Heat Transfer of Viscous MHD Nanofluid Flow in the Presence of Solar Radiation With Entropy

Unsteady magnetohydrodynamic squeezing Darcy-Forchheimer flow of Fe3O4 Casson nanofluid: Impact of heat source/sink and thermal radiation

In this research article, three-dimensional Casson nanofluid under influences of Arrhenius stimulation energy and thermal radiation is considered. The flow is induced by a turning disk. Temperature, velocity, and concentration slips at the outward of the turning disk are deliberated. The effect of Brownian movement and thermophoresis is examined due to the nanosized particles in a Casson fluid dispersed over the turning disk. The appropriate transformation methods for reducing a set of Partial differential equations (PDEs) to nonlinear Ordinary differential equations (ODEs) and further solved by the homotopy analysis method (HAM). Numerical simulation using Schmidt number, magnetic, Casson, Brownian movement, and thermophoresis parameters on outspread, temperature, tangential velocities, and nanoparticles are portrayed. Local Nusselt number, Skin friction, and Sherwood number are plotted and investigated. The graphical results show that the tangential velocity of nanofluids decreases because of an addition in Reynolds’ number, while the radial velocity displays the converse patterns. The tangential and radial velocities reduce with the increment magnetic factor. It is also perceived that an augmentation in estimations of radiation parameters enhances the heat transfer rate. Increasing the values of non-dimensional activation energy raises the mass transfer rate.

Response surface methodology (RSM) and artificial neural network (ANN) simulations for thermal flow hybrid nanofluid flow with Darcy-Forchheimer effects

This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM) and numerically by shooting procedure. Effects of various governing parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness.

Tangent hyperbolic nanofluid flowing over a stretching sheet through a porous medium with the inclusion of magnetohydrodynamic and slip impact

Purpose – The current study is mainly motivated by the need to the development of the transient MHD mixed convection stagnation-point flow and heat transfer of an electrically conducting nanofluid over a vertical permeable stretching/shrinking sheet by means of Tiwari-Das nanofluid model. The purpose of this paper is to investigate the effects of the parameters governing the flow i.e. the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter on dimensionless velocity and temperature distributions, skin friction coefficient and local Nusselt number. Design/methodology/approach – The mathematical model has been formulated based on Tiwari-Das nanofluid model. Three different types of water-based nanofluid with copper, aluminum oxide (alumina) and titanium dioxide (titania) as nanoparticles are considered in this investigation. Using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved analytically by the well-know homotopy analysis method. The present simulations agree closely with the previous studies in the especial cases. Findings – The results show that by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter or reducing the velocity ratio parameter, the skin friction coefficient enhances. Furthermore, the local Nusselt number enhances with different rates by increasing the nanoparticle volume fraction, the unsteadiness parameter, the magnetic parameter, the wall transpiration parameter, the mixed convection parameter and the velocity ratio parameter. Besides, the skin friction coefficient and the local Nusselt number are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Originality/value – Tiwari-Das nanofluid model has not been applied for the flow with these characteristics as mentioned in the paper. A comprehensive survey on boundary layer behavior has been presented. There are few studies regarding as analysis on thermal and hydrodynamics boundary layer. All plots presented in the paper are new and did not report in any other study. The effects of the parameters governing the flow on skin friction coefficient and local Nusselt number have been illustrated in the paper while there are some conflicts with previous published article that have been interpreted in details in the paper.

Carbon nanotubes (CNTs) are gaining popularity due to their expanding uses in industrial and technical processes, such as geothermal reservoirs, water and air filters, coatings, solar collection, ceramic material reinforcement, electrostatic dissipation, etc . In addition, the CNTs have superior electrical conductivity and biocompatibility. Based on the aforementioned applications, the current work examines the time-dependent and Darcy–Forchheimer flow of water/glycerin-based Casson hybrid nanofluid formed by single-walled CNTs and multi-walled CNTs over a Riga plate under velocity slip. The energy expression is modeled through nonlinear thermal radiation and viscous dissipation impacts. The incorporation of convective boundary condition into the current model improves its realism. By employing suitable variables, the governing models are re-framed into ordinary differential equations. The bvp4c and the homotopy analysis method are used to find the computational results of the re-framed equations and boundary conditions. The novel characteristics of a variety of physical parameters on velocity, temperature, skin friction coefficient (SFC), and local Nusselt number (LNN) are discussed via graphs, charts, and tables. It is found that the fluid velocity decays when enriching the Forchheimer number, unsteady and porosity parameters. The radiation parameter plays an opposite role in convective heating and cooling cases. The modified Hartmann number enhances the surface drag force, and the Forchheimer number declines the SFC. The unsteady parameter develops the heat transfer rate, and the Forchheimer number suppresses the LNN. The simulated flow problem has many applications in engineering sectors, including ceramic manufacture, heating and cooling systems, energy storage units, thermodynamic processes, and other fields.

While quantum computing provides an exponential advantage in solving linear differential equations, there are relatively few quantum algorithms for solving nonlinear differential equations. In our work, based on the homotopy perturbation method, we propose a quantum algorithm for solving n-dimensional nonlinear dissipative ordinary differential equations (ODEs). Our algorithm first converts the original nonlinear ODEs into the other nonlinear ODEs which can be embedded into finite-dimensional linear ODEs. Then we solve the embedded linear ODEs with quantum linear ODEs algorithm and obtain a state ϵ-close to the normalized exact solution of the original nonlinear ODEs with success probability Ω(1). The complexity of our algorithm is O(gηT poly(log(nT/ϵ))), where η, g measure the decay of the solution. Our algorithm provides exponential improvement over the best classical algorithms or previous quantum algorithms in n or ϵ.

In this paper, we propose a method of solution for both nonlinear Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs). Shehu Transform is combined with Homotopy Analysis Method (HAM) to handle both homogeneous and nonhomogeneous problems in the family of differential equations considered. The properties of homotopy derivatives are exploited while handling the nonlinear terms encountered. Several examples are solved using HAM and the Shehu Transform Homotopy Analysis Method (STHAM) proposed in this work, and the effectiveness of the proposed method is obvious in terms of reduction in the volume of computations and time. All computations are carried out with the aid of Mathematica 12.0.

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet with a power-law surface velocity, slip velocity, and variable thickness. The flow is caused by nonlinear stretching of the sheet. The governing partial differential equations are transformed into a nonlinear ordinary differential equation with appropriate boundary conditions for various physical parameters. The remaining ordinary differential equation is solved numerically by using the Chebyshev spectral method. The effects of the slip parameter and the wall thickness parameter on the flow profile and local skin friction are presented. A comparison of obtained numerical results is made with previously published results in some special cases, and excellent agreement is noted.

This study incorporates the impact of shape factor and slip conditions on a radiative hybrid magnetic nanofluid over slanted sheet being convectively heated within a porous medium, providing valuable insights for enhancing thermal management systems in manufacturing techniques such as the extrusion of plastic films, cooling of metallic plates, and the drawing of polymer fibers. The effect of viscous dissipation, thermal radiation, aligned magnetic field, velocity slip, heat generation, buoyancy force, porosity, and thermal slip on the dynamics of fluid movement are comprehensively discussed. The governing equations were simplified into nonlinear ordinary differential equations through similarity variables and Bvp4c solver in MATLAB was utilized to observe the effects of pertinent parameters on temperature and velocity profiles, alongside the local Nusselt number and skin friction coefficient. It was determined that the hybrid nanofluid’s effective thermal conductivity was most significantly enhanced by blade-shaped nanoparticles. The local Nusselt number enhanced with upsurge of thermal radiation parameter and Biot number whereas opposite trend was observed with incrementation in other parameters. The augmentation in thermal slip and velocity slip resulted in lowering local skin friction coefficient. This research highlights the complex interplay between various physical factors and their influence on the dynamics of hybrid nanofluids, offering potential strategies for optimizing performance of thermal systems comprising hybrid nanofluids.

This paper is devoted to introduce a numerical simulation using the implicit finite difference method (FDM) with the theoretical study for the effect of viscous dissipation on the steady flow with heat transfer of Newtonian fluid towards a permeable stretching surface embedded in a porous medium with a second-order slip. The governing non-linear partial differential equations are converted into non-linear ordinary differential equations (ODEs) by using similarity variables. Exact solutions corresponding to momentum and energy equations for the case of no slip conditions are obtained. The resulting ODEs are successfully solved numerically with the help of FDM. Graphically results are shown for non-dimensional velocities and temperature. The effects of the porous parameter, the suction (injection) parameter, Eckert number, first- and second-order velocity slip parameter and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.

The steady, three dimensional mixed convection flow of a Cu-water nanofluid past a stretching sheet is investigated. The homogenous model is adopted to simplify the physical problem. With a set of similarity transformations, the governing equations are reduced to a set of ordinary differential equations, which are then solved by means of the homotopy analysis method (HAM). The novel HAM technique for the choice of the convergent control auxiliary parameters ħ and optimal parameters of the initial guesses, as well as the new approach of the computational errors are introduced. with the help of these novel methods, the highly accurate analytical approximations are obtained for both the velocity and the temperature profiles. Besides, the effects of the nanoparticle volume fraction φ on the local skin friction and the local Nusselt number are presented and discussed. It is found that the nanofluid can improve on the heat transfer characteristics to a large extent. As far as we know, this problem has not been considered before and the results are new and original.

Axisymmetric flow and heat transfer over an unsteady stretching sheet in power law fluid

Casson nanofluid flow has drawn substantial interest due to its industrial uses, including textile industry, paints and coatings biomedical application, drilling muds, cement slurries, tissue engineering, etc. In this article, we analyse the chemically radiative Casson fluid model across a porous sheet undergoing nonlinear stretching. It evaluates the implications regarding heat generation along with viscous dissipation. The scientific nanofluid framework laid out by Buongiorno has been exploited. Through employing the proper similarity transformations, the partial differential equations which illustrate the phenomena could be transfigured into ordinary differential equations. The Homotopy Analysis Method (HAM), a semi-analytical technique intermittently exploited across diverse scientific and technical domains to address nonlinear ordinary and partial differential equations, is endorsed to analyze the simplified equations. Calculations are executed to ascertain the numerical solutions related to temperature, concentration, and velocity fields, accompanied by the skin friction coefficient, local Nusselt number, and local Sherwood number. Visualizations of interpretations are accompanied by pertinent explanations grounded in scientific principles. The temperature distribution has been enhanced due to radiative and viscous dissipation characteristics. Additionally, it has been noted that a delay in fluid movement results from an improvement in the porous medium parameter and magnetic field values. It has been discovered that the Nusselt number is exhibiting a downward trend as the porous medium parameter and thermophoresis parameter increase. The current numerical results have been effectively validated against previous difficulties.