Transient two-dimensional natural convection flow of a nanofluid past an isothermal vertical plate using Buongiorno’s model

2017 ◽  
Vol 27 (1) ◽  
pp. 23-47 ◽  
Author(s):  
Marneni Narahari ◽  
Suresh Kumar Raju Soorapuraju ◽  
Rajashekhar Pendyala ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Natural Convection ◽  
Vertical Plate ◽  
Volume Fraction ◽  
Convection Flow ◽  
Nanoparticle Volume Fraction ◽  
Natural Convection Flow ◽  
Content Type

Purpose The purpose of this paper is to present a numerical investigation of the transient two-dimensional natural convective boundary-layer flow of a nanofluid past an isothermal vertical plate by incorporating the effects of Brownian motion and thermophoresis in the mathematical model. Design/methodology/approach The problem is formulated using the Oberbeck–Boussinesq and the standard boundary-layer approximations. The governing coupled non-linear partial differential equations for conservation of mass, momentum, thermal energy and nanoparticle volume fraction have been solved by using an efficient implicit finite-difference scheme of the Crank–Nicolson type, which is stable and convergent. Numerical computations are performed and the results for velocity, temperature and nanoparticle volume fraction are presented in graphs at different values of system parameters such as Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number, Lewis number and dimensionless time. The results for local and average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. Findings It is found that the velocity, temperature and nanoparticle volume fraction profiles enhance with respect to time and attain steady-state values as time progresses. The local Nusselt number is found to decrease with increasing thermophoresis parameter, while it increases slightly with increasing Brownian motion parameter. To validate the present numerical results, the steady-state local Nusselt number results for the limiting case of a regular fluid have been compared with the existing well-known results at different Prandtl numbers, and the results are found to be in an excellent agreement. Research limitations/implications The present analysis is limited to the transient laminar natural convection flow of a nanofluid past an isothermal semi-infinite vertical plate in the absence of viscous dissipation and thermal radiation. The unsteady natural convection flow of a nanofluid will be investigated for various physical conditions in a future work. Practical implications Unsteady flow devices offer potential performance improvements as compared with their steady-state counterparts, and the flow fields in the unsteady flow devices are typically transient in nature. The present study provides very useful information for heat transfer engineers to understand the heat transfer enhancement with the nanofluid flows. The present results have immediate relevance in cooling technologies. Originality/value The present research work is relatively original and illustrates the transient nature of the natural convective nanofluid boundary-layer flow in the presence of Brownian motion and thermophoresis.

Natural convection flow in a vertical micro-annulus with time-periodic thermal boundary conditions

2018 ◽  
Vol 14 (5) ◽  
pp. 1064-1081
Author(s):  
Basant Kumar Jha ◽  
Michael O. Oni
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
The Impact ◽  
Time Periodic

PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

MHD natural convection flow in cavities filled with square solid blocks

2014 ◽  
Vol 24 (8) ◽  
pp. 1813-1830 ◽  
Author(s):  
Majid Ashouri ◽  
Mohammad Behshad Shafii ◽  
Hossein Rajabi Kokande
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Code ◽  
Thermal Conductivity Ratio ◽  
Convection Flow ◽  
Conductivity Ratio ◽  
Natural Convection Flow ◽  
Content Type

Purpose – The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks. Design/methodology/approach – The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works. Findings – The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks. Originality/value – No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

Unsteady natural convection flow of a rotating fluid past an exponential accelerated vertical plate with Hall current, ion-slip and magnetic effect

2018 ◽  
Vol 14 (2) ◽  
pp. 216-235 ◽  
Author(s):  
Jitendra Kumar Singh ◽  
Srinivasa C.T.
Keyword(s):  
Natural Convection ◽  
Closed Form ◽  
Vertical Plate ◽  
Hall Current ◽  
Convection Flow ◽  
Rotating Fluid ◽  
Natural Convection Flow ◽  
Content Type ◽  
Ion Slip ◽  
Unsteady Natural Convection

PurposeThe purpose of this paper is to deal with an unsteady natural convection flow of a rotating fluid past an exponential accelerated vertical plate. The effect of Hall current, ion-slip and magnetic field is considered. Two types of plate temperature, namely, uniform and ramped temperature are considered to model heat transfer analysis.Design/methodology/approachThe Laplace transform technique is employed to find the closed form solutions for velocity, temperature and concentration.FindingsThe effects of flow governing parameters on the velocity profile, temperature profile, concentration profile, skin friction, Nusselt and Sherwood numbers are discussed and presented through graphs and tables. It is found that fluid velocity in the primary flow direction decreases with the increase in the magnetic parameter.Originality/valueFirst time in the literature, the authors obtained closed form solution to natural convection flow of a rotating fluid past an exponential accelerated vertical plate.

Two-phase natural convection flow of a dusty fluid

2015 ◽  
Vol 25 (7) ◽  
pp. 1542-1556 ◽  
Author(s):  
Sadia Siddiqa ◽  
M. Anwar Hossain ◽  
Suvash C Saha
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Prandtl Number ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Two Phase ◽  
Metal Mixture ◽  
Content Type ◽  
Dusty Fluid ◽  
Wide Range

Purpose – The purpose of this paper is to conduct a detailed investigation of the two-dimensional natural convection flow of a dusty fluid. Therefore, the incompressible boundary layer flow of a two-phase particulate suspension is investigated numerically over a semi-infinite vertical flat plate. Comprehensive flow formations of the gas and particle phases are given in the boundary layer region. Primitive variable formulation is employed to convert the nondimensional governing equations into the non-conserved form. Three important two-phase mechanisms are discussed, namely, water-metal mixture, oil-metal mixture and air-metal mixture. Design/methodology/approach – The full coupled nonlinear system of equations is solved using implicit two point finite difference method along the whole length of the plate. Findings – The authors have presented numerical solution of the dusty boundary layer problem. Solutions obtained are depicted through the characteristic quantities, such as, wall shear stress coefficient, wall heat transfer coefficient, velocity distribution and temperature distribution for both phases. Results are interpreted for wide range of Prandtl number Pr (0.005-1,000.0). It is observed that thin boundary layer structures can be formed when mass concentration parameter or Prandtl number (e.g. oil-metal particle mixture) are high. Originality/value – The results of the study may be of some interest to the researchers of the field of chemical engineers.

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.

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