MHD Williamson Nanofluid Flow over a Slender Elastic Sheet of Irregular Thickness in the Presence of Bioconvection

Advancing Renewable Energy Systems: A Numerical Approach to Investigate Nanofluidics' Role in Engineering Involving Physical Quantities

Nanofluids, with their enhanced thermal properties, provide innovative solutions for improving heat transfer efficiency in renewable energy systems. This study investigates a numerical simulation of bioconvective flow and heat transfer in a Williamson nanofluid over a stretching wedge, incorporating the effects of chemical reactions and hydrogen diffusion. The system also includes motile microorganisms, which induce bioconvection, a phenomenon where microorganisms' collective motion creates a convective flow that enhances mass and heat transport processes. This mechanism is crucial for improving the distribution of nanoparticles and maintaining the stability of the nanofluid. The unique rheological behavior of Williamson fluid, extensively utilized in hydrometallurgical and chemical processing industries, significantly influences thermal and mass transport characteristics. The governing nonlinear partial differential equations (PDEs), derived from conservation laws and boundary conditions, are converted into dimensionless ordinary differential equations (ODEs) using similarity transformations. MATLAB's bvp4c solver is employed to numerically analyze these equations. The outcomes highlight the complex interplay between fluid parameters and flow characteristics. An increase in the Williamson nanofluid parameters leads to a reduction in fluid velocity, with solutions observed for the skin friction coefficient. Higher thermophoresis and Williamson nanofluid parameters elevate the fluid temperature, enhancing heat transfer efficiency. Conversely, a larger Schmidt number boosts fluid concentration, while stronger chemical reaction effects reduce it. These results are generated by fixing parametric values as 0.1<ϖ<1.5, 0.1 Collapse

Key Words

• bioconvection
• chemical reaction
• heat and mass transfer
• nanotechnology
• non-Newtonian/Williamson nanofluid
• numerical simulation
• renewable energy applications
• stretching wedge

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Affiliation(s)

Muhammad Abdul Basit Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China School of Energy Science and Engineering, University of Science and Technology of China, Guangzhou 510640, China
Muhammad Imran Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan; (M.I.) Department of Mathematics and Science Education, Faculty of Education, Biruni University, İstanbul 34015, Turkey
Tayyiba Anwar-Ul-Haq Department of Mathematics, Government College University Faisalabad, Faisalabad 38000, Pakistan; (M.I.)
Chang-Feng Yan Guangzhou Institute of Energy Conversion, Chinese Academy of Sciences, Guangzhou 510640, China School of Energy Science and Engineering, University of Science and Technology of China, Guangzhou 510640, China
Daniel Breaz Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania
Luminita-Ioana Cotîrlă Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania;
Alin Danciu Department of Mathematics, Babes Bolyai University, 400084 Cluj-Napoca, Romania;

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Comparative study of some non-Newtonian nanofluid models across stretching sheet: a case of linear radiation and activation energy effects

The use of renewable energy sources is leading the charge to solve the world's energy problems, and non-Newtonian nanofluid dynamics play a significant role in applications such as expanding solar sheets, which are examined in this paper, along with the impacts of activation energy and solar radiation. We solve physical flow issues using partial differential equations and models like Casson, Williamson, and Prandtl. To get numerical solutions, we first apply a transformation to make these equations ordinary differential equations, and then we use the MATLAB-integrated bvp4c methodology. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. In addition to numerical and tabular studies of the skin friction coefficient, Sherwood number, and local Nusselt number, important components of the flow field are graphically shown and analyzed. Consistent with previous research, this work adds important new information to the continuing conversation in this area. Through the examination of dimensionless velocity, concentration, and temperature functions under varied parameters, our work explores the physical properties of nanofluids. Comparing the Casson nanofluid to the Williamson and Prandtl nanofluids, it is found that the former has a lower velocity. Compared to Casson and Williamson nanofluid, Prandtl nanofluid advanced in heat flux more quickly. The transfer of heat rates are 25.87 % , 33.61 % and 40.52 % at R d = 0.5 , R d = 1.0 , and R d = 1.5 , respectively. The heat transfer rate is increased by 6.91 % as the value of Rd rises from 1.0 to 1.5. This study is further strengthened by a comparative analysis with previous research, which is complemented by an extensive table of comparisons for a full evaluation.

Impacts of entropy generation in second-grade fuzzy hybrid nanofluids on exponentially permeable stretching/shrinking surface

The present investigation aims to use entropy analysis to analyze the unsteady Magnetohydrodynamic (MHD) flow in a second-grade fuzzy hybrid [Formula: see text] nanofluid over an exponentially shrinking/stretching surface. The model for hybridization of the mixture of alumina [Formula: see text] and copper (Cu) nanoparticles in the sodium alginate (SA) base fluid under heat source/sink, nonlinear thermal radiation, and viscous dissipation. The fundamental partial differential equations (PDEs) are simplified using an appropriate similarity conversion to generate the ordinary differential equations (ODEs). The analytical computation occurs in the MATHEMATICA program implementing the homotopy analysis method (HAM). In terms of code validity, our results are preferable to previous findings. The features of several parameters against the velocity, surface friction coefficient, entropy, temperature, and Nusselt number are described through graphs. According to our findings, the rise in the Brinkman and Reynolds numbers enhanced the total entropy of the system. Furthermore, the nanoparticle volume fraction and viscus dissipation magnifies the fluid temperature while retards the flow profile throughout the domain. Fluid velocity declined due to the Lorentz force using magnetic impact applications. The imprecision of nanofluid and hybrid nanofluid volume fractions was modelled as a triangular fuzzy number (TFN) [0%, 1%, 2%] for comparison. The double parametric approach was applied to deal with the fuzziness of the associated fuzzy parameters. The nonlinear ODEs convert into fuzzy differential equations (FDEs) and use HAM for the fuzzy solution. From our observation, the hybrid nanofluid displays the maximum heat transfer compared to nanofluids. This important contribution will support industrial growth, particularly in the processing and manufacturing sectors. The percentage increase in skin friction factor is 18.3 and 15.0 when [Formula: see text] and [Formula: see text] take input in the ranges of 0 ≤ [Formula: see text] ≤ 0.8 and 0 ≤ [Formula: see text] ≤ 1, respectively.

A new explicit numerical scheme for enhancement of heat transfer in Sakiadis flow of micro polar fluid using electric field

This article suggests a fourth-order numerical approach for solving ordinary differential equations (ODEs) that are both linear and nonlinear. The suggested scheme is an explicit predictor-corrector scheme. For linear ODE, the proposed numerical scheme's stability area is discovered. The proposed strategy yields the same stability region as the traditional fourth-order Runge-Kutta method. In addition, partial differential equations (PDEs) are used to develop the mathematical model for the flow of non-Newtonian micro-polar fluid over the sheet and heat and mass transit using electric field effects. These PDEs are further transformed into dimensionless boundary value problems. Boundary value problems are resolved using the proposed shooting-based scheme. The findings show that increasing values of ion kinetic work and Joule heating parameters cause the temperature profile to climb. The results produced by the suggested strategy are compared to those discovered through earlier studies. The results of this study could serve as a starting point for future fluid-flow investigations in a secure industrial environment.

MHD dissipative Powell-Eyring fluid flow due to a stretching sheet with convective boundary conditions and slip velocity

The novelty and motivation of this research can be emphasized by examining how the heat transfer mechanism of a non-Newtonian Powell-Eyring fluid, which flows because of a stretched sheet, is affected by factors like viscous dissipation, the slip velocity phenomenon, and Joule heating. In addition, the investigation delves into the heat transfer behavior of the fluid flow when it comes into contact with a convectively heated stretched surface that is influenced by varying fluid properties. This analysis also takes into account the influence of changing fluid characteristics and the presence of magnetic field. The numerical solutions of modelled equations that governing the problem are detected using the shooting technique. Also, in order to confirm the validity of the present investigation, a proper comparison with certain published works as a particular case of the present model is presented, and a perfect agreement is noted. With the use of diagrams and tables, the flow problem's effective parameters are thoroughly discussed. Likewise, through a tabular representation, the values of the local Nusselt number and the skin-friction coefficient are computed and analyzed. Many significant conclusions can be drawn from numerical results. Most importantly, the local Nusselt number rises monotonically with both the surface convection parameter and the slip velocity parameter, but the local skin-friction coefficient has the opposite trend. The results indicate that the nanofluid temperature is enhanced by factors such as the surface convection parameter, magnetic field, and viscous dissipation. On the other hand, the slip velocity phenomenon leads to the opposite effect.

Significance of melting heat in bioconvection flow of micropolar nanofluid over an oscillating surface

Pharmaceuticals, biological polymer synthesis, eco-friendly uses, sustainable fuel cell innovations, microbial-enhanced extraction of petroleum, biological sensors, biological technology, and continual mathematical modeling refinement are all examples of how bioconvection is applied. This study examines the bio convectional viscoelastic-micropolar nano liquid flow with non-uniform heat sink/source, motile microorganisms that move across a stretched sheet. Thermal radiation and thermal conductivity are also explored. Brownian and thermophoresis diffusion effects are taken into account. The system of a higher partial differential equation is transformed to ODEs by using the appropriate similarity functions. Such reported equations are implemented with the computational tool MATLAB shooting approach using a bvp4c solver. The variations of numerous flow parameters comprise velocity, temperature, concentration, and motile microorganism profile. Various important, interesting transport numbers are numerically and graphically demonstrated with physical justifications. The bouncy ratio parameter reduces the fluid's velocity profile whereas the material parameter increases it. For increased melting parameters, the micro rotation profile improves, but it deteriorated. For the Prandtl number and temperature ratio parameters, the temperature profile is negative. The melting parameter influences the concentration profile. The microorganism's profile is decreased bioconvective Lewis numbers and is higher for the magnetic parameter. The current model has many features in the manufacturing industries, engineering works, physics, and applied mathematics.

Numerical investigation of MHD flow of hyperbolic tangent nanofluid over a non-linear stretching sheet

This research investigates two-dimensional MHD incompressible boundary layer Hyperbolic Tangent nanofluid flow across a non-linear stretching plate. Similarity transformations are employed to convert the governing non-linear partial differential equations (PDEs) into coupled non-linear ordinary differential equations (ODEs). The MATLAB built-in routine bvp4c has been used for finding the numerical solutions of the dimensionless velocity, temperature, and concentration profiles. The current findings are validated with already published results. The influence of some important parameters on the velocity, temperature, and concentration profiles are displayed through graphs and tables. It is observed that for increasing values of magnetic parameter M and hyperbolic Tangent parameter We, the boundary layer thickness of the velocity profile decreases while it increases for the temperature profile.

Effects of Double Diffusive Convection and Inclined Magnetic Field on the Peristaltic Flow of Fourth Grade Nanofluids in a Non-Uniform Channel

This study explored the impact of double diffusive convection and inclined magnetic field in nanofluids on the peristaltic pumping of fourth grade fluid in non-uniform channels. Firstly, a brief mathematical model of fourth grade fluid along inclined magnetic fields and thermal and concentration convection in nanofluids was developed. A lubrication approach was used to simplify the highly non-linear partial differential equations. An analytical technique was then used to solve the highly non-linear differential equations. The exact solutions for the temperature, nanoparticle volume fraction and concentration were calculated. Numerical and graphical outcomes were also examined to see the effects of the different physical parameters of the flow quantities. It was noted that as the impact of Brownian motion increased, the density of the nanoparticles also increased, which led to an increase in the nanoparticle fraction. Additionally, it could be observed that as the effects of thermophoresis increased, the fluid viscosity decreased, which lowered the fraction of nanoparticles that was made up of less dense particles.

Micropolar Dusty Fluid: Coriolis Force Effects on Dynamics of MHD Rotating Fluid When Lorentz Force Is Significant

The main objective of this investigation to examine the momentum and thermal transportation of rotating dusty micropolar fluid flux with suspension of conducting dust particles across the stretched sheet. The novelty of the flow model is the exploration of the significance of boosting the volume concentration of dust particles in fluid dynamics. The governing PDEs of the problem for both phase models are transmuted into nonlinear coupled non-dimensional ODEs by utilizing suitable similarity modifications. The bvp4c technique was utilized in MATLAB script to acquire a graphical representation of the experimental results. This study illustrates the analysis of repercussions of pertinent parameters on non-Newtonian fluid and the dusty phase of fluid. By improving the volume concentration of dust particles and rotating parameters, the axial velocity for both phases depreciates, whereas temperature and transverse velocity for both phases have the opposite behavior. The micro-rotation distribution rises with higher contributions of rotating and material parameters, whereas it decreases against larger inputs of volume concentration of dust particles. The growing strength of the dust volume fraction (ϕd) caused the coefficient of skin friction to decrease along the x direction, and the skin friction coefficient is raised along the y direction.

Insight into Significance of Bioconvection on MHD Tangent Hyperbolic Nanofluid Flow of Irregular Thickness across a Slender Elastic Surface

This numerical investigation effectively establishes a unique computing exploration for steady magnetohydrodynamic convective streams of tangent hyperbolic nanofluid traveling across a nonlinearly elongating elastic surface with a variable thickness. In addition, the importance of an externally imposed magnetic field of tangent hyperbolic nanofluid is comprehensively analyzed by considering the substantial impact of thermal conductivity and thermal radiation consequences. The governing PDEs (partial differential equations) are transmuted into a nonlinear differential structure of coupled ODEs (ordinary differential equations) using a series of variable similarity transformations. Furthermore, these generated ODEs (ordinary differential equations) are numerically set using a novel revolutionary Runge-Kutta algorithm with a shooting approach constructed in a MATLAB script. In this regard, extensive comparison studies are carried out to validate the acquired numerical results. The interactions between the associated profiles and the relevant parameters are rationally explored and shown using graphs and tabular forms. The velocity distribution declined with improving Weissengberg number We and power-law index m, while the reverse performance can be observed for temperature. As enhancement in Brownian motion, Thermophoretic and radiation parameters significantly rise in temperature distribution. The use of many different technological and industrial systems, including nano-bioconvective systems, nano-droplet evaporation, nano-ink jet printing, and microbial fuel cells, would benefit this research study.

Magneto-Nanofluid Flow via Mixed Convection Inside E-Shaped Square Chamber

Nanofluids play a crucial role in the augmentation of heat transfer in several energy systems. They exhibit better thermal conductivity and physical strength compared to normal fluids. Here, we conduct an evaluative investigation of the magnetized flow of water–copper nanofluid and its heat transport inside a symmetrical E-shaped square chamber via mixed convective impact with a heated corner. The chamber was constructed symmetrically with an inclined magnetic field strength, and the upper surface of the chamber was isolated and set to move at a fixed velocity. The heated corner was set at a fixed hot temperature in both the left and lower directions. The right side was maintained at a fixed cold temperature, while the remaining portions of the left and lower parts were isolated. The investigation was implemented computationally, solving each of the energy and Navier–Stokes models via the application of a symmetrical finite volume method. The following topics have been addressed in this study: the consequences of the magnetic field, the volumetric fraction of nanoparticles, the heat generation–absorption parameters, and the effects of heat-source length and Richardson number on the fluid comportment and heat transport. The outputs of this symmetric study enabled us to arrive at the following derivation: the magnetic field reduces the fluid circulation inside the E-shaped square chamber. The augmentation of the Richardson number leads to an increase in the heat transfer. Moreover, the decrease in heat generation coefficient lowers the nanofluid temperature and weakens the flow fields.

Computational Analysis for Bioconvection of Microorganisms in Prandtl Nanofluid Darcy-Forchheimer Flow across an Inclined Sheet

The two-dimensional boundary layer flow of a Prandtl nanofluid was explored in the presence of an aligned magnetic field over an inclined stretching/shrinking sheet in a non-Darcy permeable medium. To transform the PDEs of the leading equations into ODEs, a coupled boundary value problem was formed and suitable similarity functions were used. To obtain numerical answers, an efficient code for the Runge–Kutta technique with a shooting tool was constructed with a MATLAB script. This procedure is widely used for the solution of such problems as it is efficient and cost-effective with a fifth-order accuracy. The significance of immersed parameters on the velocity, temperature, concentration, and bioconvection is shown through figures. Furthermore, the physical parameters of the skin friction coefficient and the Nusselt numbers are demonstrated in tables. The declining behavior of the flow velocity against the porosity parameter Kp and the local inertia co-efficient Fr is shown, and the both parameters of the Darcy resistance and Darcy–Forchheimer resistance are responsible for slowing the fluid speed. The increasing values of the Schmidt number Sc decrease the concentration of the nano entities.

Significance of Dust Particles, Nanoparticles Radius, Coriolis and Lorentz Forces: The Case of Maxwell Dusty Fluid

This study aimed to analyze the momentum and thermal transport of a rotating dusty Maxwell nanofluid flow on a magnetohydrodynamic Darcy–Forchheimer porous medium with conducting dust particles. Nanouids are the most important source of effective heat source, having many applications in scientific and technological processes. The dust nanoparticles with superior thermal characteristics offer a wide range of uses in chemical and mechanical engineering eras and modern technology. In addition, nanofluid Cu-water is used as the heat-carrying fluid. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. An efficient code for the Runge–Kutta technique with a shooting tool is constructed in MATLAB script to obtain numeric results. The study is compared to previously published work and determined to be perfect. It is observed that the rising strength of the rotating and magnetic parameters cause to recede the x- and y-axis velocities in the two phase fluid, but the temperature function exhibits an opposite trend. By improving the diameter of nanoparticles Dm, the axial velocity improves while transverse velocity and temperature show the opposite behaviors. Furthermore, it is reported that the inclusion of dust particles or nanoparticles both cause to decline the primary and secondary velocities of fluid, and also dust particles decrease the temperature.