Simultaneous flow of ions and heat to a plate electrode in the region of natural convection

1979 ◽  
Vol 44 (6) ◽  
pp. 1857-1868 ◽  
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Natural Convection ◽  
Convective Diffusion ◽  
Navier Stokes ◽  
Exponential Polynomials ◽  
Plate Electrode ◽  
Transfer Equations ◽  
Boundary Layer Region ◽  
Layer Region

The Sherwood criterion was calculated for a flow of ions to the surface of a plate electrode during natural convection by solving the Navier-Stokes, convective diffusion, and convective heat transfer equations. The solution for the boundary layer region was performed by the collocation method using orthogonal exponential polynomials. Values of the Sh criterion were obtained for Sc ##m <500; 2 000>, Pr ##m <5; 20>, and GrT/GrM ##m <0.2; 8.0>. A comparison with literature data revealed the best agreement with average errors of +2.0 and -1.4%. Another equation with an error of only +0.5% is proposed.

scholarly journals Transport and Deposition of Large Aspect Ratio Prolate and Oblate Spheroidal Nanoparticles in Cross Flow

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 886
Author(s):  
Hans O. Åkerstedt
Keyword(s):  
Boundary Layer ◽  
Diffusion Equation ◽  
Convective Diffusion ◽  
Planck Equation ◽  
Deposition Rates ◽  
Fokker Planck Equation ◽  
Analytical Results ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Convective Diffusion Equation

The objective of this paper was to study the transport and deposition of non-spherical oblate and prolate shaped particles for the flow in a tube with a radial suction velocity field, with an application to experiments related to composite manufacturing. The transport of the non- spherical particles is governed by a convective diffusion equation for the probability density function, also called the Fokker–Planck equation, which is a function of the position and orientation angles. The flow is governed by the Stokes equation with an additional radial flow field. The concentration of particles is assumed to be dilute. In the solution of the Fokker–Planck equation, an expansion for small rotational Peclet numbers and large translational Peclet numbers is considered. The solution can be divided into an outer region and two boundary layer regions. The outer boundary layer region is governed by an angle-averaged convective-diffusion equation. The solution in the innermost boundary layer region is a diffusion equation including the radial variation and the orientation angles. Analytical deposition rates are calculated as a function of position along the tube axis. The contribution from the innermost boundary layer called steric- interception deposition is found to be very small. Higher order curvature and suction effects are found to increase deposition. The results are compared with results using a Lagrangian tracking method of the same flow configuration. When compared, the deposition rates are of the same order of magnitude, but the analytical results show a larger variation for different particle sizes. The results are also compared with numerical results, using the angle averaged convective-diffusion equation. The agreement between numerical and analytical results is good.

scholarly journals Impacts of Freezing Temperature Based Thermal Conductivity on the Heat Transfer Gradient in Nanofluids: Applications for a Curved Riga Surface

Molecules ◽  
2020 ◽  
Vol 25 (9) ◽  
pp. 2152
Author(s):  
Adnan ◽  
Syed Zulfiqar Ali Zaidi ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
Syed Tauseef Mohyud-Din ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Volume Fraction ◽  
Freezing Temperature ◽  
Effective Density ◽  
Similarity Transformations ◽  
Flow Parameters ◽  
Boundary Layer Region ◽  
Layer Region ◽  
Effective Models

The flow of nanofluid over a curved Riga surface is a topic of interest in the field of fluid dynamics. A literature survey revealed that the impacts of freezing temperature and the diameter of nanoparticles on the heat transfer over a curved Riga surface have not been examined so far. Therefore, the flow of nanoparticles, which comprises the influences of freezing temperature and nanoparticle diameter in the energy equation, was modeled over a curved Riga surface. The model was reduced successfully in the nondimensional version by implementing the feasible similarity transformations and effective models of nanofluids. The coupled nonlinear model was then examined numerically and highlighted the impacts of various flow quantities in the flow regimes and heat transfer, with graphical aid. It was examined that nanofluid velocity dropped by increasing the flow parameters γ and S, and an abrupt decrement occurred at the surface of the Riga sheet. The boundary layer region enhances for larger γ. The temperature distribution was enhanced for a more magnetized nanofluid, and the thermal boundary layer increased with a larger R parameter. The volume fraction of the nanoparticles favors the effective density and dynamic viscosity of the nanofluids. A maximum amount of heat transfer at the surface was observed for a more magnetized nanofluid.

Simultaneous mass and heat transfer to a plate electrode in the region of free convection with antiparallel fluxes of mass and heat

1983 ◽  
Vol 48 (8) ◽  
pp. 2213-2231 ◽  
Author(s):  
Petr Novák ◽  
Ivo Roušar
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Vertical Plate ◽  
Limiting Current ◽  
Navier Stokes ◽  
Plate Electrode ◽  
Criterion Equation ◽  
Transfer Equations ◽  
Current Densities ◽  
Mass And Heat Transfer

Simultaneous transfer of heat and ions to a vertical plate electrode in the region of free convection was treated mathematically by solving the Navier-Stokes, convective diffusion, and convective heat transfer equations. The direction of flow due to heat flux was considered opposite to that due to flux of ions. A criterion equation was proposed for the calculation of the Sherwood criterion with an error smaller than 2%. This was verified experimentally by measuring the limiting current densities for electrolytes containing K4Fe(CN)6 and K3Fe(CN)6 with KOH as base electrolyte.

Unsteady Natural Convection Heat Transfer Past a Vertical Flat Plate Embedded in a Porous Medium Saturated With Fractional Oldroyd-B Fluid

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
Jinhu Zhao ◽  
Liancun Zheng ◽  
Xinxin Zhang ◽  
Fawang Liu ◽  
Xuehui Chen
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Porous Medium ◽  
Natural Convection ◽  
Prandtl Number ◽  
Fractional Derivative ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Elastic Effect

This paper investigates natural convection heat transfer of generalized Oldroyd-B fluid in a porous medium with modified fractional Darcy's law. Nonlinear coupled boundary layer governing equations are formulated with time–space fractional derivatives in the momentum equation. Numerical solutions are obtained by the newly developed finite difference method combined with L1-algorithm. The effects of involved parameters on velocity and temperature fields are presented graphically and analyzed in detail. Results indicate that, different from the classical result that Prandtl number only affects the heat transfer, it has remarkable influence on both the velocity and temperature boundary layers, the average Nusselt number rises dramatically in low Prandtl number, but increases slowly with the augment of Prandtl number. The maximum value of velocity profile and the thickness of momentum boundary layer increases with the augment of porosity and Darcy number. Moreover, the relaxation fractional derivative parameter accelerates the convection flow and weakens the elastic effect significantly, while the retardation fractional derivative parameter slows down the motion and strengthens the elastic effect.

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