Similarity Transformation Approach Research Articles

Ferrohydrodynamic on Heat Transfer in Hybrid Ferrofluid over an Elongation Sheet

Advancing hybrid ferrofluids enhances biomedical engineering and leads to better treatments for cancer and other diseases. Due to their distinctive composition, they exhibit enhanced thermal conductivity, rendering them exceptionally efficient for hyperthermia therapies, which include eliminating the growth of cancer cells at increased temperatures. This study investigates the influence of magnetism on a hybrid ferrofluid flowing past an elongation sheet. The combination of magnetite ferrite-cobalt ferrite nanoparticles (Fe_3 O_4/CoFe_2 O_4) dispersed in a water-ethylene glycol mixture, in the presence of a magnetic dipole, is analysed. The governing equations of the hybrid ferrofluid are derived using Tiwari and Das's model. Subsequently, the similarity transformation approach is applied to simplify the partial governing equations and the Keller box method is employed to solve them. The numerical results of velocity and temperature distributions for pertinent parameters, such as ferrohydrodynamics (FHD) effect and concentrations of the nanoparticles, are graphically presented. The results indicate that the FHD impact diminishes the velocity profile, but enhances the temperature field of the hybrid ferrofluid flow. The shear stress is enhanced by 90.79% and the heat transfer rate is reduced by 12.12%. The presence of hybrid nanoparticles in the fluid not only enhances the temperature distribution but also suppresses the movement of the particles. These outcomes provide insights into the interplay between magnetic fields and heat transfer, relevant to magnetic hyperthermia cancer treatment.

Nonorthogonal stagnation‐point flow of micropolar fluid past a stretching sheet in the presence of thermal radiation and chemical reaction

AbstractThis work has broad applications in areas such as materials engineering, particularly in the manufacturing of polymers, textile fibers, and nanocomposites, thus, inspired the study to examine a continuous two‐dimensional flow of micropolar fluid steadily fluctuated in an oblique impinging on a stretched surface theoretically and computationally. In addition, heat radiation and chemical reactions are taken into account in this work. The flow is composed of a uniform shear flow parallel to the sheet surface and a stagnation‐point flow. Assuming a linear variation in surface temperature, the sheet is extending at a velocity proportionate to the distance from the stagnation point. In terms of partial differential equations, the boundary‐layer regime under discussion is modeled. The nondimensional ordinary differential equations were developed using appropriate similarity variables via a similarity transformation approach. The most effective and powerful too of the numerical approach, known as the pseudospectral collocation technique, is used to solve the micropolar flow model problem. The velocity, angular velocity, temperature, and concentration profiles are portrayed through graphs. Moreover, the impression of the input values on the wall drag coefficient, thermal, and solutal transfer rate are computed in a table. A table is used to compare the numerical findings with the results found in the literature to verify the correctness of the results. It is noted that there is great agreement between the found answer and the earlier investigations. Graphs are used to show the impacts of the relevant factors in the problem, which include the magnetic parameter, the impinging angle heat transfer characteristics, the Prandtl number, the Lewis number, Brownian motion, and the thermophoresis parameter.

Thermophoresis & Soret-DuFour on MHD Mixed Convection of a Nano Fluid with a Porous Medium over a Stretching Sheet with a Non-Uniform Heat Source/Sink

This work aimed to examine the effects of thermal diffusion (Soret) and diffusion-thermo (DuFour) on MHD mixed convective flow of a viscous nanofluid across a stretching sheet under a magnetic field embedded in a porous medium in the presence of non-uniform heat source/sink and chemical reaction. The governing equations are transformed into a set of ordinary differential equations using the similarity transformation approach. They are subsequently resolved computationally by use of the efficient Keller box method. The effects of different physical factors on concentration, temperature, and velocity profiles are graphically shown. Increasing Du values decreases temperature, although concentration profiles indicate the reverse. As temperature rises, the chemical reaction parameter Kr values increase, while the concentration profile decreases. The temperature was found to rise when the space-dependent (A1) and temperature-dependent (B1) parameters for heat source/sink increased. Additionally, a tabular presentation of the skin friction coefficient, Nusselt number, and Sherwood number behaviour is provided. Mixed convection heat and mass transfer flows are very important in manufacturing for designing reliable equipment, nuclear power plants, gas turbines, and various propulsion devices for aircraft, rockets, satellites, and spacecraft. The effects of non-uniform heat sources/sinks, thermophoresis, and chemical reactions on mixed convection flow play an important role in space technology and high-temperature processes.

Modeling of nanoblood flow in an artery in presence of eco-friendly and biocompatible hybrid nanoparticles

Transferring biological fluid through arteries is a topic that has garnered serious interest in recent times, especially when it pertains to applications such as drug delivery. In our body, arteries serve as the primary conduits for blood flow and this study aims to model the blood flow in this situation. The working fluid is essentially pure blood, which acts as a base fluid, supplemented with nanoparticles of Titanium Dioxide (TiO2) and Gold (Au). Nanoparticles could change the thermal and rheological properties of blood which might be particularly advantageous for ensuring smoother flow or optimal distribution of drug molecules within the bloodstream. In the present work, a porous channel is considered with parallel walls that exhibit varying permeability on boundaries. Such a design enables the nanoblood to enter and exit the channel, mimicking certain natural processes like transvascular fluid exchange. Additionally, the variable height of the channel that expands and squeezes uniformly could be reminiscent of the pulsatile nature of blood flow seen in our arteries due to heartbeats. To understand the dynamics of this hybrid nanoblood flow, the governing equations are converted into a set of nonlinear ordinary differential equations using the similarity transformation approach. For solving these transformed equations, the research harnesses the BVP4C built-in function in MATLAB software. Through this computational approach, the research provides insights into the velocity and temperature profile of the fluid, the distribution of normal pressure, wall shear stress, and the Nusselt number concerning various parameters. The findings of the present study can be significant and useful in biological sciences and technologies and the detailed results are presented completely in the article’s body.

Investigating radiative heat transfer, varied wall thickness, and slip effects on Casson nanofluid flow over a stretched sheet with heat source

ABSTRACT Understanding the intricate interplay between variable fluid properties such as slip and thermal conductivity when flowing over porous surfaces is of utmost importance for a wide range of engineering applications. This investigation delves into this uncharted territory, connecting the analytical capabilities of HAM (Homotopy Analysis Method) to reveal captivating insights into the impact of these variables on the dynamics of Casson nanofluid flow. Besides, we documented the flow aspects which include thermal radiation, heat source, variable wall thickness and chemical reaction. We alter the partial differential flow-related conditions into nonlinear ordinary ones employing the similarity transformation approach. Then, using a popular semi-analytical technique known as the Homotopy Analysis Method (HAM), we were able to untangle them. This method yields to power series solutions to nonlinear differential equations. To illustrate the impact of the velocity, temperature and concentration profiles, parametric research has been done using tables and diagrams. In the limiting sense, the numerical results of our methodology are in great association with the outcomes of previous research. Finally, it is noted that higher values of the velocity slip parameter cause an enhancement in fluid velocity, while escalating values of the thermal slip parameter cause a decline in temperature distribution.

Optimizing entropy in mixed convective MHD dissipative nanofluid with cross-diffusion and nonlinear velocity slip

Entropy optimization is crucial for enhancing fluid dynamics and heat transfer, leading to improved efficiency, energy conservation, and environmental sustainability. Recognizing its significance, we examine the influence of radiation, Joule heating, heat sources, mixed convection, and nonlinear slip on the entropy-optimized flow of a dissipative nanofluid over a curved surface. To seamlessly integrate within the MATLAB bvp4c framework, we convert the set of multi-order ODEs, derived from fundamental PDEs via a similarity transformation approach, into a system of first-order ODEs. Graphs and analytical discussions are used to evaluate the parameters of the problem. The velocity within the boundary layer, along with entropy, experiences reduction due to the enhancement in both first- and second-order slip velocity parameters, as well as curvature parameters. The temperature plot improves with the increase in parameters such as the Soret number and Dufour number, as well as radiation. Conversely, the temperature plot reduces with the rise in suction values. The study indicates that a higher Brinkman number is associated with a lower Bejan number, while the first- and second-order velocity slip parameters have a contrasting effect, leading to an increase in the Bejan number.

Flow and Heat transfer of Hybrid nanofluid past an Exponentially Stretched Porous surface

This research looks at the flow and heat conduction properties of a hybrid nanofluid formed by an exponentially stretched porous surface. Over the last decade, there has been a substantial increase in research on nanofluids. Despite several contradictions in the published results and a poor understanding of the heat transmission mechanism in nanofluids, this fluid has emerged as a viable heat transfer medium. It takes longer for the combination nanofluid to make heat than it does for ordinary nanofluid. It has also been shown through simulations that the mixed nanofluid has better temperature performance than the nanofluid. Using the similarity transformation approach, the governing equations of the issue are turned to similarity equations. To convert nonlinear partial differential equations (PDEs) to ordinary differential equations (ODEs), the Keller Box approach is used. This strategy for solving these ODEs has been shown to be quite successful. The effects of several targeted parameters on physical quantities are shown, and the comparison of findings for validation is also recorded. The study's findings are provided as graphs, demonstrating the strong influence of the targeted elements on both nanofluid and hybrid nanofluid. Because of the existence of hybrid nanofluid, the velocity and temperature profiles have improved. Variations in the amount of Copper (Cu) nanoparticles, in particular, cause dramatic variations in the velocity and temperature profiles of the hybrid nanofluid. Furthermore, a lower Prandtl number is shown to reduce temperature and thermal boundary layer thickness. The graphical representations also show how porosity affects temperature and velocity profiles.

Dynamics of bioconvection radiative MHD flow with gyrotactic microorganisms: an intelligent computation approach

Bioconvection flows relate significantly to real-life problems, such as designing bio-conjugates, bio-microsystems, and bio-cells. This study investigates a mathematical characterization of the electrically time-dependent conducting fluid flow containing gyrotactic microorganisms with activation energy, mass, and heat transfer. It is assumed that the flow is towards the extended surface and affects thermal radiations. In model formulation, the Navier–Stokes equations are reduced to a system of ordinary differential equations (ODEs) using a similarity transformation approach. For reference solutions, the RK4 technique is used with Dorman Prince coefficients. We have designed a new backpropagation neural network architecture to formulate new solution models with Bayesian regularization. The effects of variations in two parameters, Schmidt number (sc) and Prandtl number (pr), are investigated. Our experimental outcomes are linked to the reference outputs. It was observed that there is a strong agreement between our solutions and the reference solutions. Our approach can be used for systems of fractional differential equations.

Use of Au-Zn/blood hybrid nano-fluid flow for drug delivery through the human circulatory system

Due to their versatile characteristics in imaging, surface modification, and therapeutics, Gold and Zinc nanoparticles are widely used as nano-materials for agnostic activities. The main purpose of this research is to investigate a mathematical model of a hybrid nano-fluid passing through a porous channel having Zinc and Gold as nano-particles and blood being used as a base fluid. The present model can be very useful for effective drug delivery in blood. The main reason for using gold nanoparticles for drug delivery is because they depict promising characteristics in surface modification, therapeutics and imaging. Variable permeability of both walls allows fluid to enter and leave while a slightly differing span dilates and compresses the fluid at a consistent frequency. The provided system of governing PDEs is converted into a set of odes using the similarity transformation approach. Then, using MATLAB's built-in function bvp4c, dimensionless equations are numerically solved. Plots of the velocity and temperature profiles, along with the Nusselt numbers for the relevant parameters, are shown, and the underlying physical and logical justifications are highlighted. It has been found that the channel's asymmetry, which results from varying wall permeability has a significant impact on the nature of the fluid flow.

MHD Mixed Convective Non-Newtonian Stagnation Point Flow Over an Inclined Stretching Sheet: Numerical Simulation

This paper includes numerical simulation upon MHD mixed convective heat transfer properties of stagnation point flow across an angled stretched sheet. Boundary value problem is solved using similarity transformation approach with shooting technique. The impact of different corporeal constraints like mixed convection parameter, thermal radiation parameter, chemical reaction parameter, Brownian motion and thermophoresis, Casson parameter upon velocity and temp profile as well as skin-friction coefficient , Nusselt number, Sherwood number on velocity, temp concentration profile are shown graphically. Casson parameter increases velocity and diminishes temperature profile. Chemical reaction term decreases Sherwood number and increases concentration profile.

Significance of radiant-energy and multiple slips on magnetohydrodynamic flow of single-walled carbon nanotube-water, titanium dioxide–water, multiwalled carbon nanotube–water, graphene oxide–water nanofluids

The magnetohydrodynamic flow of nanofluid is studied in the present analysis by using two parallel, rotating, and stretchable disks with a porous medium. The thermal radiation effects along with velocity slips at the interface of fluid and disk are considered in this work. The water is taken as base fluid, and carbon nanotubes (CNTs), titanium dioxide (TiO[Formula: see text]), and graphene oxide (GO) are taken as nanoparticles. The corresponding equations are modeled in terms of partial differential equations and Von Karman similarity transformation approach is adopted. The resulting equations are solved by using a finite difference method-based ND Solver. The axial, radial, and tangential velocity profiles and temperature distribution are discussed with graphs and tables. Thermal radiation and convective boundary conditions are used in the heat transfer process. When the thermal Biot number of the lower disk rises, fluid temperature enhances, whereas, the fluid temperature falls with the rise in the thermal Biot number of the lower disk. It is observed that when the thermal Biot number of lower disk rises from 0.5 to 0.8, heat transfer at lower disk is increased by about 6.66% in hexagonal-shaped CNTs-based nanofluid and 6.66% in spherical shaped TiO[Formula: see text] and GO-based nanofluid. The impact of physical parameters such as skin friction coefficient and Nusselt number are computed for governing parameters and discussed in detail.

Blood Conveying Ferroparticle Flow on a Stagnation Point Over a Stretching Sheet: Non-Newtonian Williamson Hybrid Ferrofluid

The present research investigated the characteristics of convective boundary layer flow and heat transfer of the blood carrying ferroparticle modelled known as the non-Newtonian Williamson hybrid ferrofluid. The fluid flow and the heat transfer of a stagnation point over a stretching surface are considered. The similarity transformation approach is used to reduce the partial differential equation system to an ordinary differential equation. The transformed equations are then solved numerically by Runge-Kutta-Felberg (RKF45) method in Maple software. The flow characteristic and the heat transfer of the non-Newtonian Williamson hybrid nanofluid are tested from various pertinent fluid parameters. The temperature distribution, velocity profiles, as well as variation of the Nusselt number and the skin friction coefficient are analysed and discussed. The study reveals that the non-Newtonian Williamson Hybrid ferrofluid potentially provided better performance in heat transfer capability compared to ferrofluid with the same volume of nanoparticle volume fraction.

Unsteady flow of magnetohydrodynamic hybrid nanofluid over a stretching/shrinking sheet: Multiple solutions

The main goal of this article is to perform a heat transfer analysis of unsteady magnetohydrodynamic hybrid nanofluid flow over a stretching/shrinking sheet. The hybrid nanofluid is synthesized by adding two kinds of nano-sized particles. In this examination, TiO2 and Cu nano-sized particles are taken with water as a base fluid. Using an appropriate similarity transformation approach, a set of nonlinear equations is obtained from the governing equations of the current study. To solve the changed system, the Runge–Kutta–Fehlberg approach is applied combined with the shooting method. The obtained data is presented in graphs and tables. Here, dual solutions can be seen utilizing upper and lower division solutions particularly aimed at a specific domain of unsteadiness parameter. The skin friction coefficient parameter shows a considerable improvement. Whereas in the case of the shrinking sheet, larger values of the magnetic parameter and solid volume fraction results in a significant drop in the local heat transfer rate for the upper branch case, while the lower branch case shows a different pattern.

Numerical investigation of heat transfer characteristics for blood/water-based hybrid nanofluids in free convection about a circular cylinder

This paper investigates hybrid nanofluids flowing around a circular cylinder of free convection under the constant surface heat flux. Nanoparticles of copper oxides, Gold, and Aluminum (CuO, Au, Al) are considered to support the heat transfer performance of blood/water-based hybrid nanofluids. The governing model for hybrid nanofluids which is in form of non-linear partial differential equations (PDEs) are first transformed to a more convenient form by similarity transformation approach then approximated numerically by the Keller box method. Several comparatives are performed in this work resulting in the superiority of the hybrid-nanofluid over regular nanofluid in terms of heat transfer rate, velocity, and local skin friction coefficient. Findings confirmed that the surface temperature and temperature field are augmented, with increasing volume fraction for nanoparticles. Also, Gold nanoparticles give a higher result for all examined physical properties than Aluminum and copper oxides nanoparticles.

Thermal Characterization of Coolant Maxwell Type Nanofluid Flowing in Parabolic Trough Solar Collector (PTSC) Used Inside Solar Powered Ship Application

Parabolic trough solar collectors (PTSCs) are generally utilized to reach high temperatures in solar-thermal applications. The current work investigates entropy production analysis and the influence of nano solid particles on a parabolic trough surface collector (PTSC) installed within a solar powered ship (SPS). For the current investigation, the non-Newtonian Maxwell type, as well as a porous medium and Darcy–Forchheimer effects, were used. The flow in PTSC was produced by a nonlinear stretching surface, and the Cattaneo–Christov approach was used to assess the thermal boundary layer’s heat flux. Similarity transformation approach has been employed to convert partial differential equations into solvable ordinary differential equations allied to boundary conditions. Partial differential and the boundary conditions have been reduced into a group of non-linear ordinary differential equations. A Keller-box scheme applied to solve approximate solutions of the ordinary differential equations. Single-walled carbon nanotubes -engine oil (SWCNT-EO) and Multiwalled carbon nanotubes/engine oil (MWCNT-EO) nanofluids have been utilized as working fluid. According to the findings, the magnetic parameter led to a reduction in the Nusselt number, as well as an increment in skin friction coefficient. Moreover, total entropy variance over the domain enhanced for flow rates through Reynolds number and viscosity fluctuations were monitored by using Brinkman number. Utilizing SWCNT-EO nanofluid increased the thermal efficiency between 1.6–14.9% in comparison to MWCNT-EO.

Numerical simulation of stagnation point flow in magneto micropolar fluid over a stretchable surface under influence of activation energy and bilateral reaction

In current study, because of rising impact of non-Newtonian liquids with micromaterials, aim of this study is to scrutinize heat and mass transport phenomenon in stagnation flow of magneto-micropolar fluid incorporating combined effect of binary chemical reaction and activation energy accelerated by a stretching sheet. The formulated governing partial differential equations conveying the flow model of micropolar fluid in 2D sense is mutated to system of ordinary differential equation via similarity transformation approach while the results to the modified equations are sought using Runge-Kutta Fehlberg 45 method with shooting technique. Quantities of physical and practical significances are portrayed through graphs and tables, are examined physically in a detailed manner. The impact of slip velocity damped the stagnation flow velocity and the micropolar fluid distribution. The velocity profile of the fluid is reduced for the buoyancy ration parameter while increases for the material parameter. Temperature profile is depressing for the Prandtl number while enhances for magnetic, radiation and dissipative terms. Activation energy propelled microstructure particles gyration to increase heat transfer. The solutal distribution of micropolar liquid deteriorates for escalating magnitude of reactive parameter. Verification of attained numerical results with available literature for limiting cases and found that the results were satisfactory.

A Significant Solar Energy Note on Powell-Eyring Nanofluid with Thermal Jump Conditions: Implementing Cattaneo-Christov Heat Flux Model

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump circumstances. The flow in PTSC was generated by nonlinear surface stretching, thermal radiation, and Cattaneo-Christov heat flux, which was utilized to compute heat flux in the thermal boundary layer. Using a similarity transformation approach, partial differential equations were converted into ordinary differential equations with boundary constraints. Then, the boundary restrictions and partial differential equations were merged to form a single set of nonlinear ordinary differential equations. To obtain approximate solutions to ordinary differential equations, the Keller-Box approach is utilized. Nanofluids derived from silver- and copper-based engine oil (EO) has been employed as working fluids. The researchers observed that changing the permeability parameter reduced the Nusselt number while increasing the skin frictional coefficient. Total entropy variation was also calculated using the Brinkman number for flow rates with Reynolds number and viscosity changes. The key result is that thermal efficiency is inversely proportional to particular entropy production. For example, using Cu-EO nanofluid instead of Ag-EO nanofluid increased the heat transport rate efficiency to 15–36%.

MHD Stagnation Point Flow and Heat Transfer Over a Stretching Sheet in a Blood-Based Casson Ferrofluid With Newtonian Heating

The present study investigated the magnetohydrodynamic (MHD) flow and heat transfer on a stagnation point past a stretching sheet in a blood-based Casson ferrofluid with Newtonian heating boundary conditions. The ferrite Fe3O4 and cobalt ferrite CoFe2O4 ferroparticles suspended into Casson fluid represent by human blood to form blood-based Casson ferrofluid are numerically examined. The mathematical model for Casson ferrofluid which is in non-linear partial differential equations are first transformed to a more convenient form by similarity transformation approach then solved numerically by using the Runge-Kutta-Fehlberg (RKF45) method. The characteristics and effects of the stretching parameter, the magnetic parameter, the Casson parameter and the ferroparticle volume fraction for Fe3O4 and CoFe2O4 on the variation of surface temperature and the reduced skin friction coefficient are analyzed and discussed. It is found that the blood-based Casson ferrofluid provided up to 46% higher in temperature surface compared to blood-based fluid with the presence of magnetic effects.

On the capability of a class of quantum sensors

Quantum sensors may provide extremely high sensitivity and precision to extract key information in a quantum or classical physical system. A fundamental question is whether a quantum sensor is capable of uniquely inferring unknown parameters in a system for a given structure of the quantum sensor and admissible measurement on the sensor. In this paper, we investigate the capability of a class of quantum sensors which consist of either a single qubit or two qubits. A quantum sensor is coupled to a spin chain system to extract information of unknown parameters in the system. With given initialization and measurement schemes, we employ the similarity transformation approach and the Gröbner basis method to prove that a single-qubit quantum sensor cannot effectively estimate the unknown parameters in the spin chain system while the two-qubit quantum sensor can. The work demonstrates that it is a feasible method to enhance the capability of quantum sensors by increasing the number of qubits in the quantum sensors for some practical applications.

A Measurement for Distortion Induced Saliency Variation in Natural Images

How best to measure spatial saliency shift induced by image distortions is an open research question. Our previous study has shown that image distortions cause saliency to deviate from their original places in natural images, and the degree of such distortion-induced saliency variation (DSV) depends on image content and the properties of distortion. Being able to measure DSV benefits the development of saliency-based image quality algorithms. In this article, we first investigate the plausibility of using existing mathematical algorithms for measuring DSV and their potential limitations. We then develop a new algorithm for quantifying DSV based on a deep neural network. In the algorithm, namely, saliency similarity transformation DSV (ST-DSV), we design a coarse-grained to fine-grained saliency similarity transformation approach to achieve DSV measurement. The experimental results show that the proposed ST-DSV algorithm significantly outperforms existing methods in predicting the ground truth DSV.