Local Skin Friction Coefficient Research Articles

Numerical treatment of MHD micropolar nanofluid flow with activation energy, thermal radiation, and Hall current past a porous stretching sheet

ABSTRACT This communication investigates the heat and mass transfer properties of MHD micropolar nanofluid fluid flow behaviour with activation energy, thermal radiation, and Hall current past a linear stretching sheet. The governing non-linear partial differential equations of the flow are transformed into non-linear ordinary differential equations using similarity transformation variables and solved using Runge Kutta 4th order in conjunction with the shooting methodology. The shooting approach in MAPLE is then employed to solve the associated system of ordinary differential equations. The impact of pertinent parameters is revealed and discussed on velocity, temperature, and concentration. Increasing micropolar parameters increases tangential velocity profiles while decreasing the transfer velocity profiles. The comparison table for local skin friction coefficient, Nusselt number, and Sherwood number are represented with the effects of pertinent non-dimensional variables. The model has undergone thorough validation using existing data and has shown outstanding performance. It is revealed in the study that an increase in the micropolar term increases the tangential velocity for an enhanced engineering working fluid. Also, a rise in the Hall current term boosts the heat transfer to strengthen thermal science fluids performance.

Hybrid Nanofluid Flow over a Shrinking Rotating Disk: Response Surface Methodology

For efficient heating and cooling applications, minimum wall shear stress and maximum heat transfer rate are desired. The current study optimized the local skin friction coefficient and Nusselt number in Al2O3-Cu/water hybrid nanofluid flow over a permeable shrinking rotating disk. First, the governing equations and boundary conditions are solved numerically using the bvp4c solver in MATLAB. Von Kármán’s transformations are used to reduce the partial differential equations into solvable non-linear ordinary differential equations. The augmentation of the mass transfer parameter is found to reduce the local skin friction coefficient and Nusselt number. Higher values of these physical quantities of interest are observed in the injection case than in the suction case. Meanwhile, the increase in the magnitude of the shrinking parameter improved and reduced the local skin friction coefficient and Nusselt number, respectively. Then, response surface methodology (RSM) is conducted to understand the interactive impacts of the controlling parameters in optimizing the physical quantities of interest. With a desirability of 66%, the local skin friction coefficient and Nusselt number are optimized at 1.528780016 and 0.888353037 when the shrinking parameter (λ) and mass transfer parameter (S) are −0.8 and −0.6, respectively.

Effect of slip velocity on Newtonian fluid flow induced by a stretching surface within a porous medium

This article aims to examine an unsteady 2-D laminar flow of magnetohydrodynamic fluid caused by an elastic surface immersed in a permeable medium under the influence of thermal radiation and extended heat flux. Thermal conductivity and viscosity both are supposed to vary with temperature. This flow model also includes velocity slip, heat source, and joule heating. The governing equations of the fluid, including momentum and energy equations, of the proposed problem are transfigured into a system of interconnected non-linear ordinary differential equations through similarity transformations. The resultant equations are solved efficiently by employing the shooting technique in combination with the fourth-order Runge-Kutta method. Numerical values and the effect of numerous governing factors on the flow field, temperature distribution, local skin friction coefficient, and Nusselt number are showcased via graphs and tables. The investigation reveals that velocity slip, heat source, and porosity parameters enhance the temperature field while diminishing the velocity field. Furthermore, the velocity slip parameter notably reduces both the coefficient of skin friction and the Nusselt number.

Non-Similar Analysis of Mixed Convection Biomagnetic Boundary Layer Flow Over a Vertical Plate with Magnetization and Localized Heating/Cooling

Theoretical and numerical investigation of an applied magnetic field on mixed convection flow of a biofluid through a vertical plate using contained heating or cooling is observed in this study. The mathematical formulation is that of the full Biomagnetic Fluid Dynamics (BFD) model which deals with on the ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD) principle. In this work, the study is performed on a specific biofluid, viz. human blood. Assume that the magnetization very linearly with magnetic field strength, temperature dependency of dynamic viscosity and thermal conductivity is noticed. A system of non-linear equations with appropriate boundary condition is obtained by familiarizing suitable non-dimensional variables in the physical problem. For the numerical solution, we used finite difference method which is based on an efficient technique is applied in the problem. Computations for flow profiles, local skin friction coefficient and local heat transfer coefficient are performed with the magnetic parameter Mn, the viscosity/temperature parameter θr and the thermal/conductivity parameter S∗. The effect of the localized heating or cooling is examined. The computational results presented graphically and have been validated in an appropriate manner. The study reveals that the impact of a magnetic field for blood flow in arteries is found significantly. The results presented bear the promise of valuable applications in physiology, medicine and bioengineering.

Heat transfer analysis of mixed convection boundary layer blood base nanofluids with the influence of viscous dissipation

In this research study, we delve into the analysis of two-dimensional boundary layer incompressible viscous flow of blood based nanofluids, incorporating a couple stress model. This investigation encompasses considerations of heat transmission and viscous dissipation effects. Specifically, focus on a particular type of nanoparticle, Magnesium oxide (MgO), dispersed in blood, the base fluid. By employing suitable similarity transformations, transform a set of partial differential equations (PDEs) into nonlinear ordinary differential equations (ODEs). To leverage the Homotopy Analysis Approach (HAM) to solve this system of equations. This study discerns the impacts of various factors on temperature and velocity distributions. Visualization through graphs depicting nanoparticle volume concentration, magnetic field strength, couple stress parameter, Eckert number, and Prandtl number aids in presenting our findings. These insights illuminate the intricate interplay among different parameters and offer insights for enhancing heat transfer in blood-based nanofluids. Additionally, scrutinize the thermal performance of the blood-based nanofluid, assessing the Nusselt number and local skin friction coefficient. Such analysis holds significance for ensuring patient safety and treatment efficacy, particularly in medical procedures involving blood circulation, where mixed convection plays a pivotal role. Understanding these dynamics is crucial for the design and optimization of various medical devices and therapies, ensuring optimal temperature maintenance during blood circulation-related operations.

Mixed Convection Boundary Layer Flow over a Solid Sphere in AL203-Ag/Water Hybrid Nanofluid with Viscous Dissipation Effects

The current study aims to investigate how heat transfer and skin friction develop by modifications in the fundamental advantages of fluids in the presence of mixed convection boundary layer flow over on a sphere in hybrid nanofluids. The numerical solutions for the reduced Nusselt number, local skin friction coefficient temperature profile, and velocity profiles are discovered and clearly presented. The Eckert number, the mixed convection parameter λ, and the nanoparticle volume fraction are all investigated and described. It is found that increasing the volume percentage of nanomaterial in nanofluid enhanced the value of the skin friction coefficient. The low density of nano oxides in hybrid nanofluids, such as alumina, also contributes to reduced friction between fluid and body surface. The findings of a computational investigation demonstrate that the use of a hybrid nanofluid, composed of nanometal and nano-oxide in the form of , has the potential to decrease skin friction while maintaining heat transfer characteristics comparable to that of Ag/water nanofluid. The findings in this publication are new and will be useful to boundary layer flow researchers. It can also be applied as a guideline for experimental investigations with the goal of reducing the cost of operation

Radiative and Lorentz’s effects on MHD free convective mass and heat transfer time-dependent nanofluid flow across vertical perforated plate

The current study investigates the effects of thermal radiation and Lorentz’s force on heat and mass flow in a nanofluid with a magnetic field and free convection, as it passes over a vertical permeable sheet. The dominant PDEs are turned into linked nonlinear ODEs using an appropriate similarity transformation. Using the MATLAB ODE45 tool, dimensionless ODEs are numerically computed using the finite difference procedure. Four different water-based nanofluids are considered, including copper, titanium dioxide, aluminum oxide, and silver. The influence of emerging dimensionless numbers and other parameters, such as the magnetic force parameter, the radiation parameter, the suction parameter, the Prandtl number, the Schmidt number, the Dufour number, as well as for constant values of the modified local Grashof number and local Grashof number on the concentration, velocity, and temperature profiles is emphasized and mentioned. Moreover, the visual representation of the effects of a volume percentage of up to 4% copper nanoparticles on the distributions of concentration, temperature, and velocity is also shown. The temperature profile, concentration profile, and velocity profile all grow with an increase in the volume percent of copper nanoparticles between 0.00 and 0.04. Furthermore, numerous scenarios are investigated for the distributions of the local Sherwood number, the local Nusselt number, and the local skin friction coefficient. The local Nusselt number decreases, and the local skin friction coefficient and Sherwood number increase about by 30 %, 45 %, and 60 % respectively due to increasing the value of volume fraction from 0 % to 4 %. The local skin friction coefficient increases and the local Nusselt number decreases by about 15 % and 39 % respectively for rising values of the thermal radiation number from 0.5 to 3.5. In addition, for magnetic force parameter values between 0.5 and 4.0, the local skin friction coefficient drops by about 13 %.

Dynamic simulation of unsteady Casson–Carreau fluid flow considering temperature-dependent variable-properties and thermo-solutal mixed convection over flat and slendering sheets

The present investigation delves into the intricate interplay between surface effects and fluid dynamics, focusing on the flow characteristics of Casson and Carreau fluids endowed with temperature-dependent thermophysical properties. Specifically, the study explores the ramifications of radiative, mixed convection, and magnetized processes on heat and mass transfer phenomena. A comprehensive mathematical model is developed to analyze the behavior of Casson–Carreau fluids in conjunction with microscopic particles and gyrotactic microorganisms over both flat and slender surfaces. Leveraging similarity transformations, the governing equations are transformed into dimensionless form, facilitating numerical solutions using the bvp5c solver in MATLAB. The ensuing numerical and graphical analyses elucidate key physical quantities, including local skin friction coefficients, gyrotactic microorganism density, Nusselt number, and Sherwood number, across a spectrum of physical parameters. Notably, the investigation underscores the profound influence of flat surfaces on flow patterns and highlights the heightened consumption of fluid particles with increasing variable diffusivity and thermal conductivity. Moreover, enhanced values of parameters such as variable motile microorganism diffusion coefficient, Brownian motion parameter, and temperature-dependent thermal conductivity parameter are found to augment the Nusselt number, indicative of intensified heat transfer rates. This research underscores the imperative of comprehending the intricate dynamics of fluid flow and heat transfer, offering actionable insights for enhancing engineering designs and addressing multifaceted challenges across domains encompassing chemical engineering, environmental science, and biomedical applications.

Analytical Investigation of Magnetohydrodynamic Hybrid Nanofluid Flow Over a Permeable Shrinking Sheet

The flow and heat transfer of Cu-Al2O3/water hybrid nanofluid over a shrinking sheet were investigated taking account of the magnetic field, suction, variable heat sink, and thermal radiation. At first, the governing equations were completely changed into ordinary differential equations (ODEs) with proper transformations. The novelty of this investigation is that the ODEs were analytically solved and the dual characteristics of flow properties and heat transfer were graphically presented. Results revealed that an increase in the volume fraction of Cu nanoparticles (φ2), magnetic parameter (M), and suction parameter (S) caused an increase in the local skin friction coefficient (Rex1/2Cf), local Nusselt number (Rex-1/2Nux) and region of the existence of dual solutions. With the increase of φ2, M, and S, fluid velocity increased and temperature decreased. Contrary to this, the converse was observed for increasing the volume fraction of Al2O3 nanoparticles (φ1). These findings indicated that with proper tuning of these parameters, the cooling rate of a shrinking sheet could be controlled and the possible working conditions of a system might be increased.

Utilization of OHAM on mixed convective flow of Williamson fluid model with viscous dissipation over a stretched cylinder

This research focuses on the fluid dynamics and heat transfer characteristics of the Williamson fluid over a permeable stretched cylinder, accounting for heat generation effects. Incorporating elements such as viscous dissipation, mixed convection, Joule heating, entropy generation, and magnetic field presence, the investigation utilizes the Optimal Homotopy Analysis Method for solution development. Through the process of similarity transformations, the partial differential equations undergo a conversion that results in dimensionless ordinary differential equations. Numerical results from this study align well with existing literature, emphasizing the examination of key dimensionless parameters like Reynolds number, suction parameter, magnetic field parameter, mixed convection parameter, heat source parameter and Williamson fluid parameter. The analysis extends to local Nusselt number and skin friction coefficient computations, offering insights into heat transfer and shear stress rates, correspondingly. Additionally, the research delves into the effects of several physical parameters on temperature and velocity profiles, presenting a comprehensive overview in academic discourse. The study's methodology and findings contribute to the understanding of phenomenon related to heat transfer and fluid flow, making it a valuable addition to the scholarly domain.

Employing the Akbari Ganji Method (AGM) to conduct a semi-analytical analysis of transient Eyring-Powell compressible flow in a tensile Surface under the influence of a magnetic field

This study explores the transfer of mass and heat within unstable two-dimensional flows of non-Newtonian material under conditions involving radiation generation, absorption, and thermal radiation. Additionally, it investigates the impact of magnetic hydromagnetic joule (MHD) heating on these processes. The researchers converted the partial differential equations into ordinary ones through appropriate transformations. Subsequently, a new idea was considered, involving coupling fractional differential equations using the AGM method, with an order of 0.5 < a <0.8 and the initial condition x (0) = x0. A new technique is introduced to find the exact solution of fractional differential equations by solving the correct order differential equations. The primary aim of this paper is to explore the impact of parameter variations on velocity, temperature, local skin friction coefficient, and local Nusselt and Sherwood numbers. This article investigates the effect of multi-parameter changes on local skin friction coefficient and Schmidt number. In most fluid heat transfer problems, especially in non-Newtonian fluids, fractional differential equations are widely used in liquids. The obtained results indicate that the Lorentz force, influenced by the magnetic field parameter (Ha), diminishes the velocity distribution. Additionally, it is observed that the temperature profile decreases as the radiation parameter (R) increases.

Finite difference simulation of natural convection of two-phase hybrid nanofluid along a vertical heated wavy surface

This study employs finite difference modelling to investigate the natural convection of a two-phase hybrid nanofluid consisting of Al 2 O 3 and Cu nanoparticles dispersed in water along a vertically heated wavy surface. The hybrid nanofluid has unique features that influence convective heat transfer. Numerical solutions analyze fluid flow patterns and temperature distributions, providing insights into heat exchange and thermal management. The research highlights the importance of hybrid nanofluids, notably those containing Al 2 O 3 and Cu in a water base, in improving overall heat transfer efficiency. The mathematical model accounts for laminar and incompressible fluid flow with a Prandtl number of Pr = 6.2, Lewis number Le = 10, and maximum 10 % concentration of hybrid nanoparticles. After transforming the governing equations into a non-dimensional form, the implicit finite difference method is used to solve them. The solution employs the in-house FORTRAN 90 code and compares its outcomes with the benchmark results. Various parameters, such as the Schmidt number (Sc = 1 to 10), volume fraction of nanoparticles ( ϕ = 0.0 to 0.1), wavy amplitude (A = 0.0 to 0.3), and N BT = (0.05 to 0.2), are investigated regarding temperature, velocity, local skin friction coefficient ( C f ) , local Nusselt number (Nu), streamlines, and isotherms. Elevated volume fraction generally decreases skin friction, increases temperature, and may reduce velocity. Meanwhile, higher skin friction, temperature, velocity, and local Nusselt numbers often correlate with elevated Schmidt numbers. Changes in amplitude and N BT affect skin friction, temperature, velocity, and local Nusselt numbers, providing information on the dynamics of fluid systems. For example, when the volume fraction (ϕ) increases from 0 to 0.1 at Y = 2, the temperature rises by 75 % , while the velocity gradually decreases by 11.11 % . This is in contrast to findings according to when the N BT rises from 0.05 to 0.2 at Y = 1. In this case, the temperature drops by 18.75 % , followed by a 9.68 % fall in fluid velocity. Understanding these interactions enhances comprehension of heat transfer and fluid dynamics. By investigating these interactions, we not only improve our understanding of heat transfer and fluid dynamics, but also open the door to new strategies for improving thermal systems and manufacturing procedures.

Numerical simulation and stability analysis of radiative magnetized hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface

The power electrical devices are being continuously trimmed down and must disperse a greater amount of heat flux, overheating has become a significant issue. Ferrofluids, also known as magnetic nanofluids, consist of solid magnetic nanoparticles that exhibit superior thermal conductivity compared to their underlying fluids, which can be either aqueous or oil based. This facilitates increased rates of convective heat transfer, but more importantly, it allows for external flow modification using a magnetic field. This work is unique in that it analyses hybridized ferrofluid flow over a shrinking/stretching surface with radiative magnetization and significant magnetic force. The governing equations were solved using the bvp4c function in MATLAB, after being transformed into ordinary differential equations (ODEs) by using similarity transformations. The system acquires a bimodal solution, and stability analysis validates the physical and dynamic stability of the first solution. The local skin friction coefficient, the local Nusselt number, the temperature and velocity profiles, and the substantial influence of governing effects are all studied and graphically displayed. The key findings are the values of Nux1Rex are decreasing for both second and first solutions as values of φCoFe2O4 are increasing. An increasing trend for the values of RexCf is observed for both second and first solutions as values of φCoFe2O4 increases. The results compareded with the results reported in literature and found a significant agreement.

Application of the Fibonacci wavelet approach to the MHD boundary layer analysis of a Casson fluid past a stretching sheet

The current work investigates the MHD boundary layer flow of Casson fluid over a stretching sheet with the help of Fibonacci wavelet approach. The stable laminar MHD flow, mass and heat transport properties of a nanofluid over a stretching sheet in the presence of a fluctuating magnetic field has been under scrutiny. By choosing relevant non-dimensional parameters, the governing boundary layer equation undergoes transformation into a dimensionless Falkner-Skan equation. The Fibonacci integral operational matrix is used to solve the achieved nonlinear equation and it has been used for the first time to solve stretching sheet problem in fluid dynamics. The nature of the boundary layer flow are analyzed graphically for a range of distinct values of physical parameters. Impact of parameters on axial and transverse velocity has been investigated. It can be observed that local skinfriction coefficient grows for larger values of Casson parameter for ϵ = 0.3 and decreases for higher values of Casson parameter and decreases for higher values of magnetic parameter, angle of inclination and pressure gradient parameter. To ensure the accuracy of the findings, local skin friction is recorded and contrasted with various approaches that are already documented in research.

Enhanced Energy Transfer Performance in an Inclined Magneto-Convective Sutterby Ternary Hybrid Nanoflow: Application for Nano Diesel

This study investigates sodium alginate-based nano-lubricants with added copper and aluminum oxides. The thermal performance of nano (Al2O3), hybrid (Al2O3 + CuO) and ternary (Al2O3 + CuO + TiO2) nanofluids is studied and compared in this article. Due to the significant impact of higher stream rates, the ternary nanofluid is crucial in domains such as petroleum engineering. A Sutterby nanoflow model past a stretching sheet embedded in permeable media is considered. In this fluid, the effects of thermal radiation, hotness source/sink, inclined magneto-convection under Stefan blowing, and chemical reaction are assumed. The highest-order nonlinear partial differential equation is handled by utilizing the similarity function, producing a new set of ordinary differential equations. The derived equations are then quantitatively analyzed using the bvp4c approach in MATLAB.Graphical representations of several features for specific non-dimensional variables, including heat transfer, Sherwood, drag coefficient, velocity, temperature, and concentration, are presented. An increase in the thermal curve is observed due to the heat source/sink parameter; however, the Nusselt number exhibits the opposite pattern. The participation of Nb and the thermophoresis force led to greater thermal radiation. For Sc and Kr, the mass transfer ratio of the ternary nanofluid is lower. The results show very good congruence when compared to the literature. Our results also prove that the ternary hybrid nanofluid transfers more heat from the system than the hybrid or nanofluid. With an increase in Stefan blowing, the rate of energy and mass transfer rises, while the local skin friction coefficients show a tendency in the opposite direction.

Significance of shape factor on magnetohydrodynamic buoyancy thin film flow of nanofluid over inclined sheet with slip condition: Irreversibility analysis

This work aims to examine the entropy production, heat transport, and dynamics of the unsteady thin film magnetohydrodynamic (MHD) flow of a nanofluid composed of alumina (Al2O3) and water. The fluid flow is seen to pass over an inclined sheet, taking into account the effects of buoyancy force, viscous dissipation, and joule heating. The system of partial differential equations (PDEs) is optimized under the boundary layer assumptions. Appropriate transformations are used to convert the governing partial differential equations (PDEs) and boundary conditions into dimensionless forms. Using MATLAB’s bvp4c code and a local non-similarity technique with up to second-degree truncation, we can obtain the findings of the enhanced model. The effect of multi-shape Al2O3 nanoparticles on flow, heat, and entropy-generating features is also investigated after the calculated results have been successfully aligned with published data. Mixed convection, nanoparticle volume percent, inclination angle, magnetic field intensity, mass suction, Eckert number, and Biot number are only a few of the governing parameters whose effects are graphically shown for selected values. As a result, the local Nusselt number and skin friction coefficient may be calculated. The skin friction and Nusselt number profiles exhibit a decreasing trend as the values of nanoparticle volume fraction ([Formula: see text]) magnetic [Formula: see text] and unsteadiness (A) increase toward mixed convection ([Formula: see text]). On the other hand, Nusselt number profile increases with increasing values of mass suction parameter [Formula: see text] The profiles of entropy generation and Bejan number show an upsurge as the values of the magnetic parameter [Formula: see text] and Brinkman number (Br) increase. Conversely, the entropy generation reduces with an increase in the temperature difference parameter [Formula: see text] and Bejan number increases.

The impact of a chemical reaction on the heat and mass transfer mechanisms in a dissipative and radiative nanofluid flow over a nonlinear stretching sheet

This paper presents a numerical investigation of the flow of a non-Newtonian tangent hyperbolic nanofluid over a nonlinearly stretched surface, taking into account factors such as thermal radiation, prescribed surface temperature, and a chemical reaction mechanism. Furthermore, the analysis includes the consideration of both viscous dissipation and the influence of a magnetic field within a Darcy porous medium. A mathematical framework for addressing the issue, rooted in the principles of conserving momentum, energy, and mass. The MATHEMATICA tools were employed to apply the shooting technique in order to solve the modeled equations describing the temperature, velocity, and concentration fields of the proposed physical system. Graphs are used to illustrate how certain key parameters affect the profiles of concentration, velocity, and temperature. Data tables are utilized to display information pertaining to the local Nusselt number, local Sherwood number, and local skin friction coefficient. The present results have been confirmed through a comparison with previously published findings. This research holds significant importance as it focuses on the extensive utilization of tangent hyperbolic nanofluids in cooling electronic components that produce substantial heat during their operation. The observed pattern indicates that as the local Weisbsenberg number, magnetic number, local porous parameter, and power law index increase, there is a reduction in the boundary layer thickness. Conversely, in the instances of concentration and temperature distributions, an escalation in these parameters leads to an expansion of the boundary layer thickness.

Heat and Mass Transfer Characteristics of Mixed Convection MHD Flow with the Impacts of Hall Current and Diffusion Thermo in the Presence of Brownian Motion and Thermophoresis

This study investigates the influence of Hall current diffusion, thermo-activation energy, and other parameters on the flow characteristics of an electrically conducting Jeffrey nanofluid. The Jeffrey nanofluid flow occurs across a continually expanding surface, and additional factors like thermal radiation, heat generation/absorption, and inclined plates are included in the analysis. A vertically installed transverse magnetic field is assumed to have a modest Reynolds number. The controlling partial differential equations are transformed into nonlinear ordinary differential equations using appropriate similarity transformations. These equations are then numerically solved using the Matlab bvp4c module. This study aims to analyze the impact of many factors, including the Hall current factor, the thermal radiation factor, the heat source/sink factor, the Brownian motion factor, the thermophoresis parameter, and the magnetization, on the velocity, concentration, and temperature. To do this, graphical representations will be used as a means of visualizing and discussing the impacts, as mentioned earlier. To get a deeper understanding of the internal dynamics of the emerging parameters, a numerical computation is conducted to determine the local Nusselt number, Sherwood number, and skin friction coefficient along the x and z axes. Research findings have shown that the flow velocity exhibits a decreasing trend as the linear and nonlinear thermal radiation components rise. Furthermore, augmenting the values of the Brownian motion parameter will lead to a reduction in the concentration profile of the nanoparticle.

Magnetohydrodynamics thermosolutal convection of hybrid MWCNT-Fe[formula omitted]O[formula omitted]-water nanofluid along a vertical wavy surface with wall heat and mass flux

This numerical analysis investigates the behavior of magnetohydrodynamics (MHD) thermosolutal convection in a hybrid nanofluid made up of multi-wall carbon nanotube (MWCNT)-Fe3O4 and water along a vertical wavy surface with wall heat and mass flux conditions. The mathematical model is developed using the conservation equations of mass, momentum, energy, and energy. The governing equations are converted into a non-dimensional form using the appropriate transformation, and the implicit finite difference technique is used to solve them. The effects of various parameters, such as the Schmidt number (Sc), nanoparticles volume fraction (ϕ), wavy amplitude (a), magnetic parameter (M), buoyancy ratio (Br), on the velocity, temperature, concentration distribution (Φ), streamlines, isotherms, local skin friction coefficient (Cf), local Nusselt (Nu) number, local Sherwood number (Sh) are investigated. Results show that higher amplitude and the addition of hybrid nanofluids volume fraction slow down the heat and mass transport rate, as indicated by declining local Nusselt and Sherwood numbers. However, enhancing the buoyancy ratio increases the fluid flow’s skin friction, heat, and mass transport. The velocity, temperature, concentration distribution, skin friction, and convective heat transport within the wavy surface is weakened by the addition of the magnetic parameter M.

Thermal characteristics of MHD [formula omitted] water nanofluids flow past a stretching/shrinking wedge in the view of Cattaneo-Christov heat flux

Wedge flow has a variety of potential uses, including thermal systems, geothermal power plants, aerodynamics and cooling of nuclear power plants. In this framework, the modified Cattaneo-Christov heat flux is implemented to examine the thermal characteristics in the dissipative flow of a viscous nanoliquid over a shrinking/stretching wedge. The laminar and two-dimensional flow of CoFe2O4/ water over a wedge domain is scrutinized. The self-similar solutions using bvp4c together with the stability analysis are estimated to demonstrate the physical existence of first and second solutions under relevant parameters used in the study. The findings reveals that the reverse flow phenomena, the novel form of decreasing flow exhibits physical existence which is significantly different from those in the stretching flow scenario. Thermal relaxation has a substantial impact on energy flux, which results in oscillatory heat conduction with a narrower temperature. When the volumetric friction of nanoparticles grows from 0.0 to 0.02, the local skin friction coefficients rises. The upper branch elucidation is stable and physically realistic, while the second branch solution is imaginary and having no physical existence. The rise and fall in temperature and velocity is perceived with suction parameter. However, the dropping of velocity is seen with the nanoparticle volume percentage.