at variable speeds/directions, an experimental study aimed at devising the empirical heat transfer correlation for the Taylor-Couette airflow with varying rotating speed/direction is performed. It is firstly revealed that the responsive air-gap heat convection to angular acceleration follows the characteristic of a single-degree-of-freedom (SDOF) dynamic system. Along with the heat transfer correlation for the unsteady Taylor-Couette airflow, the nonhomogeneous thermal conductivity model that considers the orthogonality effect of the bent coiled winding at its two axial ends is integrated with an iteration scheme for calculating the air bulk temperature in an entrapped air chamber. The favorable experimental validation with the maximum discrepancies between predicted and measured component temperatures less than 7 % in steady and unsteady running conditions affirms the accuracy of the proposed simulation model. At a rotating speed of 4800 rev/min and power output of 1688 W, the maximum-to-mean temperature differences of stator winding, magnetic stripe, and steel sheet of stator reach respectively 6.75 °C, 3.21 °C, and 6.94 °C. Particularly, all the maximum component temperatures are well correlative with the mean temperature of the stator winding at the various steady/unsteady operating conditions. This finding extends the application of lumped thermal network analysis that predicts the averaged components’ temperatures; and enables the on-line monitoring for the maximum component temperatures using a mean stator-winding temperature as the controlling factor.

Mixed convective-quadratic radiative MoS 2–SiO 2/H 2 O hybrid nanofluid flow over an exponentially shrinking permeable Riga surface with slip velocity and convective boundary conditions: Entropy and stability analysis

In this work, the flow of a hybrid Mo S 2 − Si O 2 /water nanofluid across a porous exponentially diminishing Riga surface with the effects of quadratic heat radiation is taken into account. We also considered the effects of mixed convection, slip velocity, and convective thermal boundary conditions. Before numerically solving the governing partial differential equations, the MATLAB function bvp4c was used to get a comprehensive description of all relevant flow characteristics. The ramifications of physical characteristics concerning fluid flow and thermal profile are investigated using graphs and tables. The primary objective of this study is to investigate the Nusselt number, skin friction coefficient, and entropy production. Using the second law of thermodynamics, the irreversibility factor is computed. For a given value of the mass suction parameter, the findings also indicate the occurrence of dual-nature solutions in the shrinking sheet area, with a stable upper solution branch and unstable bottom solution branch. In addition, the first solution produces a positive minimum eigenvalue, whereas the second solution produces a negative eigenvalue, showing the stability of the first solution. For heat transfer enhancement, the existence of quadratic thermal radiative parameter impacts is more advantageous. With a larger value for the modified Hartman number, the velocity field has expanded. Also, recent research demonstrates that raising the thermal Biot number enhances the thermal gradient. Increases in nanoparticle volume fraction and thermal radiation parameters lead to a commensurate rise in entropy production. Because of these findings, we can better regulate the temperature of various environments by controlling the flow of heat.

Dual solutions of radiative Ag-MoS_2/water hybrid nanofluid flow with variable viscosity and variable thermal conductivity along an exponentially shrinking permeable Riga surface: Stability and entropy generation analysis

ABSTRACT In this analysis, the Silver-Molybdenum disulfide ()/water hybrid nanofluid flow past a permeable exponentially shrinking Riga surface with thermal radiant energy is considered. The novelty of this work is to find out the effects of variable viscosity, variable thermal conductivity with hybrid nanofluid’s slip velocity, and convective thermal boundary conditions over a shrinking Riga surface on velocity, temperature, skin-friction coefficient, Nusselt number, and entropy generation. The MATLAB programming platform with a fourth-order method to solve boundary value problem (bvp4c) was employed to get a good account of all pertinent flow parameters before solving the controlling partial differential equations numerically. Here of Silver () and of Molybdenum disulfide () nanoparticles in the hybrid model are considered in the base fluid water. The basic achievement of this analysis is to explore the Nusselt number, skin friction coefficient along with entropy formation, and Bejan number. The irreversibility factor is calculated using the thermodynamics second law. The findings also point to the presence of dual-nature solutions in the shrinking sheet region for a given value of a high mass suction parameter, with a stable upper solution branch and unstable lower solution branch. Two solutions are found for the limited range of shrinking parameter when and the solutions terminate at in the shrinking region. Additionally, the first solution generates a positive minimum eigenvalue (), whereas the second solution generates a negative eigenvalue (), indicating the solution’s stability. Nusselt number is enhanced for variable viscosity parameter but diminished by variable thermal conductivity parameter for the stable solution. The entropy generation and the Bejan number both increase significantly with the increment of the thermal radiant-energy parameter, Biot number, and Eckert number. These results are crucial in the long term because they allow us to optimize heat transmission for cooling and heating applications. Hence, this investigation is incredibly significant in the present era, particularly in the automotive industry, home industry, paper plastics, ceramics, food packaging, food colorants, cancer treatment, cosmetics, pharmaceuticals, fabrics, paints, and soaps as well.

Inclined magnetic field and variable viscosity effects on bioconvection of Casson nanofluid slip flow over non linearly stretching sheet

In pursuit of improved thermal transportation, the slip flow of Casson nanofluid is considered in the existence of an inclined magnetic field and radiative heat flux flow over a non-linear stretching sheet. The viscosity of the fluid is considered as a function of temperature along with the convective thermal boundary condition. Numerical solutions are obtained via Runge-Kutta along with the shooting technique method for the chosen boundary values problem. To see the physical insights of the problem, some graphs are plotted for various flow and embedded parameters on temperature function, micro-organism distribution, velocity, and volume fraction of nanoparticles. A decline is observed in the velocity and the temperature for Casson fluid. Thermophoresis and Brownian motion incremented the temperature profile. It is also found that thermal transportation can be enhanced in the presence of nanoparticles and the bioconvection of microorganisms. Present results are useful in the various sectors of engineering and for heat exchangers working in various technological processors. The main findings of the problem are validated and compared with those in the existing literature as a limiting case.

Cattaneo–Christov heat flux on MHD flow of hybrid nanofluid across stretched cylinder with radiations and Joule heating effects

In the current paper, we look at the effects of thermal radiation and Joule heating on the magnetohydrodynamic flow of a hybrid nanofluid through a stretched cylinder. In addition, we used Cattaneo–Christove heat flux effects to explore the heat transfer of copper and aluminum oxide under convective thermal boundary conditions with blood as the base fluid. The flow of fluid is governed by partial differential equations, which are then transformed into a set of nonlinear ordinary differential equations. The problem was numerically solved using Mathematica’s NDSolve command after manipulating relevant non-dimensional variables and similarity transformations. It presented a graphical representation of velocity and temperature fields with variations in the physical parameters. Raising the curvature parameter increases velocity and temperature in the region very far from the stretched surface, but has the opposite effect near the cylinder's surface. The graphs also show that the volume fraction of nanoparticles has an inverse relationship with fluid velocity and temperature. The temperature of the fluid rises by combining the properties of non-uniform heat flux and thermal radiation.

Effects of copper and titania nanoparticles on MHD 3D rotational flow over an elongating sheet with convective thermal boundary condition

Copper nanoparticles (NPs) are used as highly thermal conductive material as well as alloys. In the same way, titanium dioxide nanoparticles have wide usage in coating, waste water treatment, food industries and space crafts etc. The three dimensional (3D) rotational nanofluid flow and heat transfer over an elongating sheet with thermal radiation, heat source and thermal convective boundary condition is studied. The convective heat transfer currently discussed is the superposition of thermal conduction due to temperature gradient and heat energy transfer by the flowing fluid. This phenomenon has been combined with electrically conducting nanofluid subjected to magnetic field. Further, flow model includes rotation and translation which find applications in chemical and process industries. The boundary conditions on heat transfer involves Biot number (Bi) which is important because most of the problem reported in literature involves Nusselt number which is a relative measure of heat transfer coefficient and thermal conductivity, both related to flowing fluid. The solution involves Runge-Kutta forth order method with MATLAB code. It is found that for metallic nanofluid (Cu) temperature remains positive and for metallic oxide nanofluid (TiO 2) the temperature remains negative, indicating thermal energy generation and absorption due to metal or metallic oxide as nanoparticles.

MHD Eyring–Powell nanofluid flow across a wedge with convective and thermal radiation

In this research, a theoretical investigation into the heat transport characteristics of an Eyring–Powell nanomaterial boundary layer flow on a wedge surface with passively controlled nanoparticles is carried out. In this model, thermal convective boundary conditions, thermal radiation, heat production, and absorption are also studied. The non-Newtonian Eyring–Powell fluid’s features are predicted using the model under consideration. The Buongiorno model is used to study how a temperature gradient affects thermophoresis and how nanoparticles affect the Brownian motion. The prevailing nonlinear boundary layer equations are derived and then renewed in an ordinary differential boundary value problem (ODBVP) by substituting apt similarity transformations. The acquired nonlinear ODBVP is then resolved using the bvp4c method to explore the fields of nanofluid velocity, nanofluid temperature, and nanoparticle concentration. A mathematical examination of the surface drag force coefficients and Nusselt number is carried out using various physical parameters. The Eyring–Powell fluid parameter (K1) reduces the thickness of the momentum boundary layer thickness. The thermophoresis aspect (Nt) enhances the thermal field and solutal field. The Nusselt number (NuRex−0.5) reduces the need for a stronger internal heat source mechanism.

Magnetized squeezing nanofluid flow with viscous heating and Robin boundary conditions: A Buongiorno nanofluid model

The flow of fluid that occurs when two parallel disks are squeezed together has applications in compression, the processing of polymers, the production of plastics, injection modeling, and lubrication systems. In this paper, the unsteady squeezing flow and heat transport of nanoliquid that is subjected to convective thermal boundary conditions and viscous heating have been studied numerically. This study was inspired by the exploration of the thermophysical properties of magnetic nanoparticles in squeezing tribology. The flow between two horizontal parallel disks is accounted for where the upper disk is non-static when the lower disk is fixed. The powerful Runge–Kutta method-based shooting scheme is utilized to solve the assumed problem. The influence of pertinent key parameters on involved fields is visualized graphically and scrutinized. It is exhibited that the haphazard motion of NPs contributes highly to the enhancement of thermal and concentration fields. Also, the Robin boundary conditions affect flow fields significantly. Intensifying the Brownian motion effect enhances NPs’ concentration. Radial velocity is damped in the core region with stronger magnetic field. The mass transport rate is diminished, and the heat transmission rate is enhanced. The computations are relevant to smart nano-tribological systems in mechanical and aerospace engineering.

Electro-osmotic optimized flow of Prandtl nanofluid in vertical wavy channel with nonlinear thermal radiation and slip effects

The simulations have been performed for the nonlinear radiative flow of Prandtl nanofluid following the peristaltic pumping in a wavy channel. The applications of entropy generation for the electrokinetic pumping phenomenon are also focused as a novelty. The complex wavy channel induced the flow of Prandtl nanofluid. Moreover, the formulated problem is solved by using the convective thermal and concentration boundary conditions. The Keller Box numerical procedure is adopted as a tool for the simulation task. The results are also verified by implementing the built-in numerical technique bvp4c. The comparison tasked against obtained numerical measurement has been done with already reported results with excellent manner. The physical characteristics based on the flow parameters for velocity, heat transfer phenomenon, concentration field, and entropy generation pattern is visualized graphically. It has been observed that the presence of thermal slip and concentration enhanced the heat transfer rate and concentration profile, respectively. The skin friction coefficient declines with electro-osmotic force and slip parameter. The increasing variation in Nusselt number is observed for electro-osmotic parameter for both linear and non-linear radiative phenomenon.

Mathematical model of oxytactic bacteria’s role on MHD nanofluid flow across a circular cylinder: application of drug-carrier in hypoxic tumour

A bioconvection MHD nanofluid flow which contains both nanoparticles and oxytactic bacteria is proposed. The role of oxytocic bacteria in cancer treatment is to hinder cancer development by actuating the immunity system. Oxygen-repellent bacteria as, a targeted drug delivery carriers towards infected cells, seem to be a promising tool in the fight against tumours. To depict the flow for this situation, a laminar steady incompressible nanofluid, containing oxytactic bacteria swimming heading a horizontal circular cylinder is considered. The thermal convective boundary conditions with variable physical parameters are taken. A numerical pseudospectral method is utilized. There is a considerable harmonization between the present outcome and some published papers. The current paper is supposed to give a serious understanding and deeper insight that can help develop drug-delivery applications in fluid encompassing hypoxic growth cells.

Brownian motion and thermophoretic diffusion impact on Darcy-Forchheimer flow of bioconvective micropolar nanofluid between double disks with Cattaneo-Christov heat flux

The topic of fluid flow through disks is important due to a broad range of its applications in industries, engineering, and scientific fields. The objective of the current article is to analyze the bioconvective micropolar nanofluid flow between the coaxial, parallel, and radially stretching double disks in the occurrence of gyrotactic motile microorganisms with convective thermal boundary conditions. Darcy–Forchheimer medium is considered between the double disks that allow the flow horizontally with additional effects of porosity and friction. The flow is also considered under the impacts of thermal conductivity and thermal radiations. The influence of gyrotactic microorganisms is accommodated through the bioconvection, which increases the strength of thermal transportation. Furthermore, the Cattaneo-Christov heat flux theory is also accounted. The flow model is trans moved into a system of ordinary differential equations (ODEs) utilizing appropriate similarity transformation functions. The bvp4c technique has been used to solve the transformed flow model. The implication of some prominent physical and bioconvection parameters on velocities, microrotation, thermal field, volumetric concentration of nanoparticles, and microorganisms’ fields are presented through graphs and tabular ways. It is observed that the stretching ratio parameter of the disks accelerates the axial and micro rotational velocities of the nanofluid. In contrast, the stretching Reynolds number slows down the radial velocity near the plane’s center. The temperature profile goes high against the Brownian motion, thermal radiation, and thermal conductivity parameters, while an inverse trend has been observed for increasing magnitudes of Prandtl number. The nanoparticles concentration profile is upsurged against the thermophoresis parameter. The density profile of gyrotactic motile microorganisms is de-escalated by the Peclet number and the bioconvection Lewis number. Micropolar parameters cause an increase of couple stresses and a decrement in shear stresses. A comparison with published work is provided under certain limitations to test the validity of numerical scheme accuracy.

Non-Similarity Solutions of Non-Newtonian Brinkman–Viscoelastic Fluid

The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since the experimental works are costly and high-risk procedures, the mathematical study is proposed to counter the limitations. Therefore, this work aims to study the characteristics of a fluid that combines the properties of viscosity and elasticity, together with the porosity conditions, called the Brinkman–viscoelastic model. The flow is assumed to move over a horizontal circular cylinder (HCC) under consideration of the convective thermal boundary condition. The mathematical model is transformed to the less complex form by utilising a non-dimensionless and non-similarity variable. The resulting equations are in the partial differential equation (PDE) form. Subsequently, the equations are required to be solved by employing the Keller-box method (KBM). The solutions were conveniently evaluated by observing the plotted graphs in order to capture the propensity of the fluid’s behavior in response to the adjusting parameters. The study discovered that the viscoelastic and Brinkman variables had the impact of decreasing the fluid’s velocity and increasing the temperature distribution. Nevertheless, when mixed convection and Biot numbers increased, the velocity profile exhibited the opposite pattern. Furthermore, increasing the Biot number raises the Nusselt number while decreasing the skin friction coefficient. These numerical results are critical for assisting engineers in making heat transfer process decisions and accurately verifying experimental investigations.

Heat transport and the aspects of retardation time phenomenon in the flow of highly viscoelastic nanofluid with a Newtonian heating agent

This study investigates the convective thermal and solutal characteristics in the stagnation point flow of Burgers nanofluid accelerated due to stretching cylinder. The thermal features of the flow are examined by employing Fourier's law in addition to the effects of heat source/sink and Joule heating. The essential feature of this research is to utilize the activation energy and binary chemical reaction effects to investigate the convective mass transform phenomenon. Moreover, the process of heat as well as mass convection from the surface to the fluid is also observed by employing convective thermal and concentration boundary conditions. The dimensionless similarity transformations are invoked to attain the ordinary differential equations (ODE's) from governed partial differential equations (PDE's). The numerical solutions are carried out by utilizing bvp midrich numerical procedure. The section on physical analysis is proposed to elaborate on the outcomes of this study physically. The graphical illustration of physical parameters is also depicted and physically analyzed. The rate of mass transfer is depreciated for the augmenting scales of reaction rate and temperature difference constraints. Moreover, the escalating magnitudes of thermal Biot number drive up the thermal energy transport in the flow.

Effect of volume ratio on thermocapillary convection in annular liquid pools in space

In systems with liquid/liquid or liquid/gas interface under microgravity, and even in shallow liquid layers in the terrestrial conditions, thermocapillary force takes the principal role to drive natural convections. A series of numerical simulations are conducted to investigate the stability limit of axisymmetric steady thermocapillary flow in annular liquid pools with curved and adiabatic liquid surface for eight volume ratios 0.809 ≤ Vr ≤ 1.173, where Vr is defined as (liquid vol/vol of the annular gap). Simulations provide the critical temperature difference ΔTc, frequency fc, and azimuthal wave number mc for each liquid pool. At the critical condition, oscillations start in form of standing wave. At the slightly supercritical condition (ΔT*), the standing waves turn to traveling oscillations. The calculated ΔTc values decrease with the increase of Vr. A simulation code with a convective thermal boundary condition in the liquid surface suggests that heat transfer through the liquid surface significantly increases the ΔTc value.

Chemically reactive Maxwell nanoliquid flow by a stretching surface in the frames of Newtonian heating, nonlinear convection and radiative flux: Nanopolymer flow processing simulation

AbstractThe effects of a chemical reaction and radiative heat flux in a nonlinear mixed thermo-solutal convection flow of a viscoelastic nanoliquid from a stretchable surface are investigated theoretically. Newtonian heating is also considered. The upper-convected Maxwell (UCM) model is deployed to represent the non-Newtonian characteristics. The model also includes the influence of thermal radiation that is simulatedviaan algebraic flux model. Buongiorno’s two-component nanofluid model is implemented for thermophoretic and Brownian motion effects. Convective thermal and solutal boundary conditions are utilized to provide a more comprehensive evaluation of temperature and concentration distributions. Dimensionless equations are used to create the flow model by utilizing the appropriate parameters. The computed models are presented through a convergent homotopic analysis method (HAM) approach with the help of Mathematica-12 symbolic software. Authentication of HAM solutions with special cases from the literature is presented. The impact of various thermophysical, nanoscale and rheological parameters on transport characteristics is visualized graphically and interpreted in detail. Temperatures are strongly enhanced with Brownian motion and thermophoresis parameters. Velocity is boosted with the increment in the Deborah viscoelastic number and mixed convection parameter, and the hydrodynamic boundary layer thickness is reduced. A stronger generative chemical reaction enhances concentration magnitudes, whereas an increment in the destructive chemical reaction reduces them and also depletes the concentration boundary layer thickness. Temperature and concentration are also strongly modified by the conjugate thermal and solutal parameters. Greater radiative flux also enhances the thermal boundary layer thickness. Increasing the Schmidt number and the Brownian motion parameter diminish the concentration values, whereas they elevate the Sherwood number magnitudes,i.e.enhance the nanoparticle mass transfer rate to the wall.

Stability analysis of triple solutions of Casson nanofluid past on a vertical exponentially stretching/shrinking sheet

The MHD two dimensional boundary layer flow of Casson nanofluid on an exponential stretching/shrinking sheet is considered with effects of radiation parameter, nanoparticles volume fractions (i.e. Fe3O4 and Ti6Al4V) and thermal convective boundary condition. The partial differential equations are transformed into ordinary differential equations by means of similarity transformations. The solutions of the transferred equations are achieved numerically with the help of shooting technique in Maple software. At different ranges of involved physical parameters, triple solutions are found. Therefore, stability analysis is performed by bvp4c in MATLAB to find the stable and physically reliable solution. Impacts of the physical parameter are presented through graphs and tables. Mainly, it is found that an increase in Casson and suction parameters decrease the corresponding velocity profiles while increase in Prandtl number, stretching/shrinking, and suction parameter decrease the temperature profiles. Furthermore, an increase in nanoparticles volumetric fraction, radiation and magnetic parameters as well as Biot number increase the temperature profiles and their thermal boundary layer thicknesses.