Tangent Hyperbolic Nanofluid Flow Research Articles

The unified impact of thermal radiation and heat source on unsteady flow of tangent hyperbolic nanofluid through a permeable shrinking sheet

The tangent hyperbolic nanofluid behaviour is observed in multiple practical applications and extensively used in different laboratory experiments. It motivates to focus on the two-dimensional boundary layer flow of tangent hyperbolic nanofluid past a shrinking sheet. The goal of this article is to scrutinize the mass and heat transport of an unsteady flow of non-Newtonian tangent hyperbolic nanofluid past a shrinking surface under the influences of a source of heat, thermal radiation and chemical reaction. The flow model is mathematically framed through a coupled nonlinear partial differential equations. To transform the non-linear PDEs to ODEs, we use the similarity transformations and reduced ODEs are solved by RK-IV (Runge-Kutta method of order four) with shooting technique using the computational software MATHEMATICA. The novelty which emerges from the flow pattern lies in the fact that there exist dual solutions for certain parametric domain and the range of the existing solution may be expanded by increasing the power-law index (n) and shortened by increasing the Weissenberg number (We). Another remarkable conclusion which can be drawn from the temporal stability analysis that among these two solutions, first solution is stable and realistic whereas the second solution is not physically realistic. A diversity of the parameter estimates were used to provide solution for velocity f′(η), temperature θ(η) and concentration profiles ϕ(η) of this fluid model. In addition to the above findings, there are graphs and tables with explanation for the skin friction coefficient, the Nusselt number and the Sherwood number. These characteristics of a tangent hyperbolic nanofluid are not reported yet and may be useful in the development of existing technology.

Magnetohydrodynamics tangent hyperbolic nanofluid flow over an exponentially stretching sheet: Numerical investigation

This article gives a numerical study of tangent hyperbolic nanofluid flow across an exponentially stretched sheet by considering two heat transfer situations: prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). Tangent hyperbolic nanofluid is being used extensively in the cooling of electronic components, which generate a lot of heat during operation. The improved thermal conductivity of tangent hyperbolic nanofluids can help to dissipate the heat more effectively, reducing the risk of overheating and component failure. A mathematical model of the problem is based on conservation laws of momentum, mass, and energy. The governing system of nonlinear PDEs is transformed into a system of nonlinear ODEs using appropriate similarity transformations. MATLAB's bvp4c tool was utilised to address the converted system of modelled equations. The drag coefficient, heat transfer, and mass transfer rate values are tabulated. It is observed that both the magnetic parameter (M) and Weissenberg number (We) causes to reduce the boundary layer. It is also noticed that increasing the Brownian motion parameter (Nb) and the thermophoresis parameter (Nt) leads the temperature θ(η) and concentration profile g(η) to increase for both cases of heat transfer i.e., PEST and PEHF.

Double diffusion effect on the bio-convective magnetized flow of tangent hyperbolic liquid by a stretched nano-material with Arrhenius Catalysts

The idea of activation energy appearing in a chemical reaction has been widely applied to the production of biodiesel, hydrogen, oil storage, geothermal manufacturing, base liquid mechanics, oil emulsified, food manufacturing, a significant renewable energy source, as well as sewage systems. This study aims to investigate the resultant repercussions of double diffusion, activation energy, Brownian motion, thermal radiation, thermophoresis, viscous dissipation, magnetic field, and Joule heating on bioconvection of a tangent hyperbolic nanofluid flow over a vertical stretching porous surface containing microbe (gyrotactic microorganisms). The fluid transport equations are converted into ordinary differential equations using appropriate self-similarity variables after being solved using the finite difference method. The impacts of key parameters on the fluid's transport properties are depicted in graphs and tables. When the dimensionless activation energy is higher, the mass transfer rate at the stretched nanomaterial sheet drops. The nanofluid concentration near the sheet minimizes by increasing the porosity parameter value, but the opposite behavior happens far from the sheet.

Second law analysis in Darcy‐Forchheimer flow of tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms

AbstractThis article investigates the creation of entropy and the thermal transport of fluids during hyperbolic tangent flow with Darcy‐Forchheimer flow over a stretching surface. Because of the role of shear‐thinning that the hyperbolic tangent fluid displays, the mechanics of the fluid are described with the assistance of a connected system of differential models that are constructed from a partial differential equation. The bvp4c routine, a three‐stage Lobatto‐IIIA method numerical analysis is utilized in the study. The effects of varying values of dimensionless parameters including Forchheimer number, inertia parameter, thermal radiation, Brownian motion, Prandtl number, Scimdth number, chemical reaction, Peclet number an Bioconvection Lewis number are simulated numerically. In addition, to this, the numerical values of the skin friction coefficient, the local Nusselt and Sherwood number and motile density are shown in the form of graphs and tables respectively. It has been discovered that increasing the value of the Fr and γ results in an upsurging velocity profile while a reverse trend is noted for the unsteady parameter. In addition to this, higher values of the radiation parameter Rd cause the operating fluid to be subjected to a greater quantity of heat, which results in an associated increase in the temperature profile.

DARCY-FORCHHEIMER TANGENT HYPERBOLIC NANOFLUID FLOW THROUGH A VERTICAL CONE WITH NON-UNIFORM HEAT GENERATION

The convective flows through different geometries have numerous applications in high-speed aerodynamics, nuclear cooling systems, fiber technology, and polymer engineering. In the present paper, we investigate the non-linear, mixed convective, boundary-driven, tangent hyperbolic nanofluid flow through a cone. The flow takes place under nonuniform heat sink/source. Darcy-Forchheimer effects have also been taken into account in mathematical modeling and analysis. The Buongiorno model is implemented to examine the effects of thermophoresis and Brownian motion parameters. The governing equations are constructed through the laws of conservation. The modeled flow problem is converted into a set of ordinary differential equations with the help of proposed similarity transformations. To interpret the modified system of equations, the homotopy analysis method (HAM) is applied. The roles of versatile parameters of interest are analyzed and sketched for better understanding. The velocity profile increases by increasing the Darcy number, and converse behavior is found by giving rise to the Forchheimer inertial drag parameter. The rise in temperature profile occurs by increasing a non-uniform heat source variable. The concentration profile enhances when the value of the thermophoresis parameter increases, and shows inverse behavior for the Brownian motion parameter. In the Buongiorno model, nanoparticle concentration has an inverse relation with the Brownian motion parameter. So, the concentration profile declines for greater Brownian motion parameter. To understand the behavior of flow through a cone, the values of Nusselt number and Sherwood numbers are examined.

Melting heat transfer and thermal radiation effects on MHD tangent hyperbolic nanofluid flow with chemical reaction and activation energy

In this research, we take into account tangent hyperbolic nanofluid flow along a moving stretched surface with thermal radiation, exothermic/endothermic chemical reaction and activation energy effects under melting condition. Governing PDE are transformed to dimensionless non-linear ODE with the add of appropriate similarity variables. The resulting non-linear ODE are solved numerically. The flow parameters influences on the fluid?s velocity, temperature, and concentration distributions are investigated. The results revealed that temperature profile is declining while concentration and velocity profiles are increasing for enhancing melting parameter.

Attributes of Hall current and radiation absorption in unsteady tangent hyperbolic nanofluid flow over a stretching surface with activation energy: A numerical study

This work describes the effects of Hall current and radiation absorption on magnetohydrodynamic tangent hyperbolic nanofluid flow over a stretching sheet considering binary chemical reaction with activation energy and heat source. Convective heat is applied to the sheet from the bottom, whereas a zero mass flux condition is imposed on the surface. Furthermore, the radiative heat transfer is considered in view of Rosseland’s approximation. A nonlinear set of ordinary differential equations, in non-dimensional form, is obtained by employing appropriate transformations to the governing equations. The built-in bvp4c function in MATLAB is used to find the numerical solution of the system of ordinary differential equations. A data comparison for a limiting case with previously reported results is presented to validate the numerical findings. Further, the flow, as well as heat and mass transfer characteristics, are shown graphically as a result of the impacts of various flow factors. It is noticed that the fluid flow is accelerated with the rise of the Hall current parameter. The thermophoresis parameter and activation energy have an ascending influence on the concentration profile. Moreover, Biot number and radiation absorption parameter can uplift heat transfer rate. This study has applications in nuclear power reactors, gas turbines, oil reservoirs, reactor safety, and heat insulation.

Bioconvective Homann flow of tangent hyperbolic nanofluid due to spiraling disk with convective and zero mas flux constraints

The phenomenon of bioconvection in nanomaterials presents novel applications in the biotechnology, biofuels, enzymes, biomedical engineering and energy systems. Current exploration explores the applications of bioconvection in Homann flow of nanofluid due to spiraling of disk theoretically. The generalized model namely tangent hyperbolic fluid is used to predicts the rheological and thermal impact. The stability of nanofluid is ensured with interaction of motile microorganisms. The Boungrino nanofluid model with thermophoresis and Brownian motion features is used to perform the analysis The thermal distribution of nanofluids is proceeded by utilizing the zero mass thermal constraints. The similarity variables are introduced in order to estimating the dimensionless formulation. The Keller Box method with higher efficiency is imposed with implicit finite difference numerical algorithm. The main observations reveal that with enhancing the radial velocity and azimuthal velocity decreases with increasing sparling angle. For highly viscous case, a decrement in the azimuthal velocity has been observed.

The numerical simulation of nanoparticle size and thermal radiation with the magnetic field effect based on tangent hyperbolic nanofluid flow

Tiny particles have extraordinary thermal conductivity due to their unusual characteristics, making them crucial in materials science, nanotechnology, heat exchangers, and electronics. When there is the inclusion of thermal radiation, a heat source, and a convective boundary, magnetohydrodynamic (MHD) micropolar, tangent hyperbolic flow for water-based Al2O3 nanofluid over a stretching sheet, this work intends to investigate the significance of a nanoparticle's radius. The mathematically described ordinary differential system is created by transforming a set of partial differential equations via similarity transformations. The bvp4c approach is used to solve the problem numerically (MATLAB built-in function). In this comprehensive study, the main objective is to improve heat transformation under the impact of various parameters. The velocity profiles, temperature distribution, micro-rotation distribution, and the local skin friction factor, along with the rate of heat transfer, have been displayed with several physical parameters. It is observed that the variation in velocity and the temperature profiles is the cause of increasing the size of the nanoparticles and the involving parameters that caused an increase in the rate of heat transfer. Graphs and tables have then been used to demonstrate the consequences of these physical parameters. The enhancement in the radius of nanoparticles causes a decrease in the skin friction factor, thermal layer, and micro-rotation. As the Biot number increased, the thermal layer became thicker. The impact of influential parameters on physical quantities is illustrated using three-dimensional graphs.

Tangent-hyperbolic nanoliquid flow in a microchannel, thermal and irreversibility rate analysis

ABSTRACT The objective of the current investigation is to examine the influence of buoyancy force, heat source, Brownian motion, thermophoresis, chemical reaction, transverse magnetic field and convective boundary condition on flow of tangent-hyperbolic nanofluid through an upright microchannel. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations. The RKF45 method along with the shooting technique is used to solve the fluidic system numerically. The Buongiorno model is considered to observe the influence of thermophoresis, Brownian motion and chemical reaction with mixed convection. Graphical and numerical illustrations are presented to visualize the behavior of different parameters of interest on velocity, temperature, concentration and entropy generation of the flow system. The substantial findings of this study have been recorded as the amplification in the thermal and solutal Grashof number causes an increment in the flow rate in a channel, the thermal energy builds up with Brinkman number and heat source parameter, another significant outcome of the present analysis is that there is a downfall in the concentration field with the strengthening of thermophoresis parameter.

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.

Effect of Maxwell Velocity and Smoluchowski Temperature Jump Slip Conditions on Tangent Hyperbolic Nanofluid

In this numerical investigation, three-dimensional tangent hyperbolic nanofluid flow past a stretching surface has been analyzed under the Smoluchowski thermal and Maxwell velocity slip conditions at the boundary. For the modification of the flow fields, the magnetic effect has also been incorporated. Nonlinear thermal radiation and Joule heating have also been included to improve heat transmission. The modelled PDEs have been turned into nonlinear ODEs after the application of the appropriate transformation. MATLAB bvp4c algorithm is utilized to achieve the solution of the problem. The code’s legitimacy is accomplished by repeating previously published results in the literature. Efforts are made to discuss the effects of the important parameters on velocities, energy profile, and concentration distribution in detail via graphs and tables. Based on our simulations, an enhancement in the slip parameter leads both velocities to decline. The ratio parameter causes a decline in velocity in the horizontal direction whereas it increases in the vertical direction. The heat transfer rate is boosted as the temperature ratio parameter is increased.

Impact of velocity slip and heat source on tangent hyperbolic nanofluid flow over an electromagnetic surface with Soret effect and variable suction/injection

The applicability and significance of tangent hyperbolic fluid in several engineering fields are encouraging, and the examination of the Soret effect phenomena on non-Newtonian fluids with thermal transport mechanisms is becoming more widely accepted. The effect of velocity slip on electromagnetohydrodynamic (EMHD) of tangent hyperbolic flow through a Riga plate with a heat source, suction/injection, and reactive energy, on the other hand, is unknown. The current research configuration model investigates the impact of Soret, suction/injection, activation energy, and heat source on the EMHD flow of hyperbolic tangent nanofluid via a stretched sheet. The governing equations of PDEs are transmuted into nonlinear ODEs with adequate similarity variables. The numerical output of the resulting Ordinary differential equations is performed using the MATLAB bvp4c built-in. The implication of rising attributes on temperature, velocity, concentration shapes, drag force coefficient, Sherwood number, and Nusselt number is graphically and numerically depicted. As a result, the derived findings are validated by comparing them to previous output. Remarkably, the increase in temperature of the hyperbolic tangential nanofluid flow is caused by a rise in slip velocity and Weissenberg numbers, which has a reverse effect on Suction. The EMHD parameter, on the other hand, enhances the velocity distribution, which impacts the slip velocity parameter.

Tangent hyperbolic nanofluid: Significance of Lorentz and buoyancy forces on dynamics of bioconvection flow of rotating sphere via finite element simulation

Enhanced thermal transportation for bio convection and mixed convection of Tangent hyperbolic nano fluid flow in stagnation region of rotating sphere is scrutinized in the existence of magnetic field. The nano-sized tiny particles are incorporated due to their unusual qualities like enhanced the thermal transport in the base fluid, which play significance role in modern nanotechnology. Further, improve the stability of nano-sized particles for long time period and avoid possible sedimentation, also incorporated auto-motile and gyrotactic microorganisms. The bioconvection of nano fluid transportation across spherical surface is considered important for heat storage and thermal balancing in technological processes. In this communication, time dependent partial differential formulation is transmuted to a set of dimensionless partial differential equation via similarity transformation. A numerical solution is sought through Galerkin based finite element discretization while it is coded and run on Matlab platform. The role of variables for the dependent quantities is monitored through computational procedure. The parameters of rotating sphere and Casson fluid speeded up the fluid flow in x-direction, but it recedes the flow in y-direction. The larger inputs of Brownian motion and thermophoresis parameters raised the nano fluid temperature.

Triple diffusion with heat transfer under different effects on magnetized hyperbolic tangent nanofluid flow

The core objective of the presented analysis is to explore the mixed convection and magnetohydrodynamics effects on tangent hyperbolic nanofluid flow generated by elongating surface. Mechanisms of thermal radiation and chemical reaction are incorporated in energy and concentration equations respectively. Moreover, the Soret-Dufour phenomenon is also taken into consideration. Mathematical formulation is floated under the assumption of boundary layer theory. Formulated partial differential (PD) system reduces into nonlinear ordinary differential (OD) system with the help of suitable transformations which has been solved with a technique named finite element method (FEM) and outcomes are justified through grid-free and convergence phenomenon. The characteristics of numerous effective parameters are displayed graphically and discussed. Furthermore, the physical quantities like local Nusselt number, Sherwood number and skin friction coefficient are tabulated numerically and analyzed. Solute concentration profile [Formula: see text] shown reverse trend for distinct values of [Formula: see text] and [Formula: see text] [Formula: see text] diminishes whereas [Formula: see text] boosted the [Formula: see text].

Bioconvection Mangnetohydrodynamic Tangent Hyperbolic Nanofluid Flow with Quartic Chemical Reaction Past a Paraboloid Surface

In this numerical study, the effect of quartic autocatalysis type of chemical reaction, buoyancy force and thermal radiation phenomenon and magnetic effect on tangent hyperbolic nanofluid past an upper horizontal surface of a paraboloid has been studied. By considering the Buongiorno model approach, a diffusion of unequal coefficients in the presence of gyrotactic microorganism is discussed. Implementation of microorganism's idea is used to stabilize the nanoparticles through bioconvection. The modeled PDEs of the problems are converted into nonlinear ODEs with the assistant of the similarity transformations. To tackle nonlinear ODEs, MATLAB package bvp4c is used. In addition, a hallmark of the Matlab code with the reported results in the literature is achieved by benchmarking. The variations in motion, concentration, temperature, and motile density due to sundry parameters have been analyzed in-depth via graphs. Our analysis shows that the density profile of motile of microorganism is hiked with an increment in the bioconvection Rayleigh number but decreases for higher thermal Grashof number.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

A Numerical Approach for an Unsteady Tangent Hyperbolic Nanofluid Flow past a Wedge in the Presence of Suction/Injection

The analysis of unsteady tangent hyperbolic nanofluid flow past a wedge with injection-suction, because of its beneficial uses, has gained a lot of attention. The present study is mainly concerned with tangent hyperbolic nanofluid (non-Newtonian nanofluid). First, we have converted the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) with the help of appropriate similarity transformations. Boundary conditions are also transformed by utilizing suitable similarity transformation. Now, for the obtained ODEs, we have used the numerical technique bvp 4 c and investigated the velocity, temperature, and concentration profiles. The accuracy of the flow model is validated by applying MAPLE d-solve command having good agreement while comparing the numerical results obtained by bvp4c for both suction and injection cases. The effects of distinct dimensionless parameters on the various profiles are being analyzed. The novel features such as thermophoresis and Brownian motion are also discussed to investigate the characteristics of heat and mass transfer. Graphical representation of the impact of varying parameters and the solution method for the abovementioned model is thoroughly discussed. It was observed that suction or injection can play a key role in controlling boundary layer flow and brings stability in the flow. It was also noticed that by increasing the Darcy number, velocity profile increases in both injection-suction cases.

Stratified heat transfer of magneto-tangent hyperbolic bio-nanofluid flow with gyrotactic microorganisms: Keller-Box solution technique

Abstract The purpose of the present investigation is to examine the heat, mass and microorganism concentration transfer rates in the magnetohydrodynamics (MHD) stratified boundary layer flow of tangent hyperbolic nanofluid past a linearly, uniform stretching surface comprising gyrotactic microorganisms as well as nanoparticles. The governing PDEs with relevant end point conditions are molded into a non-dimensional ordinary differential equation (ODE) form by means of the similarity transformation. The numerical solution of dimensionless problem is acquired within the frame of robust Keller-Box technique. The velocity, temperature, mass and motile microorganism density are investigated graphically within the context of different significant parameters. Numerical results have been inspected via plots and table (namely as the local Nusselt number, the local wall mass flux and the local microorganisms wall flux). This article proves that the energy, concentration and motile microorganism density reduce with increase in thermal, solutal and motile density stratification parameters. The asserted outcomes are beneficial to enhance the cooling and heating processes, energy generation, thermal machines, solar energy systems, industrial processes etc.

Significance of chemical reaction with activation energy for Riga wedge flow of tangent hyperbolic nanofluid in existence of heat source

This manuscript uncovers the heat and mass transfer of an unsteady tangent hyperbolic nanofluid flow across an extensible Riga wedge under the effects of stagnation point, heat source, and activation energy. The flow computations with modified Hartmann numbers are embedded in this investigation particularly in the unsteady tangent hyperbolic liquid stream scenario. The focus pertains to augment heat conduction in the bulk liquid as heat and mass transport media. The implications of controlling parameters on non-dimensional speed, temperature, as well as concentration profiles are visually portrayed. The governing partial differential equations are modified into non-dimensional forms by reducing the number of independent factors, which are then pursued numerically utilizing the Runge-Kutta method with the shooting tool. The velocity of Newtonian fluid improves as the magnitude of wedge angle parameter βw rises, although it is marginally lower than that of tangent hyperbolic fluid, the temperature of Newtonian fluid intensifies substantially faster than that of tangent hyperbolic fluid for higher values of βw. The skin friction factor increases with alterations to the Hartmann parameter, Weissenberg factor, wedge angle parameter as well as suction parameter. The percentage increase in skin friction factor is 13.3 and 21.93 when modified Hartmann number takes input in the range 0 ≤ Mh ≤ 0.2 and unsteady parameter 0.1 ≤ A ≤ 0.5. The Schmidt number, chemical change, and wedge angle parameters are all designed to boost the Sherwood number.