A nonlinear mathematical analysis for magneto-hyperbolic-tangent liquid featuring simultaneous aspects of magnetic field, heat source and thermal stratification

Innovation modeling and simulation of thermal convective on cross nanofluid flow over exponentially stretchable surface

This work reported to investigate convective flow of non-Newtonian fluid effect on an exponentially stretchable surface. Effect of nanoparticle is considered in heat and mass equation. The transformation technique utilized on dimensionless equations is converted to non-dimensionless equations are solved thought numerical approach Bvp4c. Influence of approatiate analysis of velocities, heat and mass transport are scrutinized through figures. Furthermore, the comparative analysis of drag forces, Nusselt number and Sherwood number are evaluated over and done with tabulated values. It is give details that the temperature field strengthens with intensification in thermophoresis and random diffusions. Similarly, rises in thermophoresis effect parameter both temperature and concentration profile increasing.

Mathematical analysis of radius and length of CNTs on flow of nanofluid over surface with variable viscosity and joule heating

The transfer of heat is a phenomenon that is significant in a variety of contexts due to the different ways in which it may be utilized in industrial settings. To increase the rate at which heat is transferred, carbon nanotubes (CNTs), which can either be single-wall or multi-walled, are suspended in base fluids, and the resulting mixture is referred to as a "nanofluid. This study looks at how heat transfers through nanofluids that are suspended in carbon nanotubes with different lengths and radii over a stretching surface. It also looks at how changing viscosity and joule heating affect motion. Water is taken as base fluid. This study looks at both carbon nanotubes with one wall and those with more than one. The flow is governed by a series of partial differential equations, which, to control the flow, are transformed into a series of nonlinear ordinary differential equations. Similarity transformation is used to convert the obtained nonlinear ordinary differential equations and accompanying boundary conditions into a form that is dimensionless. To numerically solve the transformed equation, RK-4 with shooting method is used. Graphs and in-depth discussions are used to look at how velocity and temperature profiles are affected by the leading variables. The expression for skin friction and local Nusselt number are written down and graphs show how these two numbers change for different parameter values. The temperature profile goes down when the viscosity parameter goes down, but the velocity profile goes up. When the magnetic parameter goes up, the velocity profile f'(η), goes down, but the velocity profile g(η) and temperature θ(η) both go up at the same time. The rate of heat transfer increases with the addition of φ and S. When the suction parameter (S = 2.1) with 1% of φ is used, it is reported that rate of heat transfer increases by 1.135% for Single walled and 1.275% for Multi Walled carbon nanotubes. To determine whether or not the proposed numerical model is legitimate, a comparison is made between the current results and those that have previously been published.

Mathematical analysis of mixed convective stagnation point flow over extendable porous riga plate with aggregation and joule heating effects

It is still not quite apparent how suspended nanoparticles improve heat transmission. Multiple investigations have demonstrated that the aggregation of nanoparticles is a critical step in improving the thermal conductivity of nanofluids. However, the thermal conductivity of the nanofluid would be greatly affected by the fractal dimension of the nanoparticle aggregation. The purpose of this research is to learn how nanoparticle aggregation, joule heating, and a heat source affect the behavior of an ethylene glycol-based nanofluid as it flows over a permeable, heated, stretched vertical Riga plate and through a porous medium. Numerical solutions to the present mathematical model were obtained using Mathematica's Runge-Kutta (RK-IV) with shooting technique. In the stagnation point flow next to a permeable, heated, extending Riga plate, heat transfer processes and interrupted flow phenomena are defined and illustrated by diagrams in the proposed mixed convection, joule heating, and suction variables along a boundary surface. Data visualizations showed how different variables affected temperature and velocity distributions, skin friction coefficient, and the local Nusselt number. The rates of heat transmission and skin friction increased when the values of the suction parameters were raised. The temperature profile and the Nusselt number both rose because of the heat source setting. The increase in skin friction caused by changing the nanoparticle volume fraction from φ=0.0 to φ=0.01 for the without aggregation model was about 7.2% for the case of opposing flow area (λ=-1.0) and 7.5% for the case of aiding flow region (λ=1.0). With the aggregation model, the heat transfer rate decreases by approximately 3.6% for cases with opposing flow regions (λ=-1.0) and 3.7% for cases with assisting flow regions (λ=1.0), depending on the nanoparticle volume fraction and ranging from φ=0.0 to φ=0.01, respectively. Recent findings were validated by comparing them to previously published findings for the same setting. There was substantial agreement between the two sets finding.

Irreversibility analysis of radiative flow of Prandtl nanofluid over a stretched surface in Darcy-Forchheimer medium with activation energy and chemical reaction

This communication elaborates the irreversibility analysis of the flow of Prandtl nanofluid along with thermal radiation past a permeable stretched surface embedded in a Darcy-Forchheimer medium. The activation and chemical impressions along with effects of thermophoretic and Brownian motion are as well examined. The flow symmetry of the problem is modeled mathematically and leading equations are rehabilitated into nonlinear ordinary differential equations (ODEs) through the assistance of suitable similarity variables. The Keller-box technique in MATLAB is employed to draw the impacts of the contributing elements on the velocity field, temperature distribution, and concentration. The impact of the Prandtl fluid parameter has mounting performance for the velocity whereas conflicting behavior is examined in the temperature profile. The achieved numerical results are matched correspondingly with the present symmetrical solutions in restrictive cases and fantastic agreement is scrutinized. In addition, the entropy generation uplifts for the growing values of the Prandtl fluid parameter, thermal radiation, and Brinkman number and decreases for growing numbers of the inertia coefficient parameter. It is also discovered that the coefficient of friction decreases for all parameters involved in the momentum equation. Features of nanofluids can be found in a variety of real-world fields, including microfluidics, industry, transportation, the military, and medicine.