Three-dimensional Nanofluid Flow Research Articles

Magnetohydrodynamic convection-entropy generation of a non-Newtonian nanofluid in a 3D chamber filled with a porous medium

Magnetohydrodynamic (MHD) mixed convection in a 3D (three dimensional) lid-driven cavity loaded with a power-law nanofluid is examined. The bottom wavy wall is maintained at a hot temperature, while the upper lid is at a uniformly cold temperature. The vertical walls are kept in adiabatic conditions. The steady and three-dimensional flow of nanofluids is quantitatively studied utilizing thermophysical properties and the Galerkin Finite Element Method (GFEM). The findings were shown for a variety of Grashof numbers (Gr = 103-105), Hartmann numbers (Ha = 0–20), Reynolds numbers (Re = 10–500), power-law indexes (n = 0.8,1,1.6), and undulation numbers (N = 1–4). The influence of the various parameters on flow, heat transfer, and entropy generation is illustrated by the streamlines, isotherms, and isentropic contours. Higher Re, γ, N, φ, and lower Ha enhance the heat transfer. Entropy generation is mostly due to heat transfer but also fluid-friction and magneto effects contribute. Also, the increase in Re from 50 to 500 gives an enhancement in Nuav up to 87.5 %. Furthermore, the increase in power-law index (n) from 0.8 to 1 gives a reduction in Nusselt number up to 10.58 %.

On the entropy analysis for the three-dimensional magnetohydrodynamic nanofluid over a shrinking surface

Optimized heat transfer analysis is an important aspect of the study considering three-dimensional nanofluid flow when several factors contribute to their role. Here, a new statistical approach is implemented to optimize the heat transfer rate for the flow over a contracting surface. The dissipative heat, exponential heat source and the cross-diffusion effect exploring the effects of Brownian and thermophoresis encourage the heat transport properties significantly. Although the numerical technique such as shooting based Runge-Kutta fourth-order is adopted for the transformed governing equations that depend upon the suitable similarity transformations, it is important to discuss the role of various constraints on the flow profiles and the important aspect is the entropy analysis due to the flow irreversibility. A statistical approach such as “Response Surface Methodology” (RSM) is utilized for optimizing heat transfer rate caused by certain factors. The regression analysis is conducted by “Analysis of Variance” (ANOVA) and concluded that the results of the R-square value give rise to a best fit proposed model for the said problem. Finally, the important outcomes of the study are; the heat transport phenomenon is influenced by the enhanced radiating heat along with the increasing Eckert number further, dissipating heat also favors in enhancing the heat transfer rate.

Dual solutions on three-dimensional nanofluid flow and heat transfer over a permeable non-linearly shrinking surface with second-order velocity slips

PurposeThis paper aims to present the steady dual solutions on three-dimensional flow and heat transfer of nanofluid over a permeable non-linearly shrinking surface with two-order velocity slips conditions. Boundary layer assumption is considered in the mathematical modelling. Authors comprehend from previous studies and papers that the shrinking surfaces are extremely important in current engineering and environmental systems.Design/methodology/approachUsing appropriate similarity variables, the full partial differential equations (PDF) are modified into a specific set of ordinary (similar) differential equations (ODE). The resulting non-linear ordinary differential system is then solved both analytically for some particular cases and numerically for the general case using the function bvp4c from MATLAB for characteristic values of the parameters which govern the equations. The transformed mathematical model is analysed using the bvp4c procedure. Based on the given assumptions, this study is able to produce multiple solutions of the problem.FindingsThe ordinary (similarity) differential equations have two branches solutions, upper and lower branch solutions, given some interval of shrinking and velocity slip parameters. The authors consider here a temporal stability analysis, as they want to establish which of the solutions are stable and which are not. In a distinct paragraph, the authors discuss in detail and present in a graphical manner the effects of shrinking and second-order slip flow model on the skin friction coefficient, surface wall heat flux and dimensionless velocity and temperature profiles. The analysis reveals that the second order slip has a big influence on the flow and heat transfer characteristics.Originality/valueThe present discoveries are unique and truly new for the research of the three-dimensional stretching/shrinking forced convection flow and heat transfer nanofluids. The nanofluid is a water-based nanofluid (H2O), which contains one type of nanoparticles, namely, copper (Cu). Of course, the analysis can be further extended considering other types of nanoparticles such as alumina (Al2O3). The authors assume that the thermal equilibrium is reached for the base fluid together with the suspended nanoparticles and that the nanoparticles are uniform in dimension and form.

Three Dimensional Non-linear Radiative Nanofluid Flow over a Riga Plate

Numerous techniques in designing zones happen at high temperature and functions under high temperature are in a way that involves non-linear radiation. In weakly conducting fluids, however, the currents induced by an external magnetic field alone are too small, and an external electric field must be applied to achieve an efficient flow control. Gailitis and Lielausis, devised Riga plate to generate a crossed electric and magnetic fields which can produce a wall parallel Lorentz force in order to control the fluid flow. It acts as an efficient agent to reduce the skin friction. So, in this paper, we start the numerical investigation on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. To this end, the numerical investigation is conducted on the three-dimensional flow of nanofluids with the inclusion of non-linear radiation past a Riga plate. Water (H2O) and Sodium Alginate (NaC6H9O7) are the base fluids, whereas Magnetite (Fe3O4) and Aluminium oxide (Al2O3) are the nanoparticles. The mathematical formulation for Sodium Alginate base fluid is separated through the Casson model. Suitable transformations on governing partial differential equations yield strong non-linear ordinary differential equations. Numerical solutions for the renewed system are constructed by fourth-order Runge-Kutta method with shooting technique. Various deductions for flow and heat transfer attributes are sketched and discussed for various physical parameters. Furthermore, the similarities with existing results were found for the physical quantities of interest. It was discovered, that the temperature ratio parameter and the radiation parameter enhance the rate of heat transport. Moreover, the NaC6H9O7 - Al2O3 nanofluid improves the heat transfer rate. Likewise, H2O-Fe3O4 nanofluid stimulates the local skin friction coefficients.

Cubic Auto-Catalysis Reactions in Three-Dimensional Nanofluid Flow Considering Viscous and Joule Dissipations Under Thermal Jump

In this problem, simultaneous effects of Joule and viscous dissipation in three-dimensional flow of nanoliquid have been addressed in slip flow regime under time dependent rotational oscillations. Silver nanoparticles are submerged in the base fluid (water) due to their chemical and biological features. To increment the novelty, effects of cubic autocatalysis chemical reactions and radiative heat transfer have been incorporated in the related boundary layer equations. Dimensionless partial differential system is solved by employing the proposed implicit finite difference approach. Convergence conditions and stability criteria are obtained to ensure the convergence and accuracy of solutions. A comparative analysis is proposed for no-slip nanofluid flow (NSNF) and slip nanofluid flow (SNF). Variations in skin-friction coefficients, Sherwood and Nusselt numbers against physical parameters are tabulated. It is investigated that velocity slip and temperature jump significantly control drag forces and rate of heat transfer.

Three-Dimensional Nanofluid Flow with Heat and Mass Transfer Analysis over a Linear Stretching Surface with Convective Boundary Conditions

In this study, we analyzed the three-dimensional flow of Williamson (pseudoplastic) fluids upon a linear porous stretching sheet. The thermal radiation impact was taken into account. The transformed non-linear equations were solved by the homotopy analysis method (HAM). The influence of the embedded parameters tretching parameter, Williamson parameter, porosity parameter, thermal radiation parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number and Biot number are presented on velocity, temperature and concentration functions in the graphs and explained in detail. The velocity function along the x-direction reduces with the impact of the stretching, porosity and Williamson parameters. Velocity along the y-direction increases with the stretching parameter, while it reduces with the porosity and Williamson parameters. The effect of Skin friction, heat transfer and mass transfer are shown numerically. The numerical values of surface drag force and the impact of different parameters are calculated and it is observed that increasing the stretching parameter and the porosity parameter reduces the surface drag force, while increasing the Williamson parameter augments the surface drag force. Higher values of the stretching parameter, the Prandtl number and the radiation parameter enhance the heat transfer rate, while the augmented value of the thermophoresis and Brownian motion parameters reduces the heat transfer rate, where higher values of the stretching parameter, thermophoresis and Brownian motion parameters enhance the mass transfer rate.

Minimization of Entropy Production in Three Dimensional Dissipative Flow of Nanofluid with Graphene Nanoparticles: A Numerical Study

In this study we examined the entropy generation in the three-dimensional flow of nanofluid with graphene nanoparticles. Viscous heating function is added in the energy equation to study fluid frictional effects on entropy generation. The modeled equations are converted into ordinary differential equations using appropriate dimensionless quantities. Shooting technique is implemented to acquire numerical solutions. The numerical solutions are also obtained by using Matlab built-in boundary value solver bvp4c for the validation of our numerical code. The obtained results reveal that they are in good correlation. The obtained numerical results are represented by various graphs and illustrated in great detail.

Numerical study for melting heat transfer and homogeneous-heterogeneous reactions in flow involving carbon nanotubes

Abstract Present work concentrates on melting heat transfer in three-dimensional flow of nanofluid over an impermeable stretchable surface. Analysis is made in presence of porous medium and homogeneous-heterogeneous reactions. Single and multi-wall CNTs (carbon nanotubes) are considered. Water is chosen as basefluid. Adequate transformations yield the non-linear ordinary differential systems. Solution of emerging problems is obtained using shooting method. Impacts of influential variables on velocity and temperature are discussed graphically. Skin friction coefficient and Nusselt number are numerically discussed. The results for MWCNTs and SWCNTs are compared and examined.

Three-dimensional flow of nanofluid with Cattaneo–Christov double diffusion

Three dimensional (3D) boundary-layer flow of viscous nanofluid has been investigated in the presence of Cattaneo–Christov double diffusion. A bi-directional linearly stretching sheet has been used to create the flow. Thermal and concentration diffusions are characterized by introducing Cattaneo–Christov fluxes. Novel attributes regarding Brownian motion and thermophoresis are retained. The conversion of nonlinear partial differential system to nonlinear ordinary differential system is done through suitable transformations. The resulting nonlinear systems are solved. Graphs have been sketched in order to investigate that how the temperature and concentration profiles are affected by distinct physical flow parameters. Further the skin friction and heat and mass transfer rates are numerically computed and discussed. Our findings depict that temperature and concentration distributions are decreasing functions of thermal and concentration relaxation parameters.

Three-dimensional flow of nanofluid over a non-linearly stretching sheet: An application to solar energy

This work deals with the three-dimensional flow of nanofluid over an elastic sheet stretched non-linearly in two lateral directions. Suitable boundary conditions showing the power-law variation in the velocities are imposed. Further the recently suggested model for nanofluid is considered that requires nanoparticle volume fraction at the wall to be passively rather than actively controlled. A set of similarity transformations are introduced to convert the boundary layer equations into self-similar forms. The solutions have been obtained numerically through shooting method with fourth-fifth-order Runge–Kutta integration technique. The results reveal that penetration depths of temperature and nanoparticle volume fraction are decreasing functions of the power-law index. We notice that impact of Brownian motion in the temperature and heat transfer rate from the sheet is insignificant.