Mixed Convection Stagnation Point Flow Research Articles

An investigation of variable viscosity Carreau fluid and mixed convective stagnation point flow

An investigation of variable viscosity Carreau fluid and mixed convective stagnation point flow

Mixed bioconvection stagnation point flow towards a vertical plate in alumina-copper/water

PurposeAccording to the previous research, bioconvection has been recognized as an important mechanism in current engineering and environmental systems. For example, researchers exploit this mechanism in modern green bioengineering to develop environmentally friendly fuels, fuel cells and photosynthetic microorganisms. This study aims to analyse how this type of convection affects the flow behaviour and heat transfer performance of mixed convection stagnation point flow in alumina-copper/water hybrid nanofluid. Also, the impact of a modified magnetic field on the boundary layer flow is considered.Design/methodology/approachBy applying appropriate transformations, the multivariable differential equations are transformed into a specific sort of ordinary differential equations. Using the bvp4c procedure, the adjusted mathematical model is revealed. Once sufficient assumptions are provided, multiple solutions are able to be produced.FindingsThe skin friction coefficient is declined when the nanoparticle concentration is increased in the opposing flow. In contrast, the inclusion of aligned angles displays an upward trend in heat transfer performance. The presence of several solutions is established, which simply leads to a stability analysis, hence verifies the viability of the initial solution.Originality/valueThe current findings are unique and novel for the investigation of mixed bioconvection flow towards a vertical flat plate in a base fluid with the presence of hybrid nanoparticles.

Stagnation point flow of a micropolar fluid filled with hybrid nanoparticles by considering various base fluids and nanoparticle shape factors

PurposeThe boundary-layer analysis is required to reveal the fluid flow behavior in several industrial processes and enhance the products’ effectiveness. Therefore, this research aims to investigate the buoyancy or mixed convective stagnation-point flow (SPF) and heat transfer of a micropolar fluid filled with hybrid nanoparticles over a vertical plate. The nanoparticles silver (Ag) and titanium dioxide (TiO2) are scattered into various base fluids to form a new-fangled class of (Ag-TiO2/various base fluid) hybrid nanofluid along with different shape factors.Design/methodology/approachThe self-similarity transformations are used to reformulate the leading requisite partial differential equations into renovated non-linear dimensionless ordinary differential equations. The numerical dual solutions are gained for the transmuted requisite equations with the help of the bvp4c built-in package in MATLAB software. The results are validated by comparing them with previously available published data for a particular case of the present study.FindingsThe impact of various pertaining parameters such as nanoparticle volume fraction, material parameter, shape factor and mixed convective on temperature, heat transfer, fluid motion, micro-rotation and drag force are visualized and scrutinized through tables and graphs. It is observed that dual or non-uniqueness outcomes are found for the case of buoyancy assisting flow, whereas the solution is unique in the buoyancy opposing flow case. Additionally, the fluid motion and micro-rotation profiles decelerate in the presence of nanoparticle volume fraction, while the temperature augments.Originality/valueThe mixed convective stagnation point flow conveying TiO2/Ag hybrid nanofluid with micropolar fluid with various shape factors is the significant originality of the current investigation where multiple outcomes are obtained for the assisting flow. The various base fluids such as glycerin, water and water–ethylene glycol (50%:50%) are considered in the present problem. The bifurcation values of the considered problem do not exist, probably because of various base fluids. To the best of the authors’ knowledge, this work is new and original which were not previously reported.

Mixed Convection Stagnation Point Flow of a Hybrid Nanofluid Past a Permeable Flat Plate with Radiation Effect

This article focuses on the stagnation point flow of hybrid nanofluid towards a flat plate. The cases when the buoyancy forces and the flow are in the opposite direction and the same direction are discussed. The effect of radiation and suction is also taken into account. The similarity transformations are used to convert the partial differential equations into nonlinear ordinary differential equations. These equations are computed numerically via the bvp4c function in MATLAB software. A comparison with the previously published articles is carried out, where an outstanding agreement is observed. The dual solutions exist in the case of opposing flow (λ<0) and the suction parameter S>0.6688. Meanwhile, only unique solutions exist in the case of assisting flow (λ>0). The existence of dual solutions leads to stability analysis. From the analysis, the first solution is confirmed as a stable solution. Furthermore, the heat transmission rate increases, while the skin friction coefficient decreases as the radiation rate increases. An increase in the radiation rate from 0 (no radiation) to 1.0 increases the heat transmission rate by 5.01% for water, 4.96% for nanofluid, and 4.80% for hybrid nanofluid. Finally, it is worth mentioning that the present study yields new and original results. This study has also not been done by other researchers, indicating its novelty.

Mixed convection stagnation-point flow of Cross fluid over a shrinking sheet with suction and thermal radiation

This work focuses on numerically investigating the mixed convection stagnation-point flow and heat transfer in an incompressible Cross fluid over a permeable shrinking sheet, with suction and thermal radiation effects. The governing equations defining the current problem have been first transformed into the ordinary differential equations through similarity transformations. The resulting equations obtained are then solved numerically using the bvp4c programmed in MATLAB, revealing dual (upper and lower branch) solutions for both assisting and opposing flow regions. Stability analysis has been employed afterwards to determine a stable solution between them. Following from there, the upper branch solution has been found to be stable, while the lower branch solution is unstable. In addition, the study has established that the Weissenberg number, the Prandtl number and the suction parameter are strongly influenced to uplift the range of existence for dual solutions.

Mixed convection of a three-dimensional stagnation point flow on a vertical plate with surface slip in a hybrid nanofluid

Hybrid nanofluid has become one of the major interest topics among researchers nowadays due to its significant impact in myriad applications. This paper modeled and explored the properties of flow and heat transfer of mixed convection stagnation point flow for hybrid nanofluid (alumina-copper/water) on a vertical plate with slips and suction. By using the method of similarity transformation, the governing set of partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). These derived equations are then evaluated numerically by adopting the bvp4c function that is available in Matlab software. In the presence of slips together with the opposing flow of mixed convection, the local Nusselt number (heat transfer rate) can be augmented by increasing the solid volume fraction of copper. The surge of 0.5% of copper volume fraction can accelerate the heat transfer rate by approximately 1.3% in this present analysis within the specified value of slips, mixed convection, and suction. The stability analysis is conducted due to the existence of dual solutions and only the first solution is stable for practical application.

Impact of Soret and Dufour on MHD mixed convective flow of non‐Newtonian fluid over a coagulated surface

AbstractIn the present study, we investigated the steady, two‐dimensional mixed convective stagnation point flow of an electrically conducting micropolar fluid due to stretching of a variable thicked surface in the attendance of viscous dissipation. The flow is incompressible and laminar. The combined heat and mass transfer features are investigated. Convective and diffusion conditions are considered. The nonlinear thermal radiation, thermo‐diffusion, and diffusion thermal effects are considered. The governing partial differential equations are converted to ordinary differential equations by using the appropriate similarity transformations. The obtained nonlinear and coupled ordinary differential equations are elucidated numerically using the fourth‐order Runge–Kutta based shooting technique. The influence of various nondimensional parameters on the flow field like velocity, microrotation, temperature, and concentration is examined with the assistance of graphs. Results indicate that the Dufour number has a proclivity to increase the distributions of concentration and temperature correspondingly. Also, fluid temperature and concentration enhance for increasing values of the wall thickness parameter.

Viscous dissipation and thermal radiation effects on the flow of Maxwell nanofluid over a stretching surface

An analysis is made to examine the viscous dissipation and thermal effects on magneto hydrodynamic mixed convection stagnation point flow of Maxwell nanofluid passing over a stretching surface. The governing partial differential equations are transformed into a system of ordinary differential equations by utilizing similarity transformations. An effective shooting technique of Newton is utilize to solve the obtained ordinary differential equations. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. The effects of sundry parameters on the velocity, temperature and concentration distributions are examined and presented in the graphical form. These non-dimensional parameters are the velocity ratio parameter $(A)$, Biot number $(Bi$), Lewis number $(Le)$, magnetic parameter $(M)$, heat generation/absorption coefficients $left(A^*,B^*right)$, visco-elastic parameters $left(betaright)$, Prandtl number $(Pr)$, Brownian motion parameter $(Nb)$, Eckert number $left(Ecright)$, Radiation parameter $left(Rright)$ and local Grashof number $(Gc; Gr).$ An analysis is made to examine the viscous dissipation and thermal effects on magneto hydrodynamic mixed convection stagnation point flow of Maxwell nanofluid passing over a stretching surface. The governing partial differential equations are transformed into a system of ordinary differential equations by utilizing similarity transformations. An effective shooting technique of Newton is utilize to solve the obtained ordinary differential equations. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. The effects of sundry parameters on the velocity, temperature and concentration distributions are examined and presented in the graphical form. These non-dimensional parameters are the velocity ratio parameter $(A)$, Biot number $(Bi$), Lewis number $(Le)$, magnetic parameter $(M)$, heat generation/absorption coefficients $left(A^*,B^*right)$, visco-elastic parameters $left(betaright)$, Prandtl number $(Pr)$, Brownian motion parameter $(Nb)$, Eckert number $left(Ecright)$, Radiation parameter $left(Rright)$ and local Grashof number $(Gc; Gr).$

Dual solutions of bioconvection hybrid nanofluid flow due to gyrotactic microorganisms towards a vertical plate

The impact of gyrotactic microorganisms in the mixed convection stagnation point flow of Cu-Al2O3/water hybrid nanofluid towards an immovable plate is numerically examined. The boundary layer equation coupled with the energy, nanoparticle volume fraction and conservation equations for microorganisms are simplified into a set of ordinary differential equations by adopting similarity transformation. The validation results are in a good agreement with previous studies approximately by 0% difference relative error. The results imply that the dual solutions only exist in the opposing flow up to a critical value/turning point. Beyond this turning point, the solutions are unavailable which reflects the separation of flow. The hybrid nanofluid is essential in delaying the separation process where the results show that λc,hnf=−3.5804>λc,Cu=−3.3903>λc,Al=−3.2016. Moreover, the advantage of this hybrid Cu-Al2O3/water nanofluid is in the augmentation of heat and mass transfer rates including the density of microorganisms which is higher than the Cu- and Al2O3-water nanofluids.

Non-similarity solutions of radiative stagnation point flow of a hybrid nanofluid through a yawed cylinder with mixed convection

In this new-fangled research, the mixed convective stagnation point flow of a hybrid nanofluid over a yawed cylinder with radiation impact is considered. In reality, the perception of mixed convection in the study of yawed cylinder rises in heat exchangers. To explore the heat diffusion through the system of mixed convection, the mathematical problem is formed in the form of partial differential equations which are coupled and nonlinear. A solution technique is applied and described for indulgencing non-similar thermal boundary layers. The non-similar terms involving in the transformed equations are held without approximations. The non-similar equations are solved numerically using the bvp4c technique. The exploration divulges numerous significant results involving yaw angle, hybrid nanoparticle volume fraction, mixed convection, radiation, and non-similarity phenomena. The impact of the yaw angle in enhancing the velocity of the hybrid nanofluid in the span-wise and chord-wise directions in the aiding buoyancy flow and decelerating in the opposing flow, while the contrary behavior is noticed for the dimensionless temperature profile. Also, the hybrid nanoparticles reduce the velocity in both directions in case of assisting as well as opposing flow, whereas the dimensionless temperature augments.

Quadratic Mixed Convection Stagnation-Point Flow in Hydromagnetic Casson Nanofluid over a Nonlinear Stretching Sheet with Variable Thermal Conductivity

An analysis of nonlinear mixed convection transport of hydromagnetic Casson nanofluid over a nonlinear stretching sheet near a stagnation point is deliberated in this study. The flow is confined in a porous device in the presence of thermophoresis, Ohmic heating, non-uniform heat source with temperature-dependent thermal conductivity associated with haphazard motion of tiny particles. The transport equations are translated from nonlinear partial differential equations into ordinary ones via similarity transformation technique and subsequently tackled with shooting method coupled with Runge-Kutta Fehlberg algorithm. The significant contributions of the embedded parameters on the dimensionless quantities are graphically depicted and deliberated while the numerical results strongly agree with related published studies in the limiting conditions. It is found that a rise in the magnitude of Casson fluid parameter decelerates the fluid flow while enhancing the viscous drag and thermal profiles. The inclusion of the nonlinear convection term aids fluid flow whereas heat transfer reduces with growth in the thermophoresis and Brownian motion terms.

Mixed convection stagnation point flow of the blood based hybrid nanofluid around a rotating sphere

In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, {text{TiO}}_{2} ,,{text{and}},,{text{Ag}} as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both {text{TiO}}_{2} + {text{Ag}} + Blood and {text{TiO}}_{2} + Blood. One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.

Mixed convective stagnation point flow of a hybrid nanofluid toward a vertical cylinder

PurposeThe purpose of this paper is to numerically analyze the stagnation point flow of Cu-Al2O3/water hybrid nanofluid with mixed convection past a flat plate and circular cylinder.Design/methodology/approachThe similarity equations that reduced from the boundary layer and energy equations are solved using the bvp4c solver. The duality of solutions is observed within the specific range of the control parameters, namely, mixed convection parameterλ, curvature parameterγand nanoparticles volumetric concentrationϕ1for alumina, while for copperϕ2. The stability analysis is also designed to justify the particular solutions’ stability. Additionally, the idea to obtain the solution for large value ofλandγis also presented in this paper.FindingsTwo solutions exist in opposing and assisting flows up to a critical valueλcwhereλclies in the opposing region. An upsurge of the curvature parameter tends to extend the critical value (delay the separation process), whilst increase the heat transfer performance of the working fluid. Meanwhile, the application of hybrid Cu-Al2O3/water nanofluid also can decelerate the separation of laminar boundary layer flow and produce higher heat transfer rate than the Cu–water nanofluid and pure water.Originality/valueThe results are new and original. This study benefits to the other researchers, specifically in the observation of the fluid flow characteristics and heat transfer rate of the hybrid nanofluid. Also, this paper features with the mathematical formulation for the solution with large values ofλandγ.

Dual Solutions in Mixed Convection Stagnation-Point Flow Over a Vertical Stretching Sheet with External Magnetic Field and Radiation Effect

The purpose of this research is to study the problem of mixed convection stagnation-point flow on a vertical stretching sheet with external magnetic field, with the effect of radiation is taken into account. The partial differential equations are reduced to ordinary differential equations using similarity transformation. The transformed boundary layer equations are then solved numerically via bvp4c in MATLAB software. The effects of different values of radiation parameter and Hartmann number on the skin friction coefficient and local Nusselt number, velocity and temperature profiles are presented and discussed. The effect of radiation parameter and Hartmann number are also considered for both assisting and opposing flows. Dual solutions are found to exist in the opposing flow only, while for assisting flow, unique solution exists. It is also found that the radiation parameter enhances the boundary layer separation, and the Hartmann number delays the boundary layer separation.

Integration of Group Method Analysis and Rough Sets Theory to Investigate Heat and Mass Transfer of the Flow of a Non-Newtonian Nanofluid towards a Vertical Stretching Surface

This work reports how to utilize rough set theory and group method analysis for generating a set of rules to investigate heat and mass transfer of mixed convection stagnation point flow of a non-Newtonian nanofluid towards a vertical stretching surface. By utilizing group method analysis, the main partial differential equations which describe the flow are rehabilitated to nonlinear Ordinary Differential Equations (ODEs). Then, the resultant nonlinear ODEs are solved numerically by applying the implicit finite-difference scheme. The numerical values thus obtained are depicted in tabular form and the basic principles of rough sets are applied to get all reducts and finally a group of generalized rules are extracted to predict the value of local Nusselt number and local skin-friction coefficient. The outcomes demonstrate the novelty of the current work which can be summarized as hybridization of group method analysis and rough set theory to use in the field of fluid dynamics effectively. The resultant set of generalized classification rules which performed with basic logic functions can be considered as knowledge base with high accuracy and may be valuable in many engineering applications like power production, thermal extrusion systems and microelectronics.

Modeling and dual solutions for magnetized mixed convective stagnation point flow of upper convected Maxwell fluid model with second‐order velocity slip

In the present work, we have studied a numerical solutions of MHD stagnation point flow of nanofluid over a stretching/shrinking sheet with mass suction condition. We have used the upper convected Maxwell (UCM) fluid model for the development of momentum equation and utilized it to explore the characteristics of elasticity of this model. We used the Buongiorno nanofluid model to develop the equations for the present problem. The governing flow, energy, and concentration equations are changed into the ordinary differential equations by means of suitable transformation. The subsequent ordinary ones are solved numerically using bvp4c scheme in MATLAB. The combined results of buoyancy forces, double slip (first‐ and second‐order slip), and elasticity have been investigated, and the influence of various flow parameters such as Hartmann number, suction parameter, and stretching/shrinking parameter on the skin friction coefficient, local Nusselt number, Sherwood number, and streamlines is studied and exposed through graphs. It is found that mass suction parameter and elasticity of UCM fluid increase the range of buoyancy forces for the existence of dual solutions. Also, buoyancy force increases the range of stretching/shrinking parameter where solution exists.

Mixed Convective Stagnation Point Flow towards a Vertical Riga Plate in Hybrid Cu-Al2O3/Water Nanofluid

The present work highlights the stagnation point flow with mixed convection induced by a Riga plate using a Cu-Al 2 O 3 /water hybrid nanofluid. The electromagnetohydrodynamic (EMHD) force generated from the Riga plate was influential in the heat transfer performance and applicable to delay the boundary layer separation. Similarity transformation was used to reduce the complexity of the governing model. MATLAB software, through the bvp4c function, was used to compute the resulting nonlinear ODEs. Pure forced convective flow has a distinctive solution, whereas two similarity solutions were attainable for the buoyancy assisting and opposing flows. The first solution was validated as the physical solution through the analysis of flow stability. The accretion of copper volumetric concentration inflated the heat transfer rate for the aiding and opposing flows. The heat transfer rate increased approximately up to an average of 10.216% when the copper volumetric concentration increased from 0.005 ( 0.5 % ) to 0.03 ( 3 % ) .

Cattaneo-Christov heat flux (CC model) in mixed convective stagnation point flow towards a Riga plate

This research article proposes an improved Fourier law of heat conduction (Cattaneo-Christov) in presence of heat source/sink. The heat transport characteristics are modeled for mixed convective stagnation point flow by a Riga plate. Flow is generated due to linear stretching velocity. The partial differential system is changed to ordinary differential system through implementing appropriate transformations. Series solutions are developed through semi-analytical method called as homotopy analysis method. Present research article is related to the improved Fourier law of heat conduction (Cattaneo-Christov) over a linear stretchable surface of Riga plate when fluid saturates porous space. The main outcomes of present communication are summarized as: (i) velocity of material particles decreases subject to larger inverse Darcy-number while it enhances via velocity ratio and magnetic parameters (ii) temperature distribution as well as layer thickness enhance for higher estimations of Eckert number and heat source parameter while it decays against Prandtl number (iii) skin friction coefficient decreases through higher values of inverse Darcy number and mixed convection parameter.

A Hybrid Methodology to Extract Decision Rules of Heat and Mass Transfer of the Flow of a Non-Newtonian Nanofluid Towards a Vertical Stretching Surface

In this paper a hybridization of group method analysis, hypergraph Principle and rough set theory is established for extracting a set of rules to investigate heat and mass transfer of mixed convection stagnation point flow of a non-Newtonian nanofluid towards a vertical stretching surface. First, the mathematical model describing the flow is transformed from a set of partial differential equations (PDEs) into non linear ordinary differential equations (ODEs) with the aid of group method analysis. Thereafter, the implicit finite-difference scheme is applied to find the numerical solutions of the nonlinear ODEs and the numerical values are depicted in tabular form. Then the reduction technique based on rough set is applied to find all reducts of the decision tables. Finally, the principle of hypergraph is applied to determine the minimal transversal of reducts and mining a set of generalized rules to predict the value of local Nusselt number and local skin-friction coefficient. The results show that the proposed method can effectively predict these values with high accuracy and may be valuable in many engineering applications like power production, thermal extrusion systems and microelectronics.

Entropy analysis and unsteady MHD mixed convection stagnation-point flow of Casson nanofluid around a rotating sphere

The current perusal introduces a numerical analysis to point out the flow of MHD conjugate forced and free convection with entropy generation analysis due to non-Newtonian Cassonnanofluid around a rotating sphere with convective boundary conditions. Two-phase flow of nanofluid model is employed for the problem under consideration. Both the velocity of free stream and the sphere rotates with angular velocity changed continuously with time. The highly nonlinear partial differential Structures which describe the case study are mutated into a nonlinear ordinary differential structures via utilizing appropriate dimensionless quantities. The numerical solutions of ordinary differential structures have been acquired by applying the fourth order Runge-Kutta-Fehlberg technique with shooting scheme via MATLAB. Aspects of such controlled physical parameters have been clarified and discussed in details using some charts and tables. Comparison with previous literature results is also done and is found to be very good agreement with those published earlier.