A Similarity Solution for Mixed-Convection Boundary Layer Nanofluid Flow on an Inclined Permeable Surface

2017 ◽  
Vol 9 (2) ◽  
Author(s):  
Masoud Ziaei-Rad ◽  
Abbas Kasaeipoor ◽  
Mohammad Mehdi Rashidi ◽  
Giulio Lorenzini
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Base Fluid ◽  
Volume Fraction ◽  
Nanofluid Flow ◽  
Wall Suction ◽  
Surface Angle

This paper concerns with calculation of heat transfer and pressure drop in a mixed-convection nanofluid flow on a permeable inclined flat plate. Solution of governing boundary layer equations is presented for some values of injection/suction parameter (f0), surface angle (γ), Galileo number (Ga), mixed-convection parameter (λ), volume fraction (φ), and type of nanoparticles. The numerical outcomes are presented in terms of average skin friction coefficient (Cf) and Nusselt number (Nu). The results indicate that adding nanoparticles to the base fluid enhances both average friction factor and Nusselt number for a wide range of other effective parameters. We found that for a nanofluid with φ = 0.6, injection from the wall (f0 = −0.2) offers an enhancement of 30% in Cf than the base fluid, while this growth is about 35% for the same case with wall suction (f0 = 0.2). However, increasing the wall suction will linearly raise the heat transfer rate from the surface, similar for all range of nanoparticles volume fraction. The computations also showed that by changing the surface angle from horizontal state to 60 deg, the friction factor becomes 2.4 times by average for all φ's, while 25% increase yields in Nusselt number for the same case. For assisting flow, there is a favorable pressure gradient due to the buoyancy forces, which results in larger Cf and Nu than in opposing flows. We can also see that for all φ values, enhancing Ga/Re2 parameter from 0 to 0.005 makes the friction factor 4.5 times, while causes 50% increase in heat transfer coefficient. Finally, we realized that among the studied nanoparticles, the maximum influence on the friction and heat transfer belongs to copper nanoparticles.

Effect of Nanofluid on Heat Transfer Enhancement for Mixed Convection Flow Over a Corrugated Surface

2020 ◽  
Vol 45 (4) ◽  
pp. 373-383
Author(s):  
Nepal Chandra Roy ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Thermal Boundary Layer ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow

AbstractA mathematical model for mixed convection flow of a nanofluid along a vertical wavy surface has been studied. Numerical results reveal the effects of the volume fraction of nanoparticles, the axial distribution, the Richardson number, and the amplitude/wavelength ratio on the heat transfer of Al2O3-water nanofluid. By increasing the volume fraction of nanoparticles, the local Nusselt number and the thermal boundary layer increases significantly. In case of \mathrm{Ri}=1.0, the inclusion of 2 % and 5 % nanoparticles in the pure fluid augments the local Nusselt number, measured at the axial position 6.0, by 6.6 % and 16.3 % for a flat plate and by 5.9 % and 14.5 %, and 5.4 % and 13.3 % for the wavy surfaces with an amplitude/wavelength ratio of 0.1 and 0.2, respectively. However, when the Richardson number is increased, the local Nusselt number is found to increase but the thermal boundary layer decreases. For small values of the amplitude/wavelength ratio, the two harmonics pattern of the energy field cannot be detected by the local Nusselt number curve, however the isotherms clearly demonstrate this characteristic. The pressure leads to the first harmonic, and the buoyancy, diffusion, and inertia forces produce the second harmonic.

Study of the boundary layer heat transfer of nanofluids over a stretching sheet: Passive control of nanoparticles at the surface

2015 ◽  
Vol 93 (7) ◽  
pp. 725-733 ◽  
Author(s):  
M. Ghalambaz ◽  
E. Izadpanahi ◽  
A. Noghrehabadi ◽  
A. Chamkha
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Heat Transfer Enhancement ◽  
Base Fluid ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Enhancement Ratio ◽  
Transfer Enhancement

The boundary layer heat and mass transfer of nanofluids over an isothermal stretching sheet is analyzed using a drift-flux model. The relative slip velocity between the nanoparticles and the base fluid is taken into account. The nanoparticles’ volume fractions at the surface of the sheet are considered to be adjusted passively. The thermal conductivity and the dynamic viscosity of the nanofluid are considered as functions of the local volume fraction of the nanoparticles. A non-dimensional parameter, heat transfer enhancement ratio, is introduced, which shows the alteration of the thermal convective coefficient of the nanofluid compared to the base fluid. The governing partial differential equations are reduced into a set of nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using the fourth-order Runge–Kutta and Newton–Raphson methods along with the shooting technique. The effects of six non-dimensional parameters, namely, the Prandtl number of the base fluid Prbf, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, variable thermal conductivity parameter Nc and the variable viscosity parameter Nv, on the velocity, temperature, and concentration profiles as well as the reduced Nusselt number and the enhancement ratio are investigated. Finally, case studies for Al2O3 and Cu nanoparticles dispersed in water are performed. It is found that increases in the ambient values of the nanoparticles volume fraction cause decreases in both the dimensionless shear stress f″(0) and the reduced Nusselt number Nur. Furthermore, an augmentation of the ambient value of the volume fraction of nanoparticles results in an increase the heat transfer enhancement ratio hnf/hbf. Therefore, using nanoparticles produces heat transfer enhancement from the sheet.

Laminar Mixed Convection Nanofluids Flow in a Elliptic Duct Using Two Phase Approach

2011 ◽  
Author(s):  
A. Akbarinia ◽  
M. Shariat ◽  
R. Laur
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Friction Factor ◽  
Skin Friction ◽  
Volume Fraction ◽  
Nanofluid Flow ◽  
Two Phase ◽  
Local Skin ◽  
Laminar Mixed Convection ◽  
Mean Diameter

Laminar mixed convection Al2O3-Water nanofluid flow in elliptic ducts with constant heat flux boundary condition has been simulated employing two phase mixture model. Three-dimensional Navier-Stokes, energy and volume fraction equations have been discretized using the Finite Volume Method (FVM). The Brownian motions of nanoparticles have been considered to determine the thermal conductivity and dynamics viscosity of Al2O3-Water nanofluid, which vary with temperature. Simulation effects of solid volume fraction and nanoparticles mean diameter on thermal and hydraulics behaviors of nanofluid flow in elliptic ducts have been presented and discussed. The calculated results show good agreement with the previous numerical data. Results show that in a given Reynolds number (Re) and Richardson number (Ri), increasing solid nanoparticles volume fraction increases the Nusselt number (Nu) while the skin friction factor decreases. Increasing nanoparticles mean diameter augments the local skin friction factor whereas it causes the Nusselt number to reduce. But these effects are significant for nanoparticles diameter equal to 13nm especially.

scholarly journals Effects of a Rotating Cone on the Mixed Convection in a Double Lid-Driven 3D Porous Trapezoidal Nanofluid Filled Cavity under the Impact of Magnetic Field

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 449 ◽  
Author(s):  
Ali J. Chamkha ◽  
Fatih Selimefendigil ◽  
Hakan F. Oztop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Mixed Convection ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Rotational Velocity ◽  
Rotating Cone ◽  
The Impact

Effects of a rotating cone in 3D mixed convection of CNT-water nanofluid in a double lid-driven porous trapezoidal cavity is numerically studied considering magnetic field effects. The numerical simulations are performed by using the finite element method. Impacts of Richardson number (between 0.05 and 50), angular rotational velocity of the cone (between −300 and 300), Hartmann number (between 0 and 50), Darcy number (between 10 − 4 and 5 × 10 − 2 ), aspect ratio of the cone (between 0.25 and 2.5), horizontal location of the cone (between 0.35 H and 0.65 H) and solid particle volume fraction (between 0 and 0.004) on the convective heat transfer performance was studied. It was observed that the average Nusselt number rises with higher Richardson numbers for stationary cone while the effect is reverse for when the cone is rotating in clockwise direction at the highest supped. Higher discrepancies between the average Nusselt number is obtained for 2D cylinder and 3D cylinder configuration which is 28.5% at the highest rotational speed. Even though there are very slight variations between the average Nu values for 3D cylinder and 3D cone case, there are significant variations in the local variation of the average Nusselt number. Higher enhancements in the average Nusselt number are achieved with CNT particles even though the magnetic field reduced the convection and the value is 84.3% at the highest strength of magnetic field. Increasing the permeability resulted in higher local and average heat transfer rates for the 3D porous cavity. In this study, the aspect ratio of the cone was found to be an excellent tool for heat transfer enhancement while 95% enhancements in the average Nusselt number were obtained. The horizontal location of the cone was found to have slight effects on the Nusselt number variations.

CFD Investigation of Al2O3 Nanoparticles Effect on Heat Transfer Enhancement of Newtonian and Non-Newtonian Fluids in a Helical Coil

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Javad Aminian Dehkordi ◽  
Arezou Jafari
Keyword(s):  
Heat Transfer ◽  
Aqueous Solution ◽  
Nusselt Number ◽  
Base Fluid ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Helical Coil ◽  
Al2o3 Nanoparticles ◽  
Nanoparticles Volume Fraction ◽  
Computational Fluid Dynamics Cfd

Abstract The present study applied computational fluid dynamics (CFD) to investigate the heat transfer of Newtonian (water) and non-Newtonian (0.3 %wt. aqueous solution of carboxymethylcellulose (CMC)) fluids in the presence of Al2O3 nanoparticles. To analyze the heat transfer rate, investigations were performed in a vertical helical coil as essential heat transfer equipment, at different inlet Reynolds numbers. To verify the accuracy of the simulation model, experimental data reported in the literature were employed. Comparisons showed the validity of simulation results. From the results, compared to the aqueous solution of CMC, water had a higher Nusselt number. In addition, it was observed that adding nanoparticles to a base fluid presented different results in which water/Al2O3 nanofluid with nanoparticles’ volume fraction of 5 % was more effective than the same base fluid with a volume fraction of 10 %. In lower ranges of Reynolds number, adding nanoparticles was more effective. For CMC solution (10 %), increasing concentration of nanoparticles caused an increase in the apparent viscosity. Consequently, the Nusselt number was reduced. The findings reveal the important role of fluid type and nanoparticle concentration in the design and development of heat transfer equipment.

The effect of viscous dissipation on laminar nanofluid flow in a microchannel heat sink

2009 ◽  
Vol 223 (11) ◽  
pp. 2697-2706 ◽  
Author(s):  
M Ghazvini ◽  
M A Akhavan-Behabadi ◽  
M Esmaeili
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Heat Sink ◽  
Volume Fraction ◽  
Numerical Study ◽  
Microchannel Heat Sink ◽  
Fluid Temperature ◽  
Nanofluid Flow ◽  
Aspect Ratios

The present article focuses on analytical and numerical study on the effect of viscous dissipation when nanofluid is used as the coolant in a microchannel heat sink (MCHS). The nanofluid is made from CuO nanoparticles and water. To analyse the MCHS, a modified Darcy equation for the fluid and two-equation model for heat transfer between fluid and solid sections are employed in porous media approach. In addition, to deal with nanofluid heat transfer, a model based on the Brownian motion of nanoparticles is used. The model evaluates the thermal conductivity of nanofluid considering the thermal boundary resistance, nanoparticle diameter, volume fraction, and the fluid temperature. At first, the effects of particle volume fraction on temperature distribution and overall heat transfer coefficient are investigated with and without considering viscous dissipation. After that, the influence of different channel aspect ratios and porosities is studied. The results show that for nanofluid flow in microchannels, the viscous dissipation can be neglected for low volume fractions and aspect ratios only. Finally, the effect of porosity and Brinkman number on the overall Nusselt number is studied, where asymptotic behaviour of the Nusselt number is observed and discussed from the energy balance point of view.

Impact of Stretching and Penetration of Walls on Nanofluid Flow and Heat Transfer in a Rotating System

2018 ◽  
Vol 387 ◽  
pp. 37-50 ◽  
Author(s):  
A.S. Dogonchi ◽  
D.D. Ganji ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Heat Source ◽  
Volume Fraction ◽  
Radiation Parameter ◽  
Rotating System ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer

Nanofluid flow and heat transfer in a rotating system between two parallel plates in the presence of thermal radiation and heat source impacts are examined. One of the plates of the considered system is penetrable and the other one is stretchable or shrinkable. A similarity transformation is used to convert the governing momentum and energy equations into non-linear ordinary differential equations with the relevant boundary conditions. The achieved non-linear ordinary differential equations are solved by Duan-Rach Approach (DRA). This method allows us to realize a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the stretching/shrinking parameter, the radiation parameter, the heat source parameter, the suction/blowing parameter, the Reynolds number and the volume fraction of nanofluid on the velocity and temperature profiles are explored. Also, the correlation for the Nusselt number has been developed in terms of active parameters of the present study. The outcomes indicate that the Nusselt number is a raising function of the injection parameter, nanofluid volume fraction and the radiation parameter, while it is a decreasing function of the suction and heat source parameters. Furthermore, for injection case by soaring the shrinking parameter, the probability of occurrence of the backflow phenomenon soars.

scholarly journals Marangoni Mixed Convection Boundary Layer Flow in a Nanofluid

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Amirah Remeli ◽  
Norihan Md Arifin ◽  
Roslinda Nazar ◽  
Fudziah Ismail
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Immiscible Fluids ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

The problem of Marangoni mixed convection boundary layer flow and heat transfer that can be formed along the interface of two immiscible fluids in a nanofluid is studied using different types of nanoparticles. Numerical solutions of the similarity equations are obtained using the shooting method. Three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (23AlO) and titania (2TiO) are consideredby using a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter ϕ of the nanofluid. The influences of the interest parameters on the reduced velocity along the interface, velocity profiles as well as the reduced heat transfer at the interface and temperature profiles were presented in tables and figures.

Effect of non-uniform heating on conjugate heat transfer performance for nanofluid flow in a converging duct by a two-phase Eulerian–Lagrangian method

2021 ◽  
pp. 095440892110429
Author(s):  
Md. Faizan ◽  
Sukumar Pati ◽  
Pitamber R Randive
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Volume Fraction ◽  
Constant Heat Flux ◽  
Lagrangian Model ◽  
Uniform Heating ◽  
Nanofluid Flow ◽  
Two Phase

In this paper, the effect of non-uniform heating on the conjugate thermal and hydraulic characteristics for Al2O3–water nanofluid flow through a converging duct is examined numerically. An Eulerian–Lagrangian model is employed to simulate the two-phase flow for the following range of parameters: Reynolds number (100 ≤ Re ≤ 800), nanoparticle volume fraction (0% ≤  ϕ ≤ 5%) and amplitude of the sinusoidal heat flux ( A = 0, 0.5 and 1). The results reveal a similar affinity between the applied heat flux and local Nusselt number variation qualitatively, mainly at the middle of the duct. The results also indicate that there is a considerable enhancement of Nusselt number with the increase in Reynolds number and the thermal conductivity of wall materials. In addition, increasing the particle loading contributes to an enhanced rate of heat transfer. The heat transfer rate is lower for non-uniform heating when compared with the constant heat flux and the same can be compensated by the application of volume fraction of nanoparticles

Laminar Mixed Convection of Non-Newtonian Nanofluids Flowing Vertically Upward Across a Confined Circular Cylinder

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Abhipsit Kumar Singh ◽  
Nanda Kishore
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Numerical Results ◽  
Total Drag ◽  
Drag Coefficients

Numerical results on laminar mixed convective heat transfer phenomenon between a confined circular cylinder and shear-thinning type nanofluids are presented. The cylinder is placed horizontally in a confined channel through which nanofluids flow vertically upward. The effect of buoyancy is same as the direction of the flow. Because of existence of mixed convection, governing continuity, momentum, and energy equations are simultaneously solved within the limitations of Boussinesq approximation. The ranges of parameters considered are: volume fraction of nanoparticles, ϕ = 0.005–0.045; Reynolds number, Re = 1–40; Richardson number, Ri = 0–40; and confinement ratio of circular cylinder, λ = 0.0625–0.5. Finally, the effects of these parameters on the streamlines, isotherm contours, individual and total drag coefficients, and local and average Nusselt numbers are thoroughly delineated. The individual and total drag coefficients decrease with the increasing both ϕ and Re; and/or with the decreasing both Ri and λ. The rate of heat transfer increases with the increasing Re, ϕ, Ri, and λ; however, at Re = 30–40, when ϕ > 0.005 and Ri < 2, the average Nusselt number decreases with the increasing Richardson number. Finally, correlations for the total drag coefficient and average Nusselt number are proposed as functions of pertinent dimensionless parameters on the basis of present numerical results.

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