Bvp4c Function In Matlab Research Articles

Advanced heat transfer analysis using RSM-BBD for MHD hybrid nanofluid flow over a nonuniform stretching sheet with viscous dissipation

The recent studies focus on optimizing conditions to maximize the heat transfer rate while minimizing energy consumption, a key goal for various industries in both production processes and Automotive industry efficiency. Hybrid nanofluids play a crucial role in improving heat transfer phenomena. This study examines the enhanced heat transfer properties of a water-based hybrid nanofluid containing Al2O3 and SiO2 nanoparticles as it flows through a nonlinear stretching sheet in a porous medium. The convective flow is further influenced by a magnetic field and thermal radiation, adding complexity to the flow dynamics. To simplify the analysis, dimensional physical quantities are converted to non-dimensional parameters using appropriate similarity rules. These transformed equations are then numerically solved using the bvp4c function in MATLAB. To achieve optimal heat transfer rates, a robust statistical method known as response surface methodology (RSM) is employed, and validation is performed through an analysis of variance. Graphical representation is used to examine parametric behaviour, and a brief physical description is provided. Key findings include: the hybrid nanofluid shows a 10.61% increase in heat transfer rate compared to the base fluid at R = 0.2; the drag force coefficient for the Al2O3/H2O nanofluid is reduced by 13.98% compared to other hybrid nanofluids; and an increase in the nonlinear stretching sheet parameter improves velocity distribution while reducing temperature distribution. This study can be used in automotive transmission systems to enhance heat dissipation and lubrication, improving the efficiency and durability of the transmission.

Analysis of heat and mass transfer rates in conducting Casson fluid flow over an expanding surface considering Ohmic heating and Darcy dissipation effects

In a recent scenario, the flow of Casson fluid via porous media has practical applications in various engineering processes, such, as the design of cooling systems for electronic devices, oil recovery in porous reservoirs, and polymer extrusion processes, etc. The proposed investigation illustrates the thermal and solutal transfer rates in a conducting Casson fluid flow over an expanding surface. However, the emphasis goes to the behavior of the Ohmic heating and Darcy dissipation when considering the transverse magnetic field and porous matrix. The governing flow phenomena with their dimensional form are altered into a non-dimensional set of equations with the help of suitable similarity rules. Further, an adequate numerical simulation is adopted to solve the transformed equations using the in-house bvp4c function in MATLAB. The physical parameters involved in the flow problem and their behavior on the governing flow phenomena are presented graphically and described briefly. Prior to this investigation, the conformity of the current numerical output obtained for the heat transfer rate was validated with the earlier work with a good correlation. Moreover, the major outcomes are; the non-Newtonian Casson parameter retards the axial and transverse velocity profile and the shear rate also decreases significantly. The Eckert number caused by the inclusion of the dissipative heat encourages the fluid temperature throughout.

MHD Mixed Convection Flow Over a Permeable Vertical Flat Plate Embedded in a Darcy–Forchheimer Porous Medium

AbstractThe purpose of this paper is to describe the stead MHD mixed convection flow over a permeable vertical flat plate embedded in a Darcy–Forchheimer porous medium. Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphically and in tables, illustrations of the reduced skin friction, reduced Nusselt number, velocity, and temperature profiles. Dual (upper and lower branch) solutions are discovered in this exciting analysis. Although numerous studies on the mixed convection past a vertical plate embedded in a fluid-saturated porous medium exist, none of the researchers have focused on the Darcy–Forchheimer flow with asymptotic solutions. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters, such as Darcy–Forchheimer $$G,$$ G , suction/injection $$S$$ S , MHD $$M,$$ M , and mixed convection $$\lambda$$ λ parameters.

Hybrid carbon nanotubes flow and heat transfer over a vertical thin needle with suction effect: A numerical and optimisation analysis

The present study aims to provide a numerical and optimisation analysis of the hybrid carbon nanotubes flow over a vertical thin needle under the suction effect. The thin needle is suspended in water-based hybrid nanofluids containing a combination of single- and multi-walled carbon nanotubes. The heat is transported using the mixed convection flow. A mathematical model of partial differential equations (PDEs) is developed subject to boundary conditions. The PDEs system is converted to non-dimensional ordinal differential equations (ODEs) by using the similarity solution method. Then, the first order of the ODEs system is solved in a MATLAB bvp4c function. We innovatively carry out an optimisation process using response surface methodology (RSM) to enhance the efficiency of the numerical experiment data and fill a gap in the optimised analysis. To observe the variation solutions for the reduced skin friction and heat transfer coefficients, several parameters, such as the mixed convection and suction parameters, are altered into several values. The solutions are essential for accurately forecasting the occurrence of boundary layer separation, particularly in the case of dual solutions. Our analysis reveals that the model generates multiple solutions for the opposing flow, and the boundary layer separates slowly due to the suction effect. To complete the research, RSM reveals that the highest value of the nanoparticle volume fraction and suction parameters, as well as the smallest value of the needle size, generate the maximum transmitting heat through the slender needle. Furthermore, both the numerical and RSM results show that hybrid carbon nanotubes perform better than mono‑carbon nanotubes for better practical reference.

Insights of thermal characteristics with tri-hybrid nanofluid boundary layer flow past a thin needle

The innovative ternary nanofluid that we report herein is intended to improve the performance of heat transfer and thermal conductivity compared to conventional fluids. In view of the aforementioned significance, the goal of continuing research is to investigate the fluid flow and thermal efficiency of water-ethylene glycol (EG)-based ternary nanofluids (TiO2, MoS2, and CoFe2O4) past a thin needle that is subjected to a transverse magnetic field along the normal direction of the flow as well as resistive heating. The governing transport flow equations for ternary nanofluid have been converted into a system of ordinary differential equations using self-similarity variables and solved with the use of the BVP4C function in MATLAB. The significance of each flow factor on temperature and velocity profiles is illustrated using graphs, and the local Nusselt number, and skin friction parameters are computed. The study reveals that the addition of nanoparticles exerts a greater adverse effect on the exchange of heat, and it is found that the water-ethylene glycol based ternary nanofluid has a rate of heat transfer of up to 16% compared to hybrid nanofluid even at very low volume fractions (0.0025–0.03). It is inspected that in the presence of resistive heating, the ternary nanofluid has greater heat transfer than hybrid nanofluids. It is also observed that as the volume proportion of nanoparticles increases, the Nusselt number rises and wall friction decreases.

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.

Mathematical modeling of Cross‐fluid model in a peristaltic channel with viscous dissipation and MHD effects

AbstractIn this analysis, Cross‐fluid model along wall properties is investigated. Impact of the magneto‐hydrodynamic on the non‐Newtonian model is also considered. Numerical algorithm MATLAB bvp4c function is adopted for the solution of coupled nonlinear equations along long‐wavelength and low Reynolds number approximations. Viscous dissipation phenomena are counter to discuss the energy possession during flow. Fluid velocity and stream lines for the flow are also precisely determined in this analysis. The various parameters that influence the physical characteristics of flow are plotted through the graph, and their effects are discussed in detail. From the conclusions, the consequence of the flow model parameters is found to be substantial and also noted that the present model has the potential applications to comprehend the bile conduit drive via bladder, gallstones, and blood flow features in living organisms in a much better way than prior.

Thermodynamic properties of Casson-Sutterby-micropolar fluid flow over exponential stretching curved sheet with impact of MHD and heat generation

The study focuses on the dynamic properties of models describing the flow of couples' micropolar-Casson-Sutterby fluids over an exponentially curved sheet. The study takes into account a low Reynolds number, magnetic field effects, and chemical reactions. By employing boundary layer approximations, the governing general equations are reduced to partial differential equations. Subsequent appropriate transformations simplify the motion, micropolar, and energy equations into a set of coupled nonlinear ordinary differential equations, which can be numerically elucidated using the bvp4c function in MATLAB. The study reveals that as the material constants approach zero, the flow of micropolar fluids becomes Newtonian fluids. The fluid velocity gradually increases due to the enhancement in the Sutterby fluid factor, leading to heightened fluid shear thinning and increased fluid velocity. The results can be analyzed numerically and graphically and are accompanied by a physical explanation of various parameters. The velocity exhibited a declining trend due to an increase in the Casson fluid factor. This was caused by the enrichment of fluid viscosity with higher values of the custom fluid factor, ultimately resulting in a reduction in the fluid velocity. Increasing the values of the micropolar fluid factor resulted in diminishing velocity curves.

Flow over a stretchable cylinder with nonlinear heat sources/sinks: Magnetic dipoles application

This work contributes mainly an analysis of the impact of a generated magnetic dipole on the magneto heat transport inside a deformable cylinder. Magnetic dipole signifies, magnotherapy and spectroscopy which are medical applications, generate static magnetic fields. The investigation considers the influence of non-linear heat sources and sinks, which result in a noteworthy phenomenon. The flow field is governed by accurate and nondimensional factors, which are used to convert the initial set of highly nonlinear and coupled partial differential equations into a set of nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved mathematically using the bvp4c function in MATLAB, taking into account the boundary conditions. Ultimately, this section provides an overview of the ramifications stemming from various physical constraints on the movement of fluids, including nonlinear source/sink effects and other more factors. Ultimately, the discovered results that impose limitations are juxtaposed with those documented in the scientific literature, revealing a significant connection.

Flow and Thermal Characteristics of Couple Stress Fluid over a Stretching Surface with Hybrid Nanoparticles

In the current research, a mathematical analysis of couple stress fluid flow and heat characteristics through a stretchable permeable surface with hybrid nanoparticles is conducted. The solid nanoparticles of the aluminium alloys (AA7072 and AA7075) are suspended in methanol to create the hybrid nanofluid. The similarity approach is used to reduce the governing equations into the similarity equations. Then, MATLAB's bvp4c function is employed to solve the resulting equations. The solutions for the flow and temperature fields, as well as the skin friction coefficient and Nusselt number are presented in table and graphical forms. The results demonstrate that hybrid nanofluids excel as thermal conductors, significantly augmenting the heat transfer rate. The heat transfer rate is increased by 0.38% for the nanofluid, while 0.89% increment for the hybrid nanofluid compared to the base fluid. Furthermore, a larger couple stress parameter is found to be associated with a decrease in the fluid temperature and an enhancement in fluid velocity.

Impact of magnetohydrodynamic on hybrid nanofluid flow with slip and heat source over an exponentially stretchable/shrinkable permeable sheet

This research examines the hybrid nanofluid alumina-copper/water flow over a permeable sheet, considering slip, magnetohydrodynamics, and heat source. To analyze the system, the model is transformed into nonlinear ordinary differential equations (ODEs) via the similarity transformation. Numerical solutions are attained through the implementation of the bvp4c function in MATLAB. The study analyzes velocity and temperature profiles, local skin friction, and Nusselt number for various parameters. Moreover, the impact of magnetohydrodynamics on the system is explored. Increasing the magnetic parameter leads to an enlargement of the boundary layer thickness and an elevation in the skin friction coefficient. Overall, this study sheds light on the complex behavior of hybrid nanofluid flows and provides valuable insights into the effects of slip, magnetohydrodynamics, and heat source on the model while also presenting a validated model showcasing the compelling enhancement of heat transfer through the incorporation of copper into alumina nanofluid.

Combined Convective Transport of Williamson Hybrid Nanofluid over a Shrinking Sheet

In this study, the combined convective transport of Williamson hybrid nanofluid flow over a shrinking sheet containing Alumina (Al2O3) and Copper (Cu) nanoparticles with Engine Oil (EO) as its base fluid is investigated. The mathematical model is converted to similarity equations by suitable transformations. The bvp4c function in MATLAB is utilized to solve the similarity equations numerically. The comparison of the present model with the established model for verification purposes shows a reasonable agreement. The influences of several fluid parameters on the fluid flow behaviour are analysed. Outcomes reveal the increment in combined convective transport and suction parameter improve the performance of heat transport of the fluid. Furthermore, the non-Newtonian Williamson hybrid nanofluid provided better heat transport performance compared to nanofluid with the same value of nanoparticle concentration.

Development of machine learning algorithm for assessment of heat transfer of ternary hybrid nanofluid flow towards three different geometries: Case of artificial neural network

The focus of this paper revolves around the examination of flow of ternary hybrid nanofluid, specifically the Al2O3–Cu-CNT/water mixture, with buoyancy effect, across three distinct geometries: a wedge, a flat plate, and a cone. The study takes into account the presence of quadratic thermal radiation and heat source/sink of non-uniform nature. To develop the model, the Cattaneo–Christov theory is utilized. The equations governing the flow are solved by applying similarity transformations and employing the "bvp4c function in MATLAB” for numerical analysis and solution. Conventional methods for conducting parametric studies often face challenges in producing significant conclusions owing to the inherent complex form of the model and the method involved. To address the aforementioned issue, this paper explores the potential of machine learning methods to foresee the conduct of the flow characterized by multiple interconnected parameters. By utilizing simulated data, an artificial neural network is trained using the Levenberg-Marquardt algorithm to learn and comprehend the underlying patterns. Subsequently, the trained neural network is employed to estimate the Nusselt number on the surfaces of all three geometries. This approach offers a promising alternative to traditional parametric studies, enabling more precise predictions and insights into the behavior of complex systems. The Nusselt number is highest for THNF flow over the cone. The mean squared error (MSE) values for the ANN algorithm, across all analyzed cases, range from 0 to 0.03972. The findings contribute to an improved understanding of the characteristics and dynamics of ternary hybrid nanofluid flow in various geometries, assisting in the design and optimization of heat transfer systems involving such fluids.

Heat transfer enrichment in magnetohydrodynamic cylindrical flow of Maxwell fluid with thermal radiation and Stefan blowing effects

Energy transfer and boundary layer flow on a stretching cylinder are used in extrusion procedures, fiber technology, the manufacture of polymer sheets, and the creation of plastic films. In view of these applications, this article examines a transport model for a boundary layer flow with magnetohydrodynamics derived from a Maxwell fluid flow under the influence of radiation, Brownian motion, thermo phoresies and Stefan blowing on a stretching cylinder. Using MATLAB bvp4c function, the governing equations are numerically solved after being changed into ordinary differential equations via similarity renovations. Calculations and analyses determined how various emergent parameters affected the flow field, heat transfer and mass transfer. Some characteristics were discovered to affect the width of the boundary layer. The influence on MHD (M), radiation (Rd), the Schmidt number (Stc), Brownian motion (Nb), thermo phoresies (Nt) and the Stefan blowing parameter (Sb) on the velocity, energy and concentration profile have been explored. Excellent assessment is recognized over a tabular explanation to validate the adopted numerical technique. Significantly the Stefan blowing parameter rises the profiles on velocity and temperature. For an increasing value of the Maxwell fluid parameter, the skin friction coefficient decreases compared to the Stefan parameter.

The Mixed of Hybrid Nanofluid GO-MoS2/Engine Oil Over a Shrinking Sheet with Mass Flux Effect: Reiner-Philippoff Model

The mixed convection flow and heat transfer of the hybrid nanofluid over a shrinking sheet are investigated. Molybdenum disulphide (MoS2) and graphene oxide (GO) are employed as two hybrid nanoparticles while engine oil (EO) as the base fluid is considered. In this study, the Reiner-Philippoff model as one of non-Newtonian types is deliberated since it has the ability to function on three distinct types of fluids: viscous, shear thickening and shear thinning. The Reiner-Philippoff relation, the momentum and energy equations under Tiwari and Das model are all employed in the study. Influences from mass flux are also considered in the flow. Before computation using the bvp4c function in MATLAB, the respected equations are first converted into ordinary differential equation form using the similarity transformation. When the established and current models are discovered to be identical in a specific case, a direct comparative investigation is conducted to confirm the correctness of the current model. In addition, the present results are shown graphically and in tabular form. It is hypothesized that the presence of a hybrid nanofluid significantly affects the fluid characteristic and gives more satisfactory results than a single nanofluid. The skin friction coefficient and heat transfer rate of hybrid nanofluids are greater than the nanofluids. In terms of velocity and temperature profile, the reduction in velocity and the enhancement in temperature profile are caused by a rise in the Reiner-Philippoff parameter. The same outcome is also seen when the volume fraction of hybrid nanofluids increases.

Thermal transport through carbon nanotubes based nanofluid flow over a rotating cylinder with statistical analysis for heat transfer rate

This study investigates the impact of magnetohydrodynamic effects and thermal radiation on axisymmetric flow with carbon nanotubes over a rotating cylinder. The thermal energy behavior of the nanofluid is analyzed using the Xue model, with water as the base fluid and two different types of nanoparticles: single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs). The governing flow problem is transformed through appropriate transformations, resulting in a system of ordinary differential equations. Numerical solutions are obtained using the bvp4c function in MATLAB. The results indicate that the thermal transport coefficient increases with the radiation number in both SWCNTs and MWCNTs cases. Further, the presence of nanoparticles in the nanofluid leads to an increase in the thermal transport coefficient due to the volume fraction of the nanoparticles. Moreover, the study reveals that water-based MWCNTs exhibit a higher heat transfer rate than water-based SWCNTs. These findings contribute to understanding thermal energy characteristics in nanofluids and have implications for applications such as heat exchangers, electronic cooling systems, and the thermal management of advanced materials.

The Role of Quadratic-Linearly Radiating Heat Source with Carreau Nanofluid and Exponential Space-Dependent Past a Cone and a Wedge: A Medical Engineering Application and Renewable Energy

A mathematical analysis for a steady, incompressible, laminar Carreau nanofluid flow over a porous cone and wedge is considered. The novelty of this research work is to scrutinize an exponential space-dependent Cattaneo–Christov heat flux and quadratic Rosseland approximation effects. Two-phase nanofluid model, i.e., Brownian motion, and thermophoretic effects are included. This study also employs non-linear thermal radiation and convective surface boundary conditions to investigate heat transport phenomena. The Carreau nanofluid boundary layer equations are derived using the standard boundary layer approximations. By applying the similarity transformations, the managing set of partial differential equations (PDEs) becomes a system of connected non-linear ordinary differential equations (ODEs). The resultant non-linear ODEs are solved numerically utilizing the numerical method, particularly the bvp4c function in MATLAB. The significances of the fluid motion are visualized by sketching several Carreau nanofluid flow’s relevant parameters using graphic outputs. The effects of a wide range of thermophysical variables on liquid properties including velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number are investigated and discussed. This study’s findings are compared to previously announced results within a limited range, where strong validation was seen. The results demonstrate that the opposite mechanism is observed with repercussion of Weissenberg number (We) on velocity profile and concentration, the enhancement of We increases the momentum boundary layer while it reduces the concentration boundary layer. The outcomes could be applied to the cooling of equipment, electronics, and various industrial units.

Non‐similar heat transfer analysis of magnetized flow of Ag‐Mgo/water hybrid nanofluid flow through darcy porous medium

AbstractThis study aims to examine the magnetized flow of Ag–MgO/water hybrid nanofluid over an extending sheet implanted in Darcy porous medium. Thermal radiations, Joule and viscous dissipations are incorporated into energy equation to account for heat transfer. The convective heat flux boundary condition is imposed at sheet surface. Using non‐similar conversions, governing equations are converted to a system of dimensionless partial differential equations (PDEs). These equations are transformed into ordinary ones by using local non‐similar method. MATLAB's bvp4c function is used to numerically simulate the ordinary differential equations (ODEs). The velocity and thermal profiles for positive variation of essential parameters are illustrated graphically. It was concluded that the velocity profile increases for the rising Darcy number. On the other hand, the temperature profile increased for the positive variation of magnetic number, volume fraction, radiation parameter, Eckert number and Biot number while decreasing for all other parameters. The skin friction coefficient and heat transfer rates are thoroughly investigated and findings are reported through tables. It was found that the magnitude of skin friction coefficient rises with an increase in volume fraction, suction and magnetic parameters while the heat transfer is enhanced by increases in Darcy number, suction parameter, radiation parameter, and Biot number. As per the author's knowledge, no work has previously been published on the current model using the local non‐similarity method. This work may provide insight to researchers interested in thermal systems and solar energy harvesting.

A study of effects of H–H quartic auto catalytic reaction with equal diffusivity in the swirling flow exterior to a rotating cylinder

In this study, we investigate the influence of quartic auto catalysis with equal diffusivity in the flow past a rotating cylinder. The flow-thermal fields are modeled using partial differential equations (PDEs), assuming a homogeneous–heterogeneous reaction. The resulting flow-thermal equations are appropriately ordered and solved using the BVP4c function in MATLAB. Our analysis focuses on examining the effects of varying the Reynolds number, magnetic field, radiation, and homogeneous–heterogeneous reaction parameters on the velocity, temperature, and concentration of the bulk fluid. Through extensive simulations, we find that the concentration, temperature, and velocity of the homogeneous bulk fluid are predominantly determined by the Reynolds number. We observe that higher Reynolds numbers lead to increased mixing and enhanced fluid motion, resulting in higher concentrations and temperatures. Moreover, the strength parameters associated with the homogeneous–heterogeneous reaction significantly favor the auto catalysis reaction at the surface of the rotating cylinder, indicating a self-catalytic process. To validate our findings, we compare our results with earlier studies that investigated reduced cases. Remarkably, our obtained results exhibit excellent agreement with these prior studies, further bolstering the reliability and accuracy of our research.

Dual solutions of magnetite/cobalt/manganese-zinc-aqueous nano-ferrofluids from a stretching sheet with magnetic induction effects: MHD stagnation flow computation and analysis

A theoretical study is presented for the steady magnetohydrodynamic (MHD) boundary layer stagnation point flow of a nano-ferrofluid along a linearly moving stretching sheet, as a simulation of functional magnetic materials processing. Due to having imerging applications in heat transfer, the nano-ferrofluids draw the attention which comprise an aqueous base fluid doped with a variety of magnetic nanoparticles, i.e. magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Manganese-zinc (Mn-Zn) ferrite. A partial differential equation mathematical model is developed for mass, momentum, magnetic field continuity (induction), and energy with appropriate wall and free stream boundary conditions. Following similarity transformations, the dimensionless resultant nonlinear ordinary differential boundary value problem is solved numerically using the robust bvp4c function in MATLAB which features very efficient 4th order optimized Runge–Kutta quadrature. Dual solutions for the upper branch and lower branch separated by a critical point are identified. Visualization of velocity, temperature, and induced magnetic field function are presented graphically including validation of solutions with previous studies. Furthermore, skin-friction coefficient and the local Nusselt number are also computed. The impact of the controlling parameters, i.e. Prandtl number nanoparticle volume fraction parameter reciprocal of magnetic Prandtl number magnetic parameter and stretching rate ratio parameter have been illustrated through graphs and evaluated when a desire heat transfer can occur. Furthermore, resistance between fluid and the plate can be increased with the growing magnetic Prandtl number values. Increment in magnetic parameter () produces an elevation in the induced magnetic field magnitudes. Skin friction and Nusselt number are found to be greater for cobalt nanoparticles when compared to magnetite and Mn-Zn ferromagnetic nanoparticles when there is an increase in reciprocal magnetic Prandtl number. The simulations provide a deeper insight into the manufacturing flows of functional nano-ferromagnetic materials of relevance to deposition and coating systems.