Tangent Hyperbolic Nanofluid Flow Research Articles

Heat and mass flux dynamics of tangent hyperbolic nanofluid flow with unsteady rotatory stretching disk over Darcy-Forchheimer porous medium

Abstract The purpose of the research is to examine a tangent hyperbolic nanofluid flowing in three dimensions (3D) axisymmetrically on an unsteady rotatory stretching disk over a Darcy-Forchheimer porous medium. First order initial value problems (IVPs) are generated from the governing partial differential equations (PDEs) through the use of similarity transformation and linearization. The Runge-Kutta sixth order (RK6) is utilized to solve the IVP system using the shooting technique and the built-in Python program ‘fsolve model10’. Articles that have already been published are used to validate the implemented approach. Graphs are used to examine how various parameters affect velocity, temperature, and concentration. Additionally, the behavior of heat, mass flux, and skin friction in response to different parameters is investigated. The study’s findings showed that as the Forchheimer number and velocity slip parameter increased, the nanofluid’s radial and tangential velocities decreased as well. As temperature and concentration slip parameters increase, correspondingly, thicker and thinner boundary layer structures are seen. The drag force in the tangential and radial direction behaves in the same manner. Both the rates of heat and mass transfers are initiated for an increase Eckert and Prandtl numbers and demotivated for power-law index number. The dissipation effect with radiation and chemical reaction plays a major role in heat and mass fluxes, respectively. The study can be used in various computer storage, coatings, lubricants, and coolants.

Mathematical simulation of tangent hyperbolic nanofluid flow coupled with homogenous/heterogeneous chemical reaction by using Levenberg–Marquardt back propagation over a Riga plate

Mathematical simulation of tangent hyperbolic nanofluid flow coupled with homogenous/heterogeneous chemical reaction by using Levenberg–Marquardt back propagation over a Riga plate

Bioconvective magnetohydrodynamic flow of tangent hyperbolic nanofluid across a stretched surface, with Arrhenius activation and convective heat and slip conditions

The current study investigates mixed convective flow of an unsteady MHD tangent hyperbolic nanofluid due to a stretching surface with motile microorganisms via convective heat transfer and slip conditions. The flow analysis's governing equations were converted into a nondimensional relation by using the proper alteration. The pertinent similarity transformations are utilized in the main equations, and the solutions are obtained using the integrated bvp4c software. A good agreement with previously published data indicates the efficacy of the numerical technique. The following are the main findings: increasing the magnitude of the radiation and mixed convection parameters improves the velocity profile, whereas the Weissenberg number and magnetic field demonstrate the opposite influence; improvements in heat transfer occur due to the thermal radiation parameter, Brownian movement, and thermophoretic effects; activation energy improves concentration profile, whereas Lewis number shows opposite effect; bioconvection Lewis number and Peclet number declines the Motile microorganism density. Additionally, a tabular analysis of the skin friction, motile microorganism density, Nusselt number, and Sherwood number is also provided.

Natural convection and variable fluid properties of tangent hyperbolic nanofluid flow with Cattaneo-Christov theories and heat generation

The main aim behind this work is that we have to determine the enhancement that happens in thermal conductivity by using the Buongiorno model of nanofluid when the nanofluid particles are added to the tangent hyperbolic base fluid moving above the stretched surface. The viscosity of tangent hyperbolic nanofluid is assumed to be temperature-dependent. The modified form of the Fourier law of heat conduction motivated us; therefore, the Cattaneo-Christov heat and mass flux model is considered to observe its significance for heat and mass transport. The chemical reaction and heat generation are also considered to determine their influence on temperature and concentration gradients. This study is crucial because of its application in industrial manufacturing processes such as the coating of wire, the thinning of copper, the production of paper, photographic films, hot rolling, and the purification of crude oil. In electronic cooling systems, the efficient dissipation of heat in smartphones, computers, and data centers is critical to preventing overheating. Nanofluids, with their enhanced thermal properties, can significantly improve heat transfer rates, ensuring better performance, stability, and energy savings. The partial governing equations arising from fluid flow, mass, and heat transfer are transformed into ordinary differential equations via appropriate similarity variables. The obtained ordinary differential equations are solved numerically by using the Runge-Kutta Fehlberg method in the MATLAB software. The effects of the emerging parameters are represented through graphs. According to the results, the velocity profile upsurges due to the natural convection parameters and curvature parameter, while the power law index declines the velocity profile. As the Brownian motion coefficient rises, the concentration profile diminishes while the temperature profile increases. Both the concentration and temperature profiles increase for larger values of the thermophoresis parameter. The concentration profile declines for larger values of chemical reaction parameters, and enhancement happens in the temperature region.

Thermal analysis of non-Newtonian ferro nanofluid flow due to stretching surface under buoyancy effects through numerical computation

The extent of buoyancy forces on Tangent Hyperbolic nanofluid flow over a vertically held stretchable plate in the presence of a magnetic field is mathematically modeled in this work. The governing partial differential equations that model the present problem are modified into a system of ordinary differential equations by practicing a set of suitable similarity conversions. This conversion method helps to solve this complex problem through a numerical technique. The outcomes of available research are compared with the existing literature and a reasonable accord is set. Detailed analysis on assisting and opposing flow problems is considered with graphical illustrations of multiple flow parameters. In both cases of assisting and opposing flow problems, a declining impact of buoyancy forces is observed on skin friction owing to temperature deviation. Moreover, higher convection is observed for assisting flow problems as compared to opposing flow under buoyancy impacts. It is further noticed that upon increasing the relaxation time of the fluid, the fluid flow is decelerated and the less cooling effect is generated in this case.

Numerical investigation of forced convective MHD tangent hyperbolic nanofluid flow with heat source/sink across a permeable wedge

The combined effect of wedge angle and melting energy transfer on the tangent hyperbolic magnetohydrodynamics nanofluid flow across a permeable wedge is numerically evaluated. Electronic gadgets produce an excessive amount of heat while in operation, so tangent hyperbolic nanofluid (THNF) is frequently used to cool them. THNF has the potential to dissipate heat more efficiently, thereby lowering the possibility of excessive heat and malfunctioning components. The effects of thermal radiation and heat source/sink are also examined on the flow of THNF. The flow has been formulated in the form of PDEs, which are numerically computed through the MATLAB solver BVP4c. The numerical results of BVP4c are relatively compared to the published work for validity purposes. It has been detected that the results are accurate and reliable. Furthermore, from the graphical results, it has been perceived that the rising impact of the Weissenberg number accelerates the velocity and thermal profile. The effect of the power-law index parameter drops the fluid temperature, but enhances the velocity curve. The variation in the wedge angle boosts the shearing stress and energy propagation rate, whereas the increment of Wi declines both the energy transfer rate and skin friction.

Tangent hyperbolic nanofluid flow through a vertical cone: Unraveling thermal conductivity and Darcy–Forchheimer effects

Purpose: This paper demonstrates the way tangent hyperbolic nanofluid flow through a vertical cone is influenced by varying viscosity and varying thermal conductivity. This study also seeks to illustrate the impact of convective boundary conditions on a fluid. The mathematical modeling also takes the Darcy–Forchheimer effect into account. Methodology: Using the appropriate similarity transformation, the fluid problem is reduced into a set of nonlinear ordinary differential equations. These systems of differential equations are evaluated numerically by applying the Optimal Homotopy Asymptotic Method. Findings: The nature of emergent parameters is examined in relation to the temperature distribution, nanoparticle concentration profile, and velocity profile. An increase in variable viscosity corresponds to a decrease in fluid velocity, while enhanced thermal conductivity results in elevated fluid temperature. The skin friction coefficient, Sherwood, and Nusselt numbers are numerically examined for active concerned parameters. These findings can be put into practice in a variety of fields such as polymer cooling systems and medication. Originality: Existing literature has yet to explore the combination of tangent hyperbolic nanofluids with varying viscosity and thermal conductivity under convective boundary conditions.

Numerical analysis of the heat transfer application on a convective tangent hyperbolic nanofluid flow over a porous stretching cylinder with stratification effects

The nanofluids has attractive applications in the industrials and engineering field because nanofluids offer the improvement in the thermal efficiencies of flow, which is very fruitful in the energy sector. This study emphases on the numerical exploration of heat and mass transfer efficiencies on a mixed convective flow of tangent hyperbolic nanofluid under the consideration of gyrotactic microorganisms. To analyze the magnetized boundary layer flow, the stratification boundary conditions are considered on the surface of the stretching cylinder. The thermal analysis involves the important features such as activation energy, nonuniform heat source/sink, and nonlinear thermal radiation. The flow model is altered into system of nonlinear ordinary differential equations by utilization of suitable similarity variables and Bvp4c solver on the MATLAB to find numerical solutions. The graphical and tabulated investigation is presented for various developing parameters thoroughly. The results indicate that by the increment of mixed convection parameters the fluid velocity accelerate consequently, whereas raising values of the Weissenberg number reduce the fluid velocity. TThe greater values of the Prandtl number lead to a decrease in fluid temperature, while the concentration of nanoparticles rises with the increase in activation energy parameters. Additionally, the heat transfer rate reduces due to stronger values of thermophoresis parameter, although reverse tendency is observed for the greater values of Brownian motion parameter.

Thermophoretic particle deposition in a nanofluid flow across a disc with non-fourier heat flux: An investigation using tangent hyperbolic model

Non-Newtonian nanofluids are attracting the attention of researchers and academics due to the high heat transmission rates that they possess. To improve thermal devices and exchangers, the researchers come up with innovative and expense-effective methods. One of the advanced technological approaches that can be utilized to enhance the thermal performance of devices is the utilization of nanofluids. This non- Newtonian nanofluid possesses the advanced properties of increasing heat transfer and destroying harmful bacteria. For this purpose, the present theoretical work is to explore the heat and thermophoretic particle deposition analysis on the tangent hyperbolic nanofluid flow over the rotating porous disk with presence of non-Fourier heat flux model and nanoparticle aggregation effect. Darcy-Forchheimer fluid model is adopted to develop the fluid flow system. Furthermore, the nanofluid’s viscosity and thermal conductivity are expressed through advanced modeling, employing the modified Krieger-Dougherty model for viscosity and the Maxwell-Bruggeman model for thermal conductivity. The nanoparticles and base fluid involved in this context are Molybdenum disulfide ( Mo S 2 ) and Water/carboxyl-methyl cellulose (CMC) respectively. The mathematical representation of the fluid flow and energy propagation involves a system of coupled partial differential equations (PDEs). The system of partial differential equations (PDEs) is transformed into non-dimensional ordinary differential equations (ODEs), which are then solved both analytically and numerically using the Homotopy Analysis Method(HAM) and Runge-Kutta-Fehlberg (RKF) method along with shooting technique. Exploring the graphical representation reveals a comprehensive analysis of key factors influencing velocity, temperature, and concentration. Through innovative visualization, these parameters take center stage, providing insights into their intricate interplay and dynamic relationships. The heat transfer rate is enhanced 0.24% and 1.4% by rising the values of thermal relaxation parameter and Weissenberg number. Also, the mass transfer rate is accelerated 0.8% and 0.14% due to enhancing the values of thermophoretic coefficient and thermophoresis parameter.

Numerical analysis of MHD tangent hyperbolic nanofluid flow over a stretching surface subject to heat source/sink

Numerical analysis of MHD tangent hyperbolic nanofluid flow over a stretching surface subject to heat source/sink

Numerical analysis of thermophoretic particle deposition in a magneto-Marangoni convective dusty tangent hyperbolic nanofluid flow – Thermal and magnetic features

Abstract In the current study, we focus on the Magneto-Marangoni convective flow of dusty tangent hyperbolic nanofluid (TiO2 – kerosene oil) over a sheet in the presence of thermophoresis particles deposition and gyrotactic microorganisms. Along with activation energy, heat source, variable viscosity, and thermal conductivity, the Dufour-Soret effects are taken into consideration. Variable surface tension gradients are used to identify Marangoni convection. Melting of drying wafers, coating flow technology, wielding, crystals, soap film stabilization, and microfluidics all depend on Marangoni driven flow. This study’s major objective is to ascertain the thermal mobility of nanoparticles in a fluid with a kerosene oil base. To improve mass transfer phenomena, we inserted microorganisms into the base fluid. By using similarity transformations, the resulting system of nonlinear partial differential equations is converted into nonlinear ordinary differential equations. Using a shooting technique based on RKF-45th order, the numerical answers are obtained. For various values of the physical parameters, the local density of motile microorganisms, Nusselt number, skin friction, and Sherwood number are calculated. The findings demonstrated that as the Marangoni convection parameter is raised, the velocity profiles of the dust and fluid phases increase, but the microorganisms, concentration, and temperature profiles degrade in both phases.

Heat transfer exploration for bioconvected tangent hyperbolic nanofluid flow with activation energy and joule heating induced by Riga plate

Tangent hyperbolic nanofluid enhances heat transfer in various applications, such as cooling systems and electronics, due to its improved thermal conductivity and stability. Therefore current analysis explore the inspiration of joule heating and activation energy on Tangent hyperbolic nanofluid in the existence of motile microorganism. For motivation the impact of Riga plate, variable thermal conductivity, thermal radiation and heat source are the part of this investigation. The appropriate similarity variable are assumed to transformed the set of governing partial differential equations considering the influential effects of Joule heating and activation energy into ordinary differential equations. MATLAB via bvp5c tool is engaged to solve resulting system. The effects of dimensionless parameters like Weissenberg number We, Power-law index Power-law index n, Hartmann number M, thermal radiation Rd, Brownian motion Nb, Prandtl number Pr, Peclet number Pe and thermophoresis Nt on velocity f′(η) temperature θ(η), volumetric concentration of nano particles φ(η) and density profile χ(η) are displayed in graphical and tabulated form. It is noted that improving the Weissenberg number We, Hartmann number M and Power-law index n, the speed of flow decreased. By increasing value of Prandtl number Pr the temperature curve reduced, inverse relation is observed for growing value of Rd.

Convective boundary layer flow of MHD tangent hyperbolic nanofluid over stratified sheet with chemical reaction

<abstract> <p>We investigated the combined impact of convective boundary conditions, thermal conductivity, and magnetohydrodynamic on the flow of a tangent hyperbolic nanofluid across the stratified surface. Furthermore, the ramifications of Brownian motion, thermophoresis, and activation energy were considered. Heat generation, chemical reactions, mixed convection, thermal conductivity, and other elements were considered when analyzing heat transfer phenomena. The governing equations were converted via similarity transformations into non-dimensional ordinary differential equations in order to analyze the system. Using the shooting method, the problem's solution was determined. We showed the mathematical significance of the temperature, concentration profiles, and velocity of each fluid parameter. These profiles were thoroughly described and shown graphically. The findings demonstrated that as the Weissenberg number and magnetic number increased, the fluid velocity profile decreased. Higher heat generation and thermophoresis parameters resulted in an increase in the temperature profile. Higher Brownian motion and Schmidt parameter values resulted in a drop in the concentration profile. Tables were used to discuss the numerical values of skin friction ($ {C}_{fx} $), Nusselt number ($ {Nu}_{x} $), and Sherwood number ($ S{h}_{x} $). For the greater values of Weissenberg number and mixed convection parameters, skin friction numerical values fell while Nusselt numbers rose.</p> </abstract>

AN APPLICATION OF ARTIFICIAL NEURAL NETWORK TOWARD THE MATHEMATICAL MODELING OF MHD TANGENT HYPERBOLIC NANOFLUID ACROSS A VERTICAL STRETCHING SURFACE

The Levenberg-Marquardt (LM) back propagation (BP) artificial neural networks (ANNs) (LM-BP-ANNs) procedure is used in this analysis to show the computational strategy of neural networks for the simulation of magnetohydrodynamics tangent hyperbolic nanofluid flow comprised of motile microorganism across a vertical slender stretching surface. The fluid flow were examined under the significance of chemical reaction, magnetic field, activation energy, and heat source. The modeled equations were simplified to the ordinary system of differential equations using similarity variables substitution. The Lobatto IIIA formula based on the finite difference method was employed for the nano-liquid flow problem with an accuracy up to five decimal points. The robustness of Lobatto IIIA is its straightforward execution of very nonlinear coupled differential equations. Several operations involving testing, authentication, and training were carried out by developing a scheme for different fluid problem elements using reference datasets. The accuracy of LM-BP-ANNs was tested through mean-square error, error histogram, curve fitting figures, and regression plot. Moreover, the examination of flow model factors for concentration, mass, and momentum outlines are expressed through graphs. It was perceived that the velocity field declines with the flourishing influence of the magnetic field and lessens with the upshot of Weissenberg number and power law index.

Impact of chemical processes on magnetized tangent hyperbolic nanofluid with bio-convection aspects

The study of nanofluids has remarkable uses for researchers because of their fascinating implications in medication delivery, biotechnology, aerodynamic procedures, food privilege, nanotechnology, cool atomic reactors, chemotherapy, next generation film collectors and many more. Currently, the bioconvection technology is measured as a necessary procedure with suppressed compensation in bio-fuel, bio-technology, medical sciences, enzymes, bio-reactors, petroleum chamber machinery, nano-drug delivery, etc. The foremost plan of this exploration is to evaluate the influence of magnetohydrodynamics 3-dimensional flow of tangent hyperbolic nanofluid with gyrotactic motile microorganism through a linear stretching surface. Furthermore, the impressions of mixed convection, Joule heating along with viscous dissipation are as well a part of our research. The analytical expression of tangent hyperbolic liquid flow provides the governing non-linear partial differential equations; a proper transformation is used to transmit this system of equations in ordinary differential equations. To find out the numerical solution, the dimensionless equations are determined by means of BVP4C technique in MATLAB. The influences of miscellaneous substantial parameters on temperature, concentration along with motile microorganisms are accomplished by means of graphs. It can be observed that the heat transfer profile of tangent hyperbolic nanoliquid escalates by increasing the approximations of Eckert number, heat sink/source and power law index factor. A conflicting behavior is observed for Brownian motion parameter, stretching rate parameter along with Schmidt number in concentration profile. Furthermore, Peclet number and bioconvection Lewis number have decreasing impacts for microorganism profile. These nano fluid models with gyrotactic microorganisms are implemented in biodiesel fabrication, heat control systems, food factories, biomechanics, biomedical engineering, thermal exchangers, waste water treatment plant aero dynamical systems, and fundamental sustainable energy resources.

Numerical simulation for thermal radiative flow of tangent hyperbolic nanofluid due to Riga plate in the presence of joule heating

In this paper, numerical simulation for the two-dimensional flow of tangent hyperbolic fluid in the manifestation of nanoparticles, heat source and joule heating is considered. For motivation of problem, the role of Riga plate is investigated. Chemical reaction and Brownian motion are the parts of the analysis. The set of PDEs of Tangent hyperbolic nanofluids with swimming germs is converted in to couple of ODEs by employing well-known approach namely shooting scheme. The resulting highly nonlinear and coupled ODEs are solved by using ND solve tool of Wolfram Mathematica 11. Numerical outcome of involving parameters of interest like Lewis number Le, Prandtl number Pr, Chemical diffusion k, Peclet number Pe, Weissenberg number We, Bioconvection Lewis number Lb, nonlinear radiation, Biot number Bi, modified Hartmann number Q and magnetic parameter M on tangent hyperbolic nanofluids velocity f″, temperature θ, concentration φ and density of germs distribution are discussed in the form of graphical trend and tables. We professed that the speed of fluid degenerated for the increasing value of power-law index n and magnetic parameter M. The Nusselt number growths for growing values of the thermophoresis parameter Nt, Biot number Bi and radiation parameter Nr.

Variable thermal conductivity and chemical reaction aspects in MHD tangent hyperbolic nanofluid flow over an exponentially stretching surface

This work objective focuses on studying the combined influences of variable thermal conductivity, chemical reaction, and magnetohydrodynamics (MHD) on the flow of a tangent hyperbolic nanofluid flow over an exponentially stretching surface, considering a first-order velocity slip condition. Additionally, thermophoresis and Brownian motion impacts are taken into account. The phenomena of heat transfer are analyzed considering several factors such as thermal radiation, Joule heating and nonlinear heat source. On the other hand, mass transfer is explored under the effect of chemical reaction. Tangent hyperbolic fluid is an important branch of non-Newtonian fluids known for its ability to describe shear thinning effects. Understanding fluid flow on exponentially stretched surfaces is of great significance due to its applications in various industrial processes. These applications include fluid film condensing methods, plastic production for making plastic covers, fiber manufacturing (where it is used to spin fibers), glass blowing, metallurgical procedures, and the paper industry. The concept of magnetohydrodynamics (MHD) is significant due to its various engineering applications, such as MHD generators, flow meters, heat reservoirs, small components in different devices, and cooling systems for nuclear reactors. To analyze the system, using similarity transformations, the governing equations of continuity, velocity, and concentration are transformed into non-dimensional differential equations. The numerical solution is obtained using the shooting technique. The study presents the physical significance of all the fluid parameters involved, focusing on the velocity, temperature, and concentration profiles. These profiles are presented graphically and discussed in detail. The results show that the fluid velocity profile increases with enhancing values of the [Formula: see text] and the magnetic number M. The thermal profile increases with higher [Formula: see text] and [Formula: see text] The concentration profile decreases with higher values of [Formula: see text] and [Formula: see text].

Numerical investigation of MHD tangent hyperbolic nanofluid flow across a vertical stretching surface subject to activation energy

Numerical investigation of MHD tangent hyperbolic nanofluid flow across a vertical stretching surface subject to activation energy

Investigation of Thermal Radiative Tangent Hyperbolic Nanofluid Flow Due to Stretched Sheet

The current study illuminates the enactment of a tangent hyperbolic nanofluid past a bidirectional stretchable surface. The phenomena of heat and mass transfer with joule heating, chemical reaction, and thermal radiation have been debated. For the motivation of the problem, convective boundary conditions are part of this study. The modeled partial differential equations are mended into ordinary differential equations with the help of appropriate self-similarity transformations. Furthermore, the resulting system of ODEs is numerically handled by using well-established shooting scheme and acquired numerical outcomes are compared with ND Solve command of Mathematica. The Effects of prominent parameters on velocity, temperature and volumetric concentration distribution are inspected through graphs. The influence of emerging parameters involved in this study on flow and heat removal features are deliberated in detail. As we are increasing the values of power-law index n, Prandtl number Pr and Magnetic parameter M, outcomes increment in skin friction coefficient while decline in the Nusselt number is seen.

Significance of gyrotactic microorganisms on the MHD tangent hyperbolic nanofluid flow across an elastic slender surface: Numerical analysis

Abstract In the current study, we numerically analyze the significance of motile microbes on the magnetohydrodynamic steady convective streams of tangent hyperbolic (TH) nanofluid flow across an elastic nonlinearly stretching surface of an irregular thickness. The consequences of an external magnetic field, thermal radiation, and thermal conductivity are also examined on the TH nanofluid. The governing system of equations (nonlinear set of partial differential equations) is transfigured into a system of ordinary differential equations (ODEs) by using the similarity variable conversions. Furthermore, the reduced form of nonlinear ODEs is numerically computed through the parametric continuation method (PCM) using MATLAB software. The relative evaluation is carried out to authenticate the numerical outcomes. It has been observed that the energy field accelerates with the Rayleigh number, Weissenberg number, and Brownian motion. The mass propagation ratio improves with the effect of activation energy and decreases with the influence of chemical reactions. Furthermore, the motile microbes’ profile declined with the outcome of the Peclet and Lewis numbers. The skin friction increases up to 7.3% with various magnetic values ranging from 0.5 to 1.5. However, the energy transfer rate declines to 5.92%. The thermal radiation boosts the energy propagation rate and flow velocity by up to 11.23 and 8.17%, respectively.