Crosswise stream of hydrogen-oxide (H2O) through a porous media containing copper nanoparticles

Transport theories in porous media are quite operative to analyse heat transferral phenomenon in biological tissues, reducing bio convective flow instabilities by means of porous media and many more. Inspired by these remarkable features, the present study is conducted to analyse heat transfer phenomenon for obliquely striking nanofluid through a porous media. Copper (Cu) nanoparticles are suspended in traditional Hydrogen Oxide based fluid. Scaling group of transformations is conveniently employed to reduce governing transport equations and is tackled numerically afterwards. Influence of nanoparticles volume fraction, stretching ratio and porosity parameter on physical measures of concern such as normal and tangential skin friction and corresponding heat flux at wall is portrayed. Streamline patterns are traced out to discover the influence of porosity factor on actual flow behavior. It was observed that solid volume fraction of copper nanoparticles enhanced the skin friction coefficients and heat flux. Increasing the porosity parameter leads to greater heat flux and tangential skin friction co-efficient.     

Electromagnetohydrodynamic boundary layer flow in hybrid nanofluid with thermal radiation effect: Numerical simulation

Hybrid nanofluid boundary layer flow past a stretching surface with zero mass flux boundary condition is explored in this article. The main aim of this article is to analyze the electromagnetohydrodynamic role in a hybrid nanofluid containing silver and molybdenum disulfide nanoparticles. The self-similar solution is embedded to reduce the governing partial differential equation into algebraic equations and a shooting algorithm is applied to obtain the solution of the resultant boundary value problem. Variation in momentum, energy, and nanoparticle concentration is explained through graphical profiles. Nusselt number and drag force coefficients are computed for various flow parameters and their impact on the nanofluid and hybrid nanofluid is computed and presented and explained in a comparative fashion. It is observed that the velocity profile shows the opposite nature with respect to the electric field and magnetic field. For electric field parameter velocity accelerates whereas for magnetic parameter velocity diminishes. Nusselt number increases with electric field parameter and nanoparticle volume fraction.     

Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field

In this paper, we examine the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The analytical solutions of the resulting ODEs are obtained, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. Comparison with published results is presented.     

Features of the exponential form of internal heat generation,Cattaneo–Christov heat theory on water-based graphene–CNT–titanium ternary hybrid nanofluid flow

To increase energy efficiency, the flow of fluids containing nanoparticles is crucial in industrial applications notably in nuclear reactors and nuclear system cooling. In light of this, this study examines the flow of a water-based ternary hybrid nanofluid (graphene, single-walled carbon nanotubes, and titanium dioxide) across a curved stretching sheet with suction. The non-Fourier heat flux model is also considered in the modeling. The existing partial differential equations are converted into ordinary differential equations through the use of similarity variables. These ordinary differential equations are then numerically solved using the Runge–Kutta–Fehlberg fourth- and fifth-order method along with a shooting approach. The collection of graphical findings for the key variables on the temperature and velocity profiles is investigated. Results reveal that the heat transport in ternary hybrid nanoliquid rises as the heat source/sink parameter rises. The Biot number influences the thermal profile positively, whereas the increasing curvature parameter values reduce heat transport. The curvature parameter has a positive impact on skin friction but the suction parameter has a negative impact on skin friction.     

Computation of Darcy-Forchheimer flow of Sisko nanofluid over a stretching cylinder

This study investigates the Darcy-Forchheimer flow of Sisko nanofluid with viscous dissipation and convective thermal boundary conditions. The Buongiorno two-component nanoscale model is deployed for nanofluid characteristics, which take into account the physical phenomena responsible for the slip velocity between the base fluid and the nanoparticles such as thermophoresis and Brownian diffusion. The Darcy- Forchheimer model employed here includes the effects of boundary and inertial forces. The nonlinear coupled partial differential equations governing the fluid flow are converted into the nonlinear ordinary differential equations by choosing suitable similarity transformations. The nondimensionalized differential equations are then solved utilizing the finite difference based bvp-4c tool in MATLAB software. The numerical solutions are presented graphically to demonstrate the impact of involved physical parameters on temperature, velocity, and nanoparticle volume fraction. Moreover, the rate of heat transfer, mass transfer, and skin friction are physically interpreted. The present investigation reveals that the Darcy number enhances the velocity and depleted the temperature while the Forchheimer number depleted the velocity and enhances the temperature of the Sisko nanofluid. The thermophoresis, Brownian diffusion parameters, and the Forchheimer number contribute to the reduction in the heat transfer rate while the Darcy number enhances it. The skin friction at the wall can be controlled by controlling the values of Darcy number.     

Convective Heat Transfer in a Vertical Rectangular Duct Filled with a Nanofluid

An analysis is performed to study natural convective heat transfer in a vertical rectangular duct filled with a nanofluid. One of the vertical walls of the duct is cooled by a constant temperature, while the other wall is heated by a constant temperature. The other two sides of the duct are thermally insulated. The transport equations for a Newtonian fluid are solved numerically with a finite volume method of second‐order accuracy. The influence of pertinent parameters such as Grashof number, Brinkman number, aspect ratio and solid volume fraction on the heat transfer characteristics of natural convection is studied. Results for the volumetric flow rate and skin friction for Copper and Diamond nanoparticles are also drawn. The Nusselt number for various types of nanoparticle such as silver, copper, diamond and titanium oxide are also tabulated. The results indicate that inclusion of nanoparticles into pure water improves its heat transfer performance; however, there is an optimum solid volume fraction which maximizes the heat transfer rate.     

Numerical investigation of the MHD forced convection and entropy generation in a straight duct with sinusoidal walls containing water–Al2O3 nanofluid

This paper examines forced convection heat transfer and entropy generation of a nanofluid laminar flow through a horizontal channel with wavy walls in the presence of magnetic field, numerically. The Newtonian nanofluid is composed of water as base fluid and Al₂O₃ as nanoparticle which is exposed to a transverse magnetic field with uniform strength. The inlet nanofluid with higher temperature enters the cool duct and heat is exchanged along the walls of a wavy channel. The effects of the dominant parameters including Reynolds number, solid volume fraction, Hartmann number, and different states of amplitude sine waves are studied on the local and average Nusselt number, skin friction, and total entropy generation. Computations show excellent agreement of the present study with the previous literature. The computations indicate that with the increasing strength of a magnetic field, Nusselt number, skin friction, and total entropy generation are increased. It is found that increasing the solid volume fraction of nanoparticles will increase the Nusselt number and total entropy generation, but its effect on the skin friction is negligible. Also, results imply that increasing amplitude sine waves of the geometry has incremental effect on both Nusselt number and skin friction, but its effect on the total entropy generation is not so tangible.     

Nanofluid Flow in a Porous Channel with Suction and Chemical Reaction using Tiwari and Das's Nanofluid Model

In this paper, an analysis is made for a nanofluid flow in a porous channel by introducing the conservation equation of nanoparticle volume fraction into Tiwari and Das's nanofluid model. The suction and chemical reaction are also considered in this work. The governing partial differential equations are simplified by employing a new variable and transformed into a system of high‐order nonlinear ordinary differential equations by similarity transformations. The Keller box method is used to solve this problem numerically. In addition, the influences of significant physical parameters on the distributions of the velocity and temperature as well as nanoparticle concentration are graphically presented and discussed in detail. It is found that there exists a critical value of the permeable parameter which determines the influence law of nanoparticle volume fraction parameter on skin friction coefficient and local Sherwood number. The results also indicate that the concentration increases sharply with the Schmidt number and chemical reaction parameter.     

Cattaneo–Christov double-diffusion model with Stefan blowing effect on copper–water nanofluid flow over a stretching surface

We often encounter many processes where the cooling rate is a key factor in deciding the features of a desired product. Due to increasing demands of controlled cooling systems, an effort is made to theoretically study the effect of volume fraction on mixed convective Cu–water nanofluid flow over a stretching surface with activation energy and thermal radiation. The nonlinear dynamical system is simplified using apt similarity variables and the obtained ordinary differential equations are dealt numerically using Runge–Kutta–Fehlberg method and shooting scheme. The thermal and solutal equations are modeled considering Cattaneo–Christov double-diffusion model. The flow problem is studied considering velocity slip and zero mass flux state at the surface. As a novelty, the present case considers the blowing effect at the surface to study massive species transport during nanofluid flow with Cattaneo–Christov double-diffusion model. The results show that an increase in strength of thermal radiation increases temperature and buoyancy ratio parameter, thereby escalating the skin friction coefficient. When thermal relaxation parameter changes from 0.001 to 0.005, heat transfer coefficient improves by 24.36%. Furthermore, with the change in value of the blowing parameter from 0.1 to 0.1015, the maximum value concentration of nanoparticles that is attained during the flow is increased by 7.15%.     

Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid

An analysis is carried out to study the problem of the steady flow and heat transfer over a static or moving wedge with a prescribed surface heat flux in a nanofluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, before being solved numerically by the Keller box method and the Runge-Kutta-Fehlberg method with shooting technique. The features of the flow and heat transfer characteristics are analyzed and discussed. Three different types of nanoparticles are considered, namely copper Cu, alumina Al₂O₃ and titania TiO₂ with water as the base fluid. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Moreover, the heat transfer rate at the surface increases with the Falkner-Skan power law parameter m.     

Asymmetric Forced Convection of Nanofluids in a Channel with Symmetrically Mounted Rib Heaters on Opposite Walls

Laminar forced convection of nanofluids in a vertical channel with symmetrically mounted rib heaters on surfaces of opposite walls is numerically studied. The fluid flow and heat transfer characteristics are examined for various Reynolds numbers and nanoparticles volume fractions of water-Al₂O₃ nanofluid. The flow exhibits various structures with varying Reynolds number. Even though the geometry and heating is symmetric with respect to a channel vertical mid-plane, asymmetric flow and heat transfer are found for Reynolds number greater than a critical value. Introduction of nanofluids in the base fluid delays the flow solution bifurcation point, and the critical Reynolds number increases with increasing nanoparticle volume fraction. A skin friction coefficient along the solid-fluid interfaces increases and decreases sharply along the bottom and top faces of the heaters, respectively, due to sudden acceleration and deceleration of the fluid at the respective faces. The skin friction coefficient, as well as Nusselt numbers in the channel, increase with increasing volume fraction of nanoparticles.     

Numerical Study of Pressure Drop and Thermal Characteristics of Al2O3–Water Nanofluid Flow in Horizontal Annuli

In this paper the results of numerical study of the mixed convection heat transfer of Al₂O₃–water nanofluid in a horizontal annuli are presented. Steady, laminar flows in symmetric configurations are considered. Single-phase fluid approach is adopted for nanofluid modeling. The governing equations are discretized using the finite-volume method. A SIMPLE-like algorithm has been applied for pressure–velocity coupling on the collocated arrangement. In order to validate the code performance, the numerical results are compared with those available in the literature and good agreement is achieved. The effects of some important parameters such as nanoparticle volume fraction, aspect ratio, Grashof number, and heat flux ratio are studied and discussed in detail. In general, it is observed that the local Nusselt number increases with increase in nanoparticle concentration, Grashof number, and radius ratio. However, when increasing the nanoparticle concentration there are considerable increments in pressure drop and pumping power, which are not desirable. On the other hand, changes in the skin friction coefficient are negligible.     

Bioconvective electromagnetic nanofluid transport from a wedge geometry: Simulation of smart electro‐conductive bio‐nanopolymer processing

A mathematical model is presented for steady, two‐dimensional, stagnation‐point flow, heat, mass, and micro‐organism transfer in a viscous, incompressible, bioconvective, electromagnetic nanofluid along a wedge with Stefan blowing effects, hydrodynamic slip, and multiple convective boundary conditions. Gyrotactic micro‐organisms are present in the nanofluid and bioconvection arises, characterized by micro‐organisms swimming under a competing torque. Similarity transformations are used to render the system of governing partial differential equations into a system of coupled similarity equations. The transformed equations are solved numerically with the BVP5C method. The impact of emerging parameters on dimensionless velocity, temperature, magnetic induction function, nanoparticle volume fraction, and density of motile micro‐organisms is studied graphically. Furthermore, the responses of the local skin friction, local Nusselt number, local Sherwood number, and the wall gradient of density of motile micro‐organism number to variation in these parameters are elaborated. Validation of solutions with previous studies based on special cases of the general model is included. The simulations are relevant to the processing of biological, electro‐conductive nanomaterials and industrial hygienic coating systems exploiting combined electromagnetics, nanosystems, and microscopic, bio‐propulsion mechanisms.     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.     

Nanofluid Flow and Heat Transfer in Boundary Layers: The Influence of Concentration Diffusion on Heat Transfer Enhancement

ABSTRACT

The present work uses a perturbation procedure to deduce the small perturbation differential equations for velocity, temperature, and the diffusion equation for nanoparticle volume concentration. Thermophysical variables are obtained from conventional means (e.g., mixture and field theory estimates) for nanofluids consisting of alumina nanoparticles dispersed in water (alumina–water nanofluid) and gold nanoparticles dispersed in water (gold–water nanofluid), and, in the case of gold–water nanofluid, molecular dynamics results are used to estimate such properties, including the transport coefficients. The very thin diffusion layer, at large Schmidt numbers, is found to have a great impact on the velocity and temperature profiles, owing to the transport property dependency and has a profound influence on surface conduction heat transfer rate enhancement and skin friction suppression for the case of nanofluid concentration withdrawal at the wall. In this case, the diffusional heat transfer rate is negligible, again, owing to the large Schmidt numbers encountered. Possible experiments directed at this interesting phenomenon are discussed.     

Three‐dimensional boundary layer flow over a rotating disk with power‐law stretching in a nanofluid containing gyrotactic microorganisms

The nanofluid model containing microorganisms over a rotating disk with power‐law stretching is constructed in this paper. The combined effects of nanoparticles and microorganisms in nanofluid are investigated by solving the governing equations numerically. The numerical solutions of the skin friction coefficient and local Nusselt number are in agreement with the corresponding previously published results. The quantities of physical interest are graphically presented and discussed in detail. It is found that the power‐law stretching index has produced profound influence on the flow as well as the heat and mass transfer.     

Nonlinear thermal radiation on MHD tangential hyperbolic hybrid nanofluid over a stretching wedge with convective boundary condition

In this study, two distinct nanoparticles: aluminum oxide (Al₂O₃) and copper (Cu) are chosen as nanomaterials to examine the effects of nonlinear electrically conducting magnetohydrodynamic radiation on the flow of tangential hyperbolic hybrid nanofluid across a nonlinearly stretched sheet with convective boundary conditions. The equations that regulate fluid flow are represented as partial differential equations. These equations are reduced to their equivalent ordinary differential equations, which are solved using the homotopy analysis approach with the help of similarity variables. The effect of essential physical factors on fluid velocity, temperature, skin friction coefficient, and local Nusselt number is investigated and discussed. Results ascertain that the heat transfer rate of Cu/H₂O nanofluid becomes high when equated to Cu–Al₂O₃/H₂O nanofluid. Furthermore, the temperature distribution enhances with the rise in solid volume fraction while it diminishes with improved magnetic field for both nanofluid and hybrid nanofluid.     

Viscous dissipation effect on mixed convective heat transfer of MHD flow of Williamson nanofluid over a stretching cylinder in the presence of variable thermal conductivity and chemical reaction

The effect of viscous dissipation and thermal radiation on mixed convective heat transfer of an MHD Williamson nanofluid past a stretching cylinder in the existence of chemical reaction is analyzed in this study. When energy equation is formulated, the variable thermal conductivity is deliberated. By proposing applicable similarity transformations, nonlinear ordinary differential equations (ODEs) are attained from partial differential equations. These nondimensional ODEs are computed through Runge-Kutta method integrated with shooting method using MATLAB software. The results found numerically are in agreement with that of the published works of similar nature in a limiting case. The results of the local Nusselt number, skin friction coefficient, and Sherwood numbers are organized in tables. The influence of protuberant parameters on temperature, velocity, and concentration is presented by graphs. From the results, it is seen that for higher values of variable thermal conductivity parameter, the local Sherwood number and skin friction coefficient upsurge, whereas the local Nusselt number diminishes.     

H2O based different nanofluids with unsteady condition and an external magnetic field on permeable channel heat transfer

This paper investigates numerically the problem of unsteady magnetohydrodynamic nanofluid flow and heat transfer between parallel plates due to the normal motion of the porous upper plate. The governing equations are solved via the fourth-order Runge-Kutta method. Different kind of nanoparticles is examined. The effects of kind of nanoparticle, nanofluid volume fraction, expansion ratio, Hartmann number, Reynolds number on velocity and temperature profiles are considered. Also effect of different types of nanoparticles is examined. Results indicate that velocity decreases with increase of Hartmann number due to effect of Lorentz forces. Rate of heat transfer increase with increase of nanofluid volume fraction, Hartmann number and Reynolds number but it decreases with increase of expansion ratio. Also it can be found that choosing copper as a nanoparticle leads to highest enhancement.