Momentum Boundary Layer Thickness Research Articles

Comparative analysis of non‐newtonian fluids over an exponentially stretching sheet with convective boundaries

AbstractThe primary objective of this research is to explore the behavior of several non‐Newtonian fluids, including Casson, Williamson, and Maxwell fluids, over an exponentially stretching sheet considering an inclined magnetic field into account. Non‐Newtonian fluids can be encountered in many industrial and biological applications. They differentiate themselves by their sophisticated viscosity and flow properties. For the purpose of optimizing applications like coating technologies, bioengineering, and polymer processing, it is essential to comprehend their flow dynamics. This work illuminates these fluids' behaviors under convective boundary conditions, which is important for numerous industrial processes. Due to the convective boundary conditions, heat transfer at the sheet is affected by the surrounding fluid. The dominating flow field's nonlinear partial differential equations (PDEs) are synthesized into a system of coupled nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations, and the resulting equations are then numerically solved using the BVP4C solver in MATLAB software. To demonstrate the behaviors of velocity, temperature, and concentration, a parametric research has been attempted. Significant parameter's effect on velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number have been investigated, and numerical findings are shown graphically. The numerical data is validated to previously published results on a variety of particular instances and found to be in great agreement. For varying values of the porosity parameter, Darcy‐Forchheimer parameter, and magnetic field, the fluid velocity falls. It is claimed that as the Forchheimer number and the porosity parameter expands, the momentum boundary layer thickness and the velocity profile diminishes. Furthermore, at the maximum levels of Schmidt number, the temperature profile rises synchronously, although the concentration profile reflects the flip pattern.

Exploring shape and size variations significance in hybrid nanofluid flow via rotating porous channel

AbstractThe current study investigates the thermal performance characteristics of metallic (Cu) and non‐metallic (TiO2) nanoparticles (NPs), considering variations in their shapes and sizes. Specifically, analysis is conducted for four distinct stable shapes of NPs. A hybrid model is developed to analyze the influence of rotating porous walls on the system, particularly focusing on the impact of the permeable Reynolds number and NPs within a specific range of , in conjunction with a Newtonian fluid under the influence of magnetohydrodynamics (MHDs). Additionally, we examine the phenomena of expansion/contraction in heat and mass transfer enhancement with chemical reactions. The governing partial differential equations (PDEs) are transformed into nonlinear differential equations using the help of similarity transformation. A 4th‐order Runge–Kutta method (RK), coupled with the shooting technique, is employed as a mathematical strategy to numerically solve these nonlinear differential equations. Boosting the values of 𝐾𝑐𝑟 from 2 to 10 enhances the mass transfer rate between both porous channels. Higher values of 𝑅𝑒, 𝑀, and 𝑅 lead to increasing skin friction coefficients for both porous channels. Raising the values of both NP volume fractions ( from 1% to 5% results in enhanced heat transfer rates particularly for much better in platelet‐shaped NPs as compared to other shapes such as spherical, brick, and cylinder. Larger values of 𝛼, M, and Re cause the radial velocity profile to exhibit opposite behaviors in the middle of the wall and momentum boundary layer thickness.

Electromagnetic mixed convective flow of dusty hyperbolic tangent hybrid nanofluid over a stretching surface: A quadratic regression analysis using RSM

This article investigates the flow dynamics of electrically conducting dusty hyperbolic tangent fluid over a stretching sheet with thermal radiation and heat source effects. Moreover, the suspension of Aluminium oxide (Al2O3) and Tantalum nanoparticles in engine oil as base fluid at 300 K is considered. The flow and thermal dynamics are analysed using Xue and Hamilton Crosser's thermal conductivity models. Moreover, using various ranges, the effect of the Richardson number on forced, mixed and natural convection is examined. The governing partial differential equations of the flow model are converted into ordinary differential equations and then solved numerically using the boundary value problem solver BVP4C along with the shooting technique in MATLAB. The Xue model enhances the heat transfer rate by 3.55% compared to the Hamilton Crosser model ϕ1 = 0.03, ϕ2 = 0.01, R = 0.1, Q = 0.6, βt = 0.2, βv = 0.07. A moderate adjustment to the Richardson number can reduce skin friction by 0.889% in the case of forced convection. The absence of dust particles enhances the thermal and momentum boundary layer thickness. Tantalum nanoparticles outperform Al2O3 in terms of temperature and velocity. It is possible to regulate the temperature and velocity of the backflow by changing the heat source parameter and the nanoparticle volume percentage. The maximum achievable heat transfer rate in the fourth experimental run is 0.2609 when R = 2.5 and Q = 1.5 as determined by the quadratic regression analysis.

Laminar flow with temperature-dependent fluid properties between two stretching rectangular surfaces

Abstract The Navier–Stokes equations and the energy equation are used to investigate a fluid flow between two stretching rectangular surfaces subjected to a temperature difference that affects the dynamic viscosity and thermal conductivity of the fluid. The wall stretching process enhances the momentum boundary layer thickness which slows the axial motion of the fluid away from the flow boundaries. When the stretching parameter γ is equal to 1, that is the case corresponding to symmetric stretching, the minimum of the axial velocity is located at the midplane of the channel y = 0.5 if the viscosity variational parameter α equals 0. This minimum moves towards the region 0.5 < y < 1 for α > 0, but migrates towards the region 0 < y < 0.5 for α < 0. Moreover, in the case of symmetric stretching corresponding to γ = 1, the growth in Reynolds number Re tends to increase the axial velocity around the middle of the channel for α ≥ 0 in the attempt to counteract the effects of enhancing the momentum boundary layer thickness leading to the flattening of axial velocity profiles for Re ≥ 100. While the conductivity variational parameter β does not influence enough the fluid dynamics and heat transfer, the Reynolds number Re and the Péclet number Pé can increase or decrease the temperature distribution inside the channel depending on the sign of the parameter α. Practical applications related to the present study include lubrification, food manufacturing, paint industries, extrusion processes in plastic and metal industries.

Linear stability analysis of micropolar nanofluid flow across the accelerated surface with inclined magnetic field

PurposeThe purpose of this paper is to study the two-dimensional micropolar fluid flow with conjugate heat transfer and mass transpiration. The considered nanofluid has graphene nanoparticles.Design/methodology/approachGoverning nonlinear partial differential equations are converted to nonlinear ordinary differential equations by similarity transformation. Then, to analyze the flow, the authors derive the dual solutions to the flow problem. Biot number and radiation effect are included in the energy equation. The momentum equation was solved by using boundary conditions, and the temperature equation solved by using hypergeometric series solutions. Nusselt numbers and skin friction coefficients are calculated as functions of the Reynolds number. Further, the problem is governed by other parameters, namely, the magnetic parameter, radiation parameter, Prandtl number and mass transpiration. Graphene nanofluids have shown promising thermal conductivity enhancements due to the high thermal conductivity of graphene and have a wide range of applications affecting the thermal boundary layer and serve as coolants and thermal management systems in electronics or as heat transfer fluids in various industrial processes.FindingsResults show that increasing the magnetic field decreases the momentum and increases thermal radiation. The heat source/sink parameter increases the thermal boundary layer. Increasing the volume fraction decreases the velocity profile and increases the temperature. Increasing the Eringen parameter increases the momentum of the fluid flow. Applications are found in the extrusion of polymer sheets, films and sheets, the manufacturing of plastic wires, the fabrication of fibers and the growth of crystals, among others. Heat sources/sinks are commonly used in electronic devices to transfer the heat generated by high-power semiconductor devices such as power transistors and optoelectronics such as lasers and light-emitting diodes to a fluid medium, thermal radiation on the fluid flow used in spectroscopy to study the properties of materials and also used in thermal imaging to capture and display the infrared radiation emitted by objects.Originality/valueMicropolar fluid flow across stretching/shrinking surfaces is examined. Biot number and radiation effects are included in the energy equation. An increase in the volume fraction decreases the momentum boundary layer thickness. Nusselt numbers and skin friction coefficients are presented versus Reynolds numbers. A dual solution is obtained for a shrinking surface.

Prediction of Bedform Dimensions on Alluvial Bed in Unidirectional Flow

In this study, the bedform dimensions of an alluvial bed in a unidirectional flow were experimentally investigated. A series of flume experiments was conducted; 700 sets of flume and field data were used in developing formulae for predicting the bedform dimensions on alluvial beds in unidirectional flow. Bedform dimensions include the length and height of bedforms generated by the lower and upper flow regimes; the resistance coefficient for the flow in different flow regimes is introduced into the proposed formulae. The momentum boundary-layer thickness was introduced as an independent variable instead of the flow depth. Based on a large amount of flume and field data, the coefficients of each parameter were determined; four typical formulae were used to compare the accuracy of the proposed formulae. The experimental results show that the momentum boundary-layer thickness, hydraulic radius, and resistance coefficient for the flow in different regimes correlate well with the bedform dimensions. The calculation results show that the dimensionless particle size should not be ignored in the calculation of bedform dimensions. The bedform dimensions have an obvious trend of rapid increase with an increase in the ratio of flow depth to sand size (H/d). The bedform dimensions obtained using the van Rijn method and the Engelund and Hansen method did not represent the variation trend of the bedform length in the upper flow regime with an increase in H/d when H/d was greater than 103. The calculations using the proposed formulae are more accurate and reasonable than those in previous studies predicting the bedform height and length on an alluvial bed in a unidirectional flow.

Neural network and thermodynamic optimization of magnetized hybrid nanofluid dissipative radiative convective flow with energy activation

This article, motivated by hybrid magnetic coating manufacturing developments, utilizes a neural network-based computational program to study the dynamics of hybrid magnetic nanofluids with entropy generation. A new physico-chemo-mathematical model has been presented to simulate the hybrid magnetic nano-coating flow along a stretching surface to a porous medium with viscous heating. A Rosseland flux model is used for radiation heat transfer and Darcy’s model for the isotropic porous medium. The stretching sheet is porous, and wall suction or injection are possible. A robust neural network has been deployed to optimize the physical parameters controlling the transport characteristics of hybrid nanofluids. Specifically, two hybrid nanoparticle combinations are addressed, namely graphite oxide (GO)-molybdenum disulfide ( Mo S 2 ) and copper (Cu)-silicon dioxide ( Si O 2 ), both with engine oil as the base fluid. The dimensional boundary layer model is transformed via suitable scaling variables from a partial differential system into a dimensionless non-linear coupled ordinary differential system. The transformed boundary value problem is solved numerically with the BVP4C subroutine in the symbolic software MATLAB, which achieves exceptional accuracy. Validation with previous simpler studies is conducted and a good correlation is obtained. The neural network optimization analysis incorporates Bayesian regularization as the training algorithm. The Bejan entropy generation minimization (EGM) analysis shows that with increasing radiation parameter R d , both entropy generation rate and Bejan number are increased. Furthermore, an elevation in Brinkman number Br leads to an upsurge in entropy generation rate and a downtrend in the Bejan number. The numerical solution of the boundary value problem reveals that with an increment in nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , surface injection parameter ( s < 0 ) , Eckert number Ec and radiation parameter R d and with a decrement in suction parameter ( s > 0 ) and Prandtl number Pr , there is a strong enhancement in temperature magnitude and thermal boundary layer thickness. With greater nanoparticle solid volume fraction φ 2 , magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and a reduction in thermal buoyancy parameter λ , strong flow deceleration is induced, and momentum boundary layer thickness is increased. The skin friction coefficient is substantially boosted with lower values of magnetic parameter M , inverse permeability parameter ϵ , suction parameter s and higher values of thermal buoyancy parameter λ . There is a significant decrement also computed in Nusselt number with a greater radiation parameter R d . The simulations provide a good benchmark for future extensions that may consider non-Newtonian behavior.

Triple diffusive free magneto-convection of electro-conductive nanofluid from a vertical stretching sheet

In the present investigation, an analysis is carried out to study the MHD triple diffusive free thermo-solutal convection boundary layer flow of an electro-conductive nanofluid flow over a vertical stretching sheet. This problem is relevant to magnetic nanomaterials fabrication operations in which multiple species in addition to nanoparticles are present. In addition to the nanoparticle diffusion, two different salts (species) having different properties are considered. A variable magnetic field is applied transverse to the vertical sheet. It is assumed that the surface is in contact with the hot magnetic nanofluid at a temperature which provides a variable heat transfer coefficient. Buongiorno’s model is employed for the nanofluid. It is also assumed that the Oberbeck-Boussinesq approximation is valid and the mixture of nanofluid and salts is homogenous and is in local thermal equilibrium. In addition, the thermal energy equation features cross-diffusion (Soret and Dufour) terms for both components of salts having different concentration. Appropriate similarity transformations are deployed to render the model non-dimensional. The emerging transformed dimensionless non-linear non-dimensional ordinary differential boundary value problem is solved with the robust bvp4c method in MATLAB. Validation with previous studies has been included for special cases of the general model. The simulations show that the addition of nanoparticles and salts, strongly modifies Temperature and nanoparticle and salt 1 and 2 concentrations. With stronger magnetic field the velocity is suppressed as is momentum boundary layer thickness whereas temperatures are boosted.

Radiative Mixed Convection Flow of Casson Nanofluid through Exponentially Permeable Stretching Sheet with Internal Heat Generation

This paper investigates the mixed convection boundary-layer flow of Casson nanofluid with an internal heat source on an exponentially stretched sheet. The Buongiorno model, incorporating thermophoresis and Brownian motion, describes fluid temperature. The modeled system is solved numerically using bvp4c routine to analyze the impact of different fluid parameters on velocity, temperature, and concentration profiles. The analysis reveals that the suction effect, magnetic field, and Casson parameter reduce momentum boundary layer thickness and hence slow fluid motion. Conversely, buoyancy forces increase mass boundary layer thickness which results in accelerating fluid motion. Temperature and concentration profiles show similar trends for Brownian motion, radiation, and thermophoresis.

Thermal radiative and Hall current effects on magneto-natural convective flow of dusty fluid: Numerical Runge–Kutta–Fehlberg technique

This research article intends to examine the consequences of Hall impact on the natural convection of magnetohydrodynamic (MHD) fluid flowing and the thermal characteristics of the fluid flow which containing dusty particles via a vertical stretchable sheet. Slip velocity and convective boundary conditions are taken into consideration in this research article. The flow is mathematically described by partial differential equations. The governing equations are renovated into a group of nonlinear differential equations with the use of similarity conversations, which are then resolved numerically by applying Runge–Kutta–Fehlberg. The behavior of these physical factors on the rapidity and temperature profiles of the dust and fluid phases are exposed graphically in this article. Furthermore, frictional force and heat transfer are also examined and discussed. According to the investigation, the existence of suspended particles in the fluid lead to increment in momentum and thermal boundary layer thickness. The temperature of the fluid seems can be controlled by the significant parameter, such as it seem to be increase due to the magnetic, radiation, and Hall parameters, while it is seen to have decreased due to the slip thermal parameter. While the radiation accelerates up the fluid velocity, the magnetic parameter is excellent at slowing it down. The fluid phase’s temperature and velocity profiles are almost usually higher than those of the dust phase. The outcomes contribute to a better understanding of the two-phase theory’s fluid flow phenomenon.

EMHD stagnation point flow of dusty hybrid nanofluid over a permeable stretching sheet: Radiative solar applications

The primary objective of this paper is to investigate the impact of dusty hybrid nanofluid electromagnetohydrodynamics (EMHD) on the stagnation point flow in the presence of solar radiation. Base fluids contain ethylene glycol, water, silver, titanium alloy, and suspended dust particles. Nonlinear differential equations with two or more independent variables define fluid flow phenomena. The governing equations can be solved by the MATLAB solver by employing a suitable numerical method, like R–K fourth order via shooting method. The isothermals for various parametric values have been explained. Because it has the potential to greatly advance the disciplines of industrial and thermal engineering, this proposed model is useful. When compared to using a single base fluid, the combination of two additional base fluid qualities provides noteworthy results. Because we were able to acquire a lower freezing point than water and better heat conductivity than pure ethylene glycol when we employed the combination of the two base fluids. Glycol water is used in car coolant and solar heating systems for a variety of purposes. Impact of embedded physical quantities like electric field parameter, ratio of specific heat, porosity parameter, stagnation parameter, radiation parameter, heat source parameter, and fluid particle interaction parameter for both velocity and temperature are illustrated graphically. Dust particles have a notable impact on various sectors, including the food and pharmaceutical industries. Specifically, they are special importance in applications such as wastewater treatment, solids drying, and the presence of plastic-coated metal items. In the present work, we observe that the stagnation parameter enhances the momentum boundary layer (MBL) thickness because the dusty fluid dominates the dusty hybrid nanofluid while incorporating the Ag + Ti alloy/EG + Water. The radiation becomes more efficient at evenly spreading heat, potentially resulting in a more uniform temperature distribution. Silver and titanium alloy particles may affect the thermal conductivity of dusty hybrid nanofluid when compared to the dusty fluid. The porosity parameter enhances the fluid flow and penetration by the porous medium, which lowers friction between the skin and the surface and reduces resistance.

LDV measurements of boundary layer velocity profiles on flat plates with different surface roughnesses

The dynamics acting upon thin flat plates submerged in a fluid are chiefly governed by the delicate boundary layer enveloping their surfaces. Through a series of experiments, we investigated the impact of surface roughness elements on the boundary layer adjacent to a flat plate across a range of Reynolds numbers. The experiments were performed in the Chungnam National University-Cavitation Tunnel (CNU-CT). Three flat plates, each characterized by distinct surface roughness heights denoted by k, were subjected to scrutiny. One boasted a pristine smoothness, while the others bore the deliberate roughness of sandpaper, each with its own unique texture. With precision instrumentation, including Laser Doppler Velocimetry (LDV), we meticulously documented the axial velocity profile and the RMS (Root Mean Square) velocity at strategic points along the flat plates. Through these measurements, we unveiled the boundary layer's thickness, δ, and momentum thickness, θ, elucidating their variations under differing free-stream velocities. As our exploration deepened, the relationship between the local Reynolds number, Rnx, and the non-dimensional velocity profiles, u+ − y+, became apparent. A systematic shift along the log-law line ensued, with both u+ and y + increasing in tandem with the rise in Rnx. Yet, our inquiry did not conclude with observation alone. Employing empirical rigor, we quantified the drag forces acting upon flat plates of varying roughness heights, deriving them from the measured momentum thickness across a range of local Reynolds numbers, Rnx.

Impacts of nanoscaled metallic particles on the dynamics of ternary Newtonian nanofluid laminar flow through convectively heated and radiated surface

Heat transfer study influenced by various physical effects like thermal radiations, convective heat condition and thermal slip is one of the influential research domain specifically in applied thermal and chemical engineering. Therefore, the key purpose of this is to develop and discuss the heat performance of ternary nanofluid model including the effects of above mentioned parameters. The model is developed for laminar flow of ternary nanofluid about stagnation point over a cylinder's surface. Use of similarity transforms, properties of ternary nanofluids and ternary particles are exercised to obtain final model. Then, the RK-scheme is implemented for demonstration of the physical results and provided a detailed discussion. It is noticed that for λ=0.1,0.2,0.3,0.4, the ternary nanoliquid movement boosted and for λ=−0.1,−0.2,−0.3,−0.4 control the motion and MBLT (Momentum Boundary Layer Thickness) diminishes for saddle point case. Increasing the transient effects A1=0.05,0.10,0.15,0.20 causes quite rapid movement of the fluid molecules. Further, it is observed that thermal slip (α1=0.1,0.2,0.3,0.4), surface convection Bi=0.1,0.2,0.3,0.4 and thermal radiations are good physical aspects to enhance the heat transfer. Also, decrease in thermal boundary layer is observed. For composite φ=2.0%, density increases as 105 %(nano), 129 %(hybrid), 145 %(ternary), dynamic viscosity 105.18 %(nano), 113.503 %(hybrid), 122.483 %(ternary), thermal conductivity 106 %(nano), 115.5 %(hybrid), 131.71 %(ternary) and heat capacity diminishes.

Analytical and Numerical Solutions for Heat, Mass and Entropy Generation of Fourth Grade Nanofluid Flow Over A Vertical Plate

The focus of this research is to investigate magnetohydrodynamic flow, entropy generation, heat and mass transfer analysis for fourth grade nanofluid over a vertical plate in a porous medium subject to slip and convective boundary conditions. Lie group invariant similarity variable is used to transform the partial differential equations (PDEs) governing the problem to system of coupled nonlinear ordinary differential equations (ODEs). The resulting dimensionless ODEs are solved using Homotopy Perturbation Method (HPM). HPM results are validated with the numerical solutions via shooting method alongside the six order Runge-Kutta integration technique. The results revealed effects of new embedded governing flow parameters on velocity, temperature, entropy generation and concentration profiles.Furthermore, the impact of new embedded flow parameters on skin friction coefficient, Nusselt number and Sherwood number at the plate surface are investigated and the results are shown in tabular forms. The results indicate that suction on the plate can be used to control momentum, thermal and solutal boundary layer thickness. This research discovered that magnetic parameter, Eckert number, Biotsolutal number and Hartmann number can be respectively used to adjust fluid flow’s velocity, temperature, concentration and entropy generation. This research also detected that the force driving the fourth grade nanofluid flow called buoyancy driven force can be accelerated or decelerated by adjusting angle of magnetic field inclination. The present investigation has applications in industries and engineering, such as petroleum industries, chemical industries and metallurgy sciences

Computational investigations of the effects of wall surface temperature on a hypersonic inlet isolator

Flow and shock train development in a hypersonic inlet isolator at various wall surface temperatures, Tw, and freestream static temperatures, T?, were studied through numerical simulations. A non-dimensional parameter, Tw /T?, is used to characterize flow behaviors in hypersonic isolator. With the increase of Tw /T?, boundary-layer thickness increases and boundary-layer momentum thickness decreases at the entrance of isolator. Inside the isolator without the presence of backpressure, skin friction decreases with the increase of Tw /T?. The main cause is a lower velocity gradient near the wall at high temperature. A lower skin friction on high wall temperature results in a stronger separation with shock impingement. Under backpressure conditions, with the increase of Tw /T?, an upstream movement of the starting position of the shock train inside the isolator, an increase in the length of the shock train, and an increase in pressure coefficient on the wall surface are observed.

Unsteady Hiemenz Flow of Cu-SiO2 Hybrid Nanofluid with Heat Generation/Absorption

The use of hybrid nanofluid as an alternate heat transfer fluid has shown great potential, and ongoing research to improve its thermal conductivity is important. This study focuses on the impact of heat generation/ absorption on the unsteady Hiemenz flow of aqueous hybrid nanofluid containing copper and silica nanoparticles. Mathematical equations for the hybrid nanofluid model are derived using suitable similarity transformations and solved numerically using bvp4c codes in Matlab software. The results indicate that increased heat generation/absorption leads to an increase in both momentum and thermal boundary layer thickness. The effects of suction and nanoparticle concentration are also analysed and presented graphically. Additionally, a stability analysis is also performed, which discloses that the first solution produced is stable, however, the second solution is not. The findings of this study provide valuable insights into the behaviour of hybrid nanofluid in unsteady flow and can aid in the development of more efficient heat transfer fluids for various engineering applications.

Statistical investigations of profile error impact on flow and performance of a low-pressure turbine cascade

Profile error impacts on turbomachinery flow and blade performance have been attracting widespread attention. In the study, the characteristics of profile error of about one thousand real low-pressure turbine blades are extracted. Sensitivities of total pressure loss coefficient (ζ), outflow angle (β), and Zweifel lift coefficient (zw) of the blade to the basis modes of profile error are calculated. Flow solutions of the blades considering specified basis modes with high sensitivities illustrate that profile error contributes much to the variations of transition onset and flow acceleration on the suction side and flow mixing intensity in the wake. Uncertainty quantification of performance changes is then implemented by the method of moment (MM) using second-order sensitivities. With only 5% computational cost of that by Monte Carlo simulation (MCS), the MM-based statistical results are close to MCS ones with maximum relative error not exceeding 1.07%. The statistical results reveal that the variations of both β and zw are linearly dependent, whereas the variation of ζ is nonlinearly dependent on profile error. As the variation range of profile error increases, the standard deviation and skewness increase, indicating that the performance is more dispersive and the nonlinear dependence of ζ on profile error is intensified. Finally, the MCS flow fields are analyzed. Statistical shear stress near the leading edge and transition onset, statistical boundary layer momentum thickness near transition onset, statistical intermittency near transition onset, and statistical entropy in the wake are more considerable. The impact mechanisms of profile error on turbine flow and performance changes are demonstrated.

Stagnation point on MHD boundary layer flow of heat and mass transfer over a non-linear stretching sheet with effect of Casson nanofluid

ABSTRACT The present study analyzes the effects of the magnetohydrodynamic stagnation point and Casson fluid flow considered over the stretching surface. Due to the growing need for non-Newtonian nanofluid flows in industry and engineering areas, the present work focuses on the Casson nanofluid flow over a non-linear stretching surface with effects. The Casson nanofluid is more helpful for cooling and friction-reducing agents compared to Newtonian-based nanofluid flow. The mathematical explanation of the problem is elaborated with the help of partial differential equations. The coupled nonlinear form of ordinary differential equations (ODEs) is solved numerically by the Keller-Box method using a suitable MATLAB program. On the effect of the Casson parameter on the velocity parameter, it is observed that for large values of the Casson parameter, the velocity profile decreases. The reason behind this behavior is that increasing the values of the Casson parameter increases the fluid viscosity, i.e. reduces the yield stress. Therefore, the momentum boundary layer thickness reduces and the thermal boundary layer thickness increases.

Casson fluid flow with heat generation and radiation over a non-linear stretching sheet

This study investigates Casson fluid flow with heat generation and radiation over a non-linear stretching sheet. The resulting partial differential equations are converted to a system of ordinary differential equations using similarity transformation and solved numerically using shooting technique with fourth order Runge-Kutta method. The effect of radiation, heat source, and Casson parameters on the momentum and thermal boundary layers are examined through graphs using MATLAB. From the graphs it is seen that increase in the values of heat source and Prandtl number parameter increases the temperature profiles. The momentum boundary layer thickness decreases while the rate of heat transfer increases with increasing non-linear parameter. The temperature and thermal boundary layer thickness decreases with increasing radiation parameter values.

Control of radiating heat on the heat transfer of polar hybrid nanofluid flow through a vertical permeable plate

The recent applications in industrial products and engineering need high thermal efficiency for the betterment of the shape of the products, the concept of hybrid nanofluid is significant in comparison to nanofluid and pure fluid. Therefore, this analysis focuses on the flow of a micropolar hybrid nanofluid over a vertical permeable plate. The study considers free convection of an electrically conducting fluid, incorporating metal and oxide components with a water-based hybrid nanofluid. Further, the conjunction of dissipative and radiating heat with generative/absorptive heat enhances the thermal properties. The use of standard transformation rules gives rise to converting the nondimensional form of concerned PDEs to ODEs. Moreover to get rid of the solution, for the nondimensional set of equations, a shooting-based numerical technique like Runge–Kutta (RK)-fourth-order is adopted for the standard values of several components within their range. The effectiveness of these parameters is studied and displayed through graphs. The computed result of the rate coefficients at the surface is depicted in tabular form. The comparative analysis with earlier work studied by considering the base liquid shows a good correlation in particular cases. However, the important outcomes are, the magnetized nano as well as hybrid nanoparticles produces a thicker momentum boundary layer thickness whereas it enhances the fluid temperature.