Matlab Bvp4c Solver Research Articles

Investigation of the effects of various nanoparticle morphologies on mass and heat transport in SiO2-H2O unsteady magnetohydrodynamic nanofluid flow through a stretched cylinder

This article investigates the effects of the various silicon dioxide ( Si O 2 ) nanoparticles immersed in water ( H 2 O ) base fluid on velocity and heat transport over an unsteady stretching cylinder under the influence of magnetohydrodynamics ( MHD ), velocity slip, and convective boundary conditions. The physical model is initially developed in the form of partial differential equations (PDEs) by using the conservation principle. Employing suitable transformations, the set of PDEs has been transformed into a system of Ordinary differential equations (ODEs). The nonlinear equations in the proposed model are optimally and dynamically assessed. To produce numerical solutions for nonlinear systems, MATLAB's BVP4C solver technique is used. Furthermore, the numerical technique is validated by calculating residual error. The recent investigation’s novel results include: the nanoparticles SiO 2 of play an important role in enhancing the thermal conductivity of the traditional base fluid H 2 O . The shape of the nanoparticles also plays a remarkable role in heat transfer enhancement. Increases in viscus dissipation, convective boundary conditions, and MHD parameters play a remarkable role in increasing the temperature of the nanofluid. Furthermore, platelet-shaped Si O 2 nanoparticles are reported to have the highest flow rate, highest temperature, and highest value of Nusselt numbers.

Thermal characteristics for the flow of Williamson hybrid nanofluid with distinct shape factors

AbstractThe main purpose of the present article is to investigate the flow of 2‐D, incompressible, steady, hydro magnetic Williamson hybrid nanofluid with three distinct shape factors namely spherical, cylindrical, and platelet shapes under the influence of thermal radiation and viscous dissipation effects on the flow. The aim of the current work is to investigate the thermal conduction capacity of three different shaped nanoparticles by comparison. We have modelled copper and molybdenum disulfide nanoparticles suspension in Williamson fluid blood as a conventional real fluid passing through a horizontal stretching cylinder in this case. A set of non‐linear PDEs are used to conceivably formulate the problem's physical model. The transformation from these modelled PDEs to ODEs is accomplished through the use of appropriate similarity variables. To address the problem, the RK method of order four is used in conjunction with shooting system in order to get first order ordinary equations from non‐linear higher order ordinary differential equations. To run the code for numerical results, computational Matlab bvp4c solver is used and graphs are depicted to explain the impact of various embedded physical quantities on the momentum and energy profiles accompanying the rates of shear stress and heat transfer for the considered Williamson hybrid nanofluid. The use of spherical shaped nanoparticles is thought to improve the thermal conductivity rate of the flowing fluid more than cylinder and platelet shaped nanoparticles. The skin friction coefficient is enhancing for larger values of magnetic parameter and curvature parameter but Weissenberg number has a negative trend. The rate of cooling is high for greater values of magnetic parameter, Williamson fluid parameter, heat generation parameter, thermal conduction parameter, viscous dissipation parameter and thermal radiation parameter.

An Efficient and Accurate Approach to Electrical Boundary Layer Nanofluid Flow Simulation: A Use of Artificial Intelligence

Engineering and technological research groups are becoming interested in neural network techniques to improve productivity, business strategies, and societal development. In this paper, an explicit numerical scheme is given for both linear and nonlinear differential equations. The scheme is correct to second order. Additionally, the scheme’s consistency and stability are guaranteed. Backpropagation of Levenberg–Marquardt, the effect of including an induced magnetic field in a mathematical model for electrical boundary layer nanofluid flow on a flat plate, is quantitatively investigated using artificial neural networks. Later, the model is reduced into a set of boundary value problems, which are then resolved using the suggested scheme and a shooting strategy. The outcomes are also contrasted with earlier studies and the MATLAB solver bvp4c for validation purposes. In addition, neural networking is also employed for mapping input to outputs for velocity, temperature, and concentration profiles. These results prove that artificial neural networks can make precise forecasts and optimizations. Using a neural network to optimize the fluid flow in an electrical boundary layer while subjected to an induced magnetic field is a promising application of the suggested computational scheme. Fluid dynamics benefits greatly from combining numerical methods and artificial neural networks, which could lead to new developments in various fields. Results from this study may aid in optimizing fluid systems, leading to greater productivity and effectiveness in numerous technical fields.

Slip Flow Over an Exponentially Stretching/Shrinking Sheet in a Carbon Nanotubes with Heat Generation: Stability Analysis

This study is to analyse the problem of slip flow via exponentially stretching/shrinking sheet in carbon nanotubes (CNTs) with heat generation effects. The governing partial differential equations are transformed into nonlinear ordinary differential equations via transformation of similarity. The bvp4c solver in Matlab is then used to resolve them numerically. Water is used as the base fluid together with single wall and multi wall CNTs. The flow parameters effect is investigated, shown in the graphs form, and physically evaluated for the dimensionless velocity, temperature, skin friction, and Nusselt numbers. The results show that there are unique solutions for stretching sheets and non-unique solutions for shrinking sheets. In addition, compared to the case of a linearly stretching/shrinking sheet, the region of the stretch/shrink parameter where the similarity solution exists for the case of exponential stretching/shrinking sheet is greater.

Entropy analysis of slip flow second-grade Cu − EO and TiO 2 − EO nanofluids using Modified Buongiorno model

The current research investigates the magnetohydrodynamic (MHD) slip flow of second-grade nanofluids past a permeable stretching sheet in a porous medium. The flow analysis is accomplished considering thermophoresis, Brownian diffusion, chemical reaction, and elastic deformation. The implementation of the Modified Buongiorno model (MBM) on second-grade nanofluid is the novel aspect of the study. The formulated coupled nonlinear equations are non-dimensionalized, applying suitable similarity transformation. Numerical resolution of the resulting equations is achieved via MATLAB solver bvp4c. In our problem, two different groups of nanofluids, Cu − EO and TiO 2 − EO, have been considered. The development of profiles of nanofluid velocity, temperature, concentration, entropy generation and Bejan number, with the flow parameters, is elaborated graphically. Tabulated values of skin friction, Nusselt number, and Sherwood number are illustrated. The principal outcomes of this study demonstrate a higher rate of heat transfer of Cu − EO nanofluid than TiO 2 − EO nanofluid. The Nusselt number significantly decelerates, and the Sherwood number accelerates due to the combined influence of the Brownian diffusion and thermophoresis parameters. The second-grade parameter and nanoparticle volume fraction boost the skin friction magnitude. Furthermore, the entropy generation increases due to the Brinkman number and concentration diffusion parameter. The present research can be utilized to enhance the effectiveness of cooling systems in automobile engines, nuclear reactors, and heat exchangers. For the validation of our result, a comparative study is made with the previous authors and concludes in good agreement.

Dynamical phenomena developed by a spiralling stretchable sheet in magnetized Casson-spinel ferrite nanofluid

Nanofluid research has sparked widespread attention due to its immense implementations in various courses, including chemical engineering, microelectronics, solar energy, cooling systems, electronics, power-saving, etc. This research offers modelling and numerical simulation for the magnetized Casson-based spinel ferrite (MnFe2O4) nanofluid stream owing to a spiralling stretchable sheet placed in a Darcy permeable medium. Diverse impacts like nonlinear heat radiation, viscous and Joule warms, and heat generation/absorption are considered in stimulating heat exchange. Under the imposed physical assumptions, equations governing the flow and heat flow are modelled. The partial derivative model is transferred to the ordinary derivative model by utilising compatible similarity variables. The resulting nonlinear linked ordinary derivative model is tackled computationally by the 4th-order Runge-Kutta integration procedure, accomplishing the best strategy shooting algorithm based on the built-in function of the bvp4c solver in MATLAB. Different attributes of the considered flow phenomenon corresponding to the pertinent model parameters are disclosed effectively via graphs and tables. Some leading outcomes are that amplification is examined in the thermal field and allied zone thickness responding to the radiation parameter and Biot number. With the upgraded rotation parameter, an augmentation is developed in the absolute value of the local skin friction coefficients. Moreover, amplifying the rotation parameter enfeebles the local Nassault number. This modelling could be effective in manufacturing and technological processes like polymeric material extrusion, stretchable/shrinkable packaging, and designing magnetic storage devices.

Impacts of multiple slip on magnetohydrodynamic Williamson and Maxwell nanofluid over a stretching sheet saturated in a porous medium

This study addresses the magnetohydrodynamic boundary layer with multiple slip conditions on Williamson and Maxwell nanofluid across a stretching sheet saturated in a porous medium. Due to the existence of nanoparticles, Brownian motion and thermophoresis effects are assumed. Here, we considered the impact of thermal radiation, viscous dissipation, Ohmic heating, and chemical reaction. The governing Partial Differential Equations (PDEs) are nondimensionalized using suitable similarity conversions and transmuted into nonlinear Ordinary Differential Equations (ODEs). Solutions are acquired numerically using the bvp4c solver in MATLAB. Moreover, the relevant physical parameters like magnetic, permeability, Brownian motion, Prandtl and Eckert number, radiation, thermophoresis, and chemical reaction on velocity, temperature, and concentration fields are depicted graphically. We perceived that augments in magnetic and permeability parameters cause a downfall in the velocity profile, while the opposite trend is notable for the remaining profiles. Velocity declines when escalating the Williamson and Maxwell parameter values. Results show that increasing velocity, thermal, and concentration slip parameters reduce the relevant profiles. Skin friction increases for increasing values of the Williamson, Maxwell, and suction parameters, whereas other parameters exhibit the opposite trend. A dual solution is performed for the velocity and temperature profiles with and without suction. Our current solution has been compared with existing literature and is determined to be in perfect accord.

IMPACT OF THERMAL RADIATION, HEAT SOURCE AND CHEMICAL REACTION ON THREE-DIMENSION FLOW PAST A NON-LINEAR STRETCHING SHEET WITH NANOPARTICLES

The main focus of the present work is to study heat and mass transfer on 3-D flow of nanofluid over a stretching sheet which is extended non-linearly in two sidewise directions. The governing equations of the problem are made dimensionless by using non-dimensional transformations and the problem is solved numerically using Matlab solver bvp4c. The temperature and concentration distributions of the fluid is determined for both linear stretching as well as non-linear stretching of the sheet for important parameters affecting the problem in graphical form and it is found that the rise in fluid temperature is always low for non-linear stretched sheet as compared to the linear one. Values of Nusselt number as well as Sherwood number are also computed to study the thermal as well as mass transfer phenomena. The numerical accuracy has also been presented by comparing the present result with existing published work.

The Significant Effect of Hydromagnetic on Carbon Nanotubes Based Nanofluids Flow and Heat Transfer Past a Porous Stretching/Shrinking Sheet

The 2D steady flow model of carbon nanotubes-based nanofluids and heat transfer past a porous stretchable or shrinkable sheet is studied analytically and numerically. A mathematical model that is governed by a system of partial differential equations (PDEs) subjected to boundary conditions is transformed into a system of dimensionless ordinary equations (ODEs). The non-dimensional ODEs system is solved using MATLAB bvp4c solver. The effect of various parameters such as magnetic field, porosity, the stretching/ shrinking velocity parameter, and CNTs volume friction on velocity and temperature profile, skin friction, Nusselt number and heat transfer rate are investigated numerically and the results are presented using graphical illustration. From the results, non-unique solutions are obtained in the cases where the sheet is shrunk, the magnetic parameter less than 0.1, or the porosity parameter is less than 30. Besides, the increment of magnetic field into the flow will increase both the skin friction and the heat transfer coefficient, while on the contrary, the decreasing in both the skin friction and the heat transfer coefficient will occur if the porosity parameter is raised. We are also showing that SWCNTs is more effective both in the skin friction and the heat transfer coefficient compared to MWCNTs.

Investigation of radiative MHD Carreau nanofluid over an inclined stretching cylinder with activating energy, Wu’s slip, and convective heating

The influence of radiation, convective heating, second-order velocity slip condition, and activating energy on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer are depicted in this study. A mathematical model of the Carreau nanofluid is carried out with the effects of thermophoresis and Brownian motion. The governing equations are transformed into a system of nonlinear coupled differential equations. Solutions of the transformed equations are derived by the Matlab BVP4c solver. Efficiency of the solver is verified by the comparison with the previous literature. Moreover, the impacts of the dimensionless velocity, temperature, and nanoparticle concentration profile are elucidated graphically.

Numerical and series solutions for Von-Kármán flow of viscoelastic fluid inspired by viscous dissipation and Joule heating effects

Present article aims at developing similarity solutions for heat transportation in swirling flow of viscoelastic fluid (obeying Jeffrey model) generated by an infinite porous rotating surface. The resulting thermal energy equation comprising frictional heating and Ohmic dissipation terms is mainly focused. Relevant equations simplified under boundary layer approximations have been solved analytically by a powerful homotopy based analytical scheme, while numerical solutions are constructed by a reliable MATLAB solver bvp4c. For homotopy based series solutions, total squared residual of the system is evaluated, and it is found to decline for increasing order of approximations. Both applied methods are shown to be in compliance with each other for wide range of viscoelastic fluid parameters. Computed solutions are utilized to understand the combined influence of viscoelasticity and viscous dissipation on heat transport phenomena associated with the Von-Kármán configuration. Subtle fluid dynamics entities such as resisting torque and Nusselt number are computed and elaborated. Results predict that the torque required by the disk drastically reduces when viscoelastic fluid assumption is applied. However, cooling rate of the disk in Newtonian fluid is better than that in viscoelastic fluid. Present results are found in agreement with that of the previous studies in a limiting situation.

Nonlinear convection unsteady flow of electro-magnetohydrodynamic Sutterby hybrid nanofluid in the stagnation zone of a spinning sphere

The heat transfer characteristics of Sutterby hybridized nanofluid flow around a spinning sphere in electro-magnetohydrodynamic nonlinear convective unsteady stagnation point flow are investigated under the influence of convective heating circumstances and quadratic thermal radiation flux. Initially, the AA7072/methanol nanofluid is created by dispersing AA7072 nanoparticles into the methanol. The suitable AA7072+AA7075/ methanol hybrid nanofluid is then created by mixing AA7075 with AA7072/methanol. The governing equations are initially built as partial differential equations, which are subsequently converted to ordinary differential equations by using a similarity transmutation technique. In the study, the numerical technique of the bvp4c solver in Matlab is used. Physical factors’ effects on temperature, concentration, and primary and secondary velocity profiles have been studied. As a result of greater unsteadiness, the magnetic field, and Sutterby fluid parameters, the flow of AA7072/methanol nanofluid and (AA7072+AA7075)/ methanol hybrid nanofluid in the flow region moves quickly in the primary direction and slowly in the rotating direction. The result also demonstrates that a rise in the thermal radiation constraint, temperature ratio parameter, magnetic field constraint, electric field constraint, ϕAA7072, and ϕAA7075 causes a rise in the temperature distribution of the (AA7072+AA7075)/methanol hybrid nanofluid and the AA7072/methanol nanofluid. Furthermore, the strongest enhancement in heat transmission rate happens at a volumetric fraction of 4% of (AA7072+AA7075) nanoparticles and AA7072 nanoparticles (i.e., increased by 5.135827% and 4.370679% when compared with ordinary fluid, respectively). The findings of the study have implications for nano-coating spin processing in the chemical engineering industry, spray applications of agricultural chemicals, drag reducers in pipe flows, and the production of domestic cleaning products.

Onset about isothermal flow of Carreau liquid over converging channel with Cattaneo-Christov heat and mass fluxes

In this paper, an innovative mathematical approach is adopted to construct new formulation for exploring thermal characteristics in Jeffery Hamel flow between non-parallel convergent-divergent channels using non-Fourier's law. Due to the occurrence of isothermal flow of non-Newtonian fluids through non-uniform surfaces in many industrial and technological processes, such as film condensation, plastic sheet deformation, crystallization, cooling of metallic sheets, design of nozzles devices, supersonic and various heat exchangers, and glass and polymer industries, the current research is focused on this topic. To modulate this flow, the flow stream is subjected in a non-uniform channel. By incorporating relaxations in Fourier's law, thermal and concentration flux intensities are examined. In the process of mathematically simulating the flow problem, we constructed a set of governing partial differential equations that were embedded with a variety of various parameters. These equations are simplified into order differential equations using the vogue variable conversion approach. By selecting the default tolerance, the MATLAB solver bvp4c completes the numerical simulation. The temperature and concentration profiles were determined to be affected in opposing ways by thermal and concentration relaxations, while thermophoresis improved both fluxes. Inertial forces in a convergent channel accelerate the fluid in a convergent channel, while in the divergent channel the stream is shrink. The temperature distribution of Fourier's law is stronger than that of the non-Fourier's heat flux model. The study has real-world significance in the food business and is pertinent to energy systems, biomedical technology, and contemporary aircraft systems.

Influence of thermophoretic deposition and viscous dissipation on magnetohydrodynamic flow with variable viscosity and thermal conductivity

AbstractIn this study, we numerically explore the impact of varying viscosity and thermal conductivity on a magnetohydrodynamic flow problem over a moving nonisothermal vertical plate with thermophoretic effect and viscous dissipation. The boundary conditions and flow‐regulating equations are converted into ordinary differential equations with the aid of similarity substitution. The MATLAB bvp4c solver is used to evaluate the numerical solution of the problem and it is validated by executing the numerical solution with previously published studies. The impacts of several factors, including the magnetic parameter, Eckert number, heat source parameter, thermal conductivity parameter, stratification parameter, Soret, Dufour, Prandtl number, and Schmidt number are calculated and shown graphically. Also, the skin friction coefficient, Nusselt number, and Sherwood number are calculated. Fluid velocity, temperature, and concentration significantly drop as the thermophoretic parameter and thermal stratification parameter increases. As thermal conductivity rises, it is seen that the velocity of the fluid and temperature inside the boundary layer rise as well. Also, the Soret effect drops temperature and concentration profile. The applications of this type of problem are found in the processes of nuclear reactors, corrosion of heat exchangers, lubrication theory, and so forth.

MHD Stagnation Point of Blasius Flow for Micropolar Hybrid Nanofluid toward a Vertical Surface with Stability Analysis

This study investigates the magnetohydrodynamics of a micropolar fluid consisting of a hybrid nanofluid with mixed convection effects. By using the dimensionless set of variables, the resulting equations of ordinary differential equations are solved numerically using the bvp4c solver in MATLAB. In the present work, the water-based alumina–copper hybrid nanofluid is analytically modeled with modified thermophysical properties. The study reveals that the highest critical value of opposing flow is the hybrid nanofluid (ϕ1 = ϕ2 = 2%). By comparing the hybrid nanofluid with Cu–water nanofluid (ϕ1= 0%, ϕ2= 1%) as well as water (ϕ1= 0%, ϕ2= 0%), hybrid nanoparticle volume fraction enhances the dynamic viscosity performance and surface shear stress. In addition, the augmentation of the nanoparticle volume fraction and magnetic field parameter will increase the physical quantities Rex1/2 Cf, Rex Mx, and Rex−1/2 Nux. The result from the stability inquiry discloses that the first solution is more physically stable and trustworthy. It is proven that magnetohydrodynamics could contribute to controlling the fluid flow in a system, i.e., engineering operations and the medical field. In addition, this theoretical research can be a benchmark for experimental research.

Darcy–Forchheimer flow of power-law (Ostwald-de Waele type) nanofluid over an inclined plate with thermal radiation and activation energy: an irreversibility analysis

Darcy–Forchheimer flow model is substantial in the fields where high flow rate effect is a common phenomenon, for instance, in petroleum engineering. Power law is used to describe fluid behaviour, permit mathematical predictions and correlate experimental data. In technical devices and the natural world, boundary layer flows near an inclined plate are common. Bluff bodies have gained attention because of their various industrial uses, such as electroplating, chemical processing of heavy metals, ash or scrubber waste treatment, and so forth. The objective of this paper is how activation energy and thermal radiation effect the characteristics of Ostwald-De Waele nanofluid flow over a convectively heated inclined plate. Furthermore, irreversibility analysis is provided in this paper. Equations that characterize the current problem are turned into a set of ordinary differential equations, which are then solved with the assistance of bvp4c solver in MATLAB. Multiple linear regression is used to explain physical parameters of interest including the Sherwood number. Major findings of this study are that the increase in entropy production is observed in the fluid flow with increasing Brinkmann number and the fluid’s velocity reduces linearly with increasing Forchheimer number. Furthermore, Outcomes of this study are compared with earlier results and found to be worthy.

Estimation of entropy generation and heat transfer of magnetohydrodynamic quadratic radiative Darcy–Forchheimer cross hybrid nanofluid (GO + Ag/kerosene oil) over a stretching sheet

The steady two-dimensional magnetohydrodynamic flow and heat transfer behavior of Darcy–Forchheimer non-Newtonian (Cross) hybrid nanofluid consisting of Go/Kerosene oil and Go + Ag/Kerosene oil through the porous medium past astretched sheet are analyzed here. The heat energy is augmented with quadratic thermal radiation, Ohmic heating, and convective boundary conditions. There is a huge market for nanotechnology, and the development of these materials can be predicted to be very light. Non-Newtonian hybrid nanofluids have several uses in the biomedical, culinary, industrial, and polymer industries. The governing set of nonlinear partial differential equations is converted to ordinary differential equations before being solved numerically. Numerical simulation is completed through MATLAB solver bvp4c by setting the default tolerance. The solver is applied recursively to achieve the desired accuracy in picking the best blend of the assorted parameters we entrenched in the system. The influence of different fluid flow parameters on the velocity, temperature, skin friction, and local Nusselt number are analyzed tabularly and graphically. It is observed that velocity and temperature profile upsurges for the higher values of Weissenberg number. It is also found that quadratic thermal radiation has a significant impact on fluid temperature and heat transfer rate. Forchheimer number and magnetic field resistance make the flow slower and cause enhancement in liquid temperature. Further, adding a volume fraction of silver with Graphene oxide becomes responsible for stabilizing the flow and enhancing heat transportation. The entropy generation becomes more significant with quadratic thermal radiation and Eckert number.

Finite Element Study of Electrical MHD Williamson Nanofluid Flow under the Effects of Frictional Heating in the View of Viscous Dissipation

This study addresses heat and mass transfer of electrical magnetohydrodynamics (MHD) Williamson fluid flow over the moving sheet. The mathematical model for the considered flow phenomenon is expressed in a set of partial differential equations. Later, linear and nonlinear ordinary differential equations (ODEs) are obtained. The finite element method tackles a reduced system of ODEs with boundary conditions. Galerkin weighted residuals and constructs of weak formulations constitute the basis of this method. An iterative procedure is considered for handling nonlinear terms in a given system of ODEs. Some results acquired using the finite element method are compared with those reported in previous research via the Matlab solver bvp4c in order to validate the obtained solutions of ODEs. It is seen that the velocity profile is decayed by enhancing the Wiesenberg number. The finite element method also converges to an accurate solution by increasing the number of elements, whereas Matlab solver bvp4c produces accurate results on small grid points. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures.

Nanofluid containing motile gyrotactic microorganisms squeezed between parallel disks

Advanced nano and microtechnologies for nano/micro-electronic devices have made substantial advances in the past few years. These technologies are rapidly incorporating advanced fluid media such as nanofluids and biological microorganisms. Inspired by bio-nanofluid applications in medicine, biological systems and biotechnology in the present study, mathematical model is evolved for unsteady bio convective conducting nanofluid along with gyrotactic micro-organisms squeezed between parallel disks. The lower disk and upper disks are solids. The temperature field is improved by the methods of haphazard motion of nanoparticles and thermophoresis parameters. The nano-bio transfer model is written as a series of non-linear partial differential equations that are reduced into a set of ordinary differential equations using suitable transforms. The dimensionless problem is then numerically solved by RK-4th order scheme utilizing MATLAB bvp4c solver’s package to investigate the impact of the squeezing parameter, Hartman number, Brownian motion and thermophoresis parameter on motile microorganism velocity, temperature, nanoparticle concentration, and density. The friction factor, Nusselt number, Sherwood number and microorganism number distributions on Hartman number, thermophoresis and Brownian motion factors are also computed. The Brownian motion and the thermophoresis factors of nanoparticles cause an increment in temperature profiles for both suction and injection. The concentration and motile microorganism are both amplified for the Brownian parameter in the case of injection, whereas they are declined for suction and the opposite trend is observed for the thermophoresis parameter. The motile microorganism is deflated for both suction and injection with thermophoresis parameter. Suction and injection adversely affect the transfer properties at the disks. The resistive magnetic body force prevails in the core zone, resulting in a decrease in velocity. The heat generation in squeeze films with motile microorganisms can be successfully removed with magnetic nanoparticles which require a longer serviceability of the lubrication system, bio-medical systems and need for less maintenance and a longer lifespan approach. The finding is pertinent to novel bio-microsystems that combine nanofluid and the bioconvection phenomenon. The percentage increase in heat, mass, and microorganism transport rates is calculated.

Carbon Nanotubes (CNTs) Nanofluids Flow and Heat Transfer under MHD Effect over a Moving Surface

The 2D steady flow of CNTs nanofluids and heat transfer over the moving plate through a uniform free stream under the effect of magnetohydrodynamics (MHD) is studied. The movement of plate is presumed in the opposite or same direction. A mathematical modelling that is governed by a system of partial differential equations (PDEs) subjected to boundary conditions is transformed into a system of nonlinear ordinary equations (ODEs). An attempt at finding the expected outcomes is successfully executed by solving ODEs system using MATLAB bvp4c solver. The effect of various parameters such as magnetic field, CNTs volume friction and moving parameter on velocity and temperature profile, skin friction, Nusselt number and heat transfer rate are investigated numerically. The results are presented using tabular and graphical illustration. From the results, the increment of magnetic field into the flow will increase in both the skin friction and the heat transfer coefficient. Besides that, non-unique solutions are obtained when the plate moves in the range of and . For comparing the performance of base fluid, kerosene works better than water as a base liquid. We are also showing that SWCNTs is more effective both in the skin friction and the heat transfer coefficient compare to MWCNTs.