Analysis of entropy generation in natural convection of nanofluid inside a square cavity having hot solid block: Tiwari and Das' model

A computational work has been performed in this study to investigate the effects of solid isothermal partition insertion in a nanofluid filled cavity that is cooled via corner isothermal cooler. Mathematical model formulated in dimensionless primitive variables has been solved by finite volume method. The study is performed for different geometrical ratio of solid inserted block and corner isothermal cooler, Rayleigh number and solid volume fraction parameter of nanoparticles. It is observed that an insertion of nanoparticles leads to enhancement of heat transfer and attenuation of convective flow inside the cavity

Double diffusion in a rectangular duct using metals or oxides suspended in a viscous fluid

In this study, double diffusive free convection of nanofluid within a confined rectangular duct is investigated numerically. The momentum and energy equations are placed in the form of difference equations and solved numerically. The left wall conditions for the concentration and temperature are lesser than those of the right wall and the upper and lower walls are insulated. Different nanofluids are considered such as mixtures with copper, diamond, silicon oxide and titanium oxide, suspended in water. Brinkman and Maxwell models are used to characterize the nanofluid. Tiwari and Das model is opted to define the nanofluid behavior. The simulations are conducted using different nanoparticles, thermal Grashof number 1 ≤ GrT ≤ 20, solute Grashof number 1 ≤ GrC ≤ 15, solid volume fraction 0 ≤ Φ ≤ 0.05, Dufour number 0 ≤ Df ≤ 1, Brinkman number 0 ≤ Br ≤ 2, and Soret number 0 ≤ Sr ≤ 5. Additionally, behavior of volumetric flow strength, skin friction, heat transport intensity and Sherwood number is also examined. The thermal Grashof number, Brinkman number, Dufour, Soret and Schmidt parameters accelerate the velocity and temperature and dwindle the concentration whereas the reversal effect was obtained for the solid volume fraction. The concentration Grashof number diminishes the velocity and temperature and intensifies the concentration. The silver nanoparticles produce the highest velocity whereas diamond nanoparticles cause the lowest velocity and temperature. The maximum temperature is attained with silicon oxide

Numerical solutions of mixed convection flow past a horizontal circular cylinder with viscous dissipation in viscoelastic nanofluid

The aim of the present study is to investigate numerically the impact of viscous dissipation on steady two-dimensional mixed convection flow past a horizontal circular cylinder in a viscoelastic nanofluid with convective boundary conditions. The Tiwari and Das model were selected in this study by choosing Carboxymethyl cellulose solution (CMC-water) as the base of fluid and copper (Cu) as the nanoparticle. The transformed boundary layer equations for momentum and energy subject to the appropriate boundary conditions were numerically solved by employing numerical scheme, namely Keller-box method. The accuracy of the present results was validated through comparison with previously published results and revealed an excellent agreement with those results. The results were analysed in detail and presented graphically for the velocity, temperature, skin friction coefficient as well as the heat transfer coefficient. The obtained results indicated that there was no significant effect for velocity and temperature profiles when values of Eckert number increased. However, it is significant for skin friction and heat transfer coefficient profiles. In the meantime, thermal conductivity of the fluid may increase by increasing the concentration of nanofluid

Mixed convection of thermomicropolar AgNPs-GrNPs nanofluid: An application of mass-based hybrid nanofluid model

Here, a mass-based hybridity model is applied to inquire about the mixed convection of a thermomicropolar binary nanofluid (TMBNF) upon a shrinking and porous plate. The nanoparticles are the silver (AgNPs) and the graphene (GrNPs), in a spherical shape, suspended in an aqua base fluid. The applied methodology considers the masses of base fluid and nanoparticles as an alternative to the first and second nanoparticles volume fraction, according to the single-phase approach named the Tiwari-Das model. By using the similarity transformation technique, the dominating PDEs are changed to a system of ODEs that can be solved numerically by the bvp4c pattern of Matlab. To validate the numerical method, a comparison is implemented for the heat transfer, the shear stress, and the gradient of microrotation values, with results reported previously that consequently a supreme agreement is observed. The variations of the angular velocity, velocity, temperature distribution, gradient of microrotation, shear stress, and the heat transfer of the TMBNF with the prominent parameters are presented and analyzed by the tabular and graphical results. The originality of this work is related to the use of the mass-based model for TMBNF flow and the derivation of a new configuration of governing equations. It is concluded that the mass-based model with its significant benefits can be utilized successfully with tremendous assurance to abundant theoretical problems of micropolar binary nanofluid flow and heat transfer. New models for the nanofluid hybridity can undoubtedly be quite helpful in the many fields where cooling technologies are essential.The work of U⋅F.-G. was supported by the government of the Basque Country for the ELKARTEK21/10 KK-2021/00014 and ELKARTEK22/85 research programs, respectively

Non-equilibrium thermodynamic analysis of double diffusive, nanofluid forced convection in microreactors with radiation effects

This paper presents a theoretical investigation of the second law performance of double diffusive forced convection in microreactors with the inclusion of nanofluid and radiation effects. The investigated microreactors consist of a single microchannel, fully filled by a porous medium. The transport of heat and mass are analysed by including the thick walls and a first order, catalytic chemical reaction on the internal surfaces of the microchannel. Two sets of thermal boundary conditions are considered on the external surfaces of the microchannel; (1) constant temperature and (2) constant heat flux boundary condition on the lower wall and convective boundary condition on the upper wall. The local thermal non-equilibrium approach is taken to thermally analyse the porous section of the system. The mass dispersion equation is coupled with the transport of heat in the nanofluid flow through consideration of Soret effect. The problem is analytically solved and illustrations of the temperature fields, Nusselt number, total entropy generation rate and performance evaluation criterion (PEC) are provided. It is shown that the radiation effect tends to modify the thermal behaviour within the porous section of the system. The radiation parameter also reduces the overall temperature of the system. It is further demonstrated that, expectedly, the nanoparticles reduce the temperature of the system and increase the Nusselt number. The total entropy generation rate and consequently PEC shows a strong relation with radiation parameter and volumetric concentration of nanoparticles

Free Convective Heat Transfer in a Closed Gap between Concentric Semi-Hemispheres

Free convective heat transfer in the closed gap between concentric semi-hemispheres is quantified by means of a numerical approach based on the volume control method using the SIMPLE algorithm. The average Nusselt number is determined for several configurations obtained by varying the cavity’s aspect ratio between 0.15 and 1.5, while the Rayleigh number varies within the 5.33 × 103–4.50 × 108 range. The results show that the correlations available in the literature dealing with concentric whole spheres cannot be used for the configuration treated here. The new correlation between the Nusselt and Rayleigh numbers proposed in this work can be applied in various engineering sectors, such as in the electronic packaging considered in this present work, buildings, and architecture

Numerical investigation of Ferrofluid Flow at lower stagnation point over a solid sphere using Keller-Box Method

In this paper, ferrofluid flow at lower stagnation point on solid sphere is investigated theoretically by considering mixed convection boundary layer flow. The sphere surface is exposed to the magnetic field and thermal radiation by taking into account constant wall temperature boundary conditions. The discovery of the existing magnetic field near the surface while the ferrofluid flowing leads to the development of phenomenology called magnetohydrodynamic. The magnetite (Fe3O4) acts as nanoparticles dispersant and suspended in the water contained in ferrofluid are assumed as Newtonian fluid and behave as single-phase fluid flow is studied. These assumptions give physical insight into the behaviour of ferrofluid flow to be analysed and discussed. The Keller-box method is applied to solve the transformed partial differential equations numerically. The numerical results found the viscosity measured from magnetite (Fe3O4) volume fraction is the main element provided to the trend of the ferrofluid velocity flow. Besides, the ferrofluid temperature at lower stagnation point on sphere is proven influence the ferrofluid viscosity and change the velocity of ferrofluid flow

The mixed of hybrid nanofluid GO-MoS2/engine oil over a shrinking sheet with mass flux effect: Reiner-Philippoff model

The mixed convection flow and heat transfer of the hybrid nanofluid over a shrinking sheet are investigated. Molybdenum disulphide (MoS2) and graphene oxide (GO) are employed as two hybrid nanoparticles while engine oil (EO) as the base fluid is considered. In this study, the Reiner-Philippoff model as one of non-Newtonian types is deliberated since it has the ability to function on three distinct types of fluids: viscous, shear thickening and shear thinning. The Reiner-Philippoff relation, the momentum and energy equations under Tiwari and Das model are all employed in the study. Influences from mass flux are also considered in the flow. Before computation using the bvp4c function in MATLAB, the respected equations are first converted into ordinary differential equation form using the similarity transformation. When the established and current models are discovered to be identical in a specific case, a direct comparative investigation is conducted to confirm the correctness of the current model. In addition, the present results are shown graphically and in tabular form. It is hypothesized that the presence of a hybrid nanofluid significantly affects the fluid characteristic and gives more satisfactory results than a single nanofluid. The skin friction coefficient and heat transfer rate of hybrid nanofluids are greater than the nanofluids. In terms of velocity and temperature profile, the reduction in velocity and the enhancement in temperature profile are caused by a rise in the Reiner-Philippoff parameter. The same outcome is also seen when the volume fraction of hybrid nanofluids increases

Unsteady free convection nanofluid flow near stagnation point of a three-dimensional body

Industrial systems gain a lot of benefit from unsteady free convection flow near the stagnation point of three-dimensional body such as the cooling of an infinite metallic plate in cooling baths and the boundary layer along material handling conveyers. In this study, a mathematical model of an unsteady free convection flow near the stagnation point of a three-dimensional body is developed. The problem considered involves the flow in nanofluid. The governing equations consist of continuity, momentum, energy and nanoparticle volume fraction are solved numerically through the Keller-box method. The effect of the physical parameters such as Brownian motion, thermophoresis and buoyancy parameters on the velocity, temperature and concentration profiles are investigated and discussed. Furthermore, various values of the physical parameter are examined by the skin friction coefficient in x- and y- directions, the local Nusselt number and Sherwood number. The results of the skin friction, velocity, temperature and concentration profile are presented and computed using FORTRAN and MATLAB software. The results have shown that Brownian motion, buoyancy, thermophoresis parameters and Lewis number give rises to the concentration profile. In addition, the skin friction is increased when the curvature parameter is increased

Magnetite water based ferrofluid flow and convection heat transfer on a vertical flat plate: Mathematical and statistical modelling

The unique magnetic properties of ferrofluid when exposed to the magnetic field led to the ferrofluid formulation in wide applications, especially as a thermal transfer. To picture the effective ferrofluid flow configurations and heat transfer mechanism at a surface, it is crucial to figure out the phenomenology of boundary layer and convective heat transfer. This study investigates a numerical solution of the mixed convection boundary layer flow of ferrofluid at the stagnation point on a vertical flat plate. Ferrofluid composed of magnetite (Fe3O4) water based exposure to the magnetic field and thermal radiation is considered. The complicated governing differential equations of fluid flow and heat transfer are simplified into simple equations using boundary layer approximation, Boussinesq approximation and similarity transformations. Then, the equations are solved numerically by employing the Keller-box method. Numerical results discovered that the ferroparticles volume fraction is the predominant factor in contributing to the trend of ferrofluid velocity, reduced skin friction and reduced Nusselt number. Further, the influence of the ferroparticles volume fraction on reduced skin friction and reduced Nusselt number are analyzed using regression analysis