Influence of free convection on the diffusion current to a sphere in a laminar forced flow regime

1985 ◽  
Vol 50 (12) ◽  
pp. 2697-2714
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Asymptotic Expansion ◽  
Free Convection ◽  
Boundary Value Problem ◽  
Concentration Gradient ◽  
Empirical Formula ◽  
Convective Diffusion ◽  
Forced Flow ◽  
Diffusion Current ◽  
Wide Range ◽  
Free And Forced Convection

The formulation and solution of a boundary value problem is presented, describing the influence of the free convective diffusion on the forced one to a sphere for a wide range of Rayleigh, Ra, and Peclet, Pe, numbers. It is assumed that both the free and forced convection are oriented in the same sense. Numerical results obtained by the method of finite differences were approximated by an empirical formula based on an analytically derived asymptotic expansion for Pe → ∞. The concentration gradient at the surface and the total diffusion current calculated from the empirical formula agree with those obtained from the numerical solution within the limits of the estimated errors.

A survey on fractional asymptotic expansion method: A forgotten theory

2019 ◽  
Vol 22 (5) ◽  
pp. 1165-1176
Author(s):  
Khosro Sayevand ◽  
José A. Tenreiro Machado
Keyword(s):  
Asymptotic Expansion ◽  
Approximate Solution ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Taylor Expansion ◽  
Perturbation Technique ◽  
Expansion Method ◽  
New Method ◽  
Wide Range ◽  
Asymptotic Expansion Method

Abstract This survey applies the fractional asymptotic expansion to analyze some differential equations with boundary value problem. The method leads to the approximate solution in a wide range of applications, and avoids the limitations of algorithms based on Taylor expansion and the perturbation technique. The new method gives approximation series efficiently and overcomes the problems revealed by other analytical schemes that were proposed in the literature.

Correlations for Laminar Mixed Convection Flows on Vertical, Inclined, and Horizontal Flat Plates

1986 ◽  
Vol 108 (4) ◽  
pp. 835-840 ◽  
Author(s):  
T. S. Chen ◽  
B. F. Armaly ◽  
N. Ramachandran
Keyword(s):  
Free Convection ◽  
Mixed Convection ◽  
Forced Flow ◽  
Flat Plates ◽  
Maximum Increase ◽  
Nusselt Numbers ◽  
Laminar Mixed Convection ◽  
Wide Range ◽  
Flow Configurations ◽  
Prandtl Numbers

Local Nusselt numbers for laminar mixed convection flows along isothermal vertical, inclined, and horizontal flat plates are presented for the entire mixed convection regime for a wide range of Prandtl numbers, 0.1 ≤ Pr ≤ 100. Simple correlation equations for the local and average mixed convection Nusselt numbers are developed, which are found to agree well with the numerically predicted values and available experimental data for both buoyancy assisting and opposing flow conditions. The threshold values of significant buoyancy effects on forced convection and forced flow effects on free convection, as well as the maximum increase in the local mixed convection Nusselt number from the respective pure convection limits, are also presented for all flow configurations. It is found that the buoyancy or forced flow effect can increase the surface heat transfer rate from pure forced or pure free convection by about 20 percent.

Combined Free and Forced Convection in a Horizontal Circular Tube

1966 ◽  
Vol 88 (2) ◽  
pp. 147-152 ◽  
Author(s):  
S. T. McComas ◽  
E. R. G. Eckert
Keyword(s):  
Free Convection ◽  
Forced Convection ◽  
Reynolds Numbers ◽  
Forced Flow ◽  
Appreciable Effect ◽  
Fluid Temperature ◽  
Bulk Fluid ◽  
Grashof Number ◽  
Free And Forced Convection ◽  
Flow Heat

The effect of free convection on laminar forced flow heat transfer in a horizontal uniformly heated tube was investigated. The Grashof number was varied from 1000 down to the order of one, the low Grashof number runs agreeing with the prediction for pure forced convection within ±8 percent. The effect of the secondary flow created by free convection was observed as a decrease in the wall to bulk fluid temperature difference required to transfer heat as compared to the pure forced flow case in the region far from the tube inlet. This effect was found to increase as the ratio of Grashof number to Reynolds numbers increased. No appreciable effect of free convection was found in the thermal development region.

Combining Forced and Free Convective Equations to Represent Combined Heat-Transfer Coefficients for a Horizontal Cylinder

1971 ◽  
Vol 93 (2) ◽  
pp. 247-248 ◽  
Author(s):  
Thomas W. Jackson ◽  
Howard H. Yen
Keyword(s):  
Free Convection ◽  
Forced Convection ◽  
Horizontal Cylinder ◽  
Forced Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Simplified Method ◽  
Analytical Correlation ◽  
Free And Forced Convection ◽  
Simple Systems

An analytical correlation of superposed free and forced convection for air for a horizontal cylinder in which the forced convection and free convection forces act in the same direction is considered. A simplified method by which the ordinary formulas for forced convection and for free convection can be used together to give the Nusselt number is presented. The method proposed herein can easily be modified to work for other combinations of free and forced flow systems. The method, therefore, may have wide application because standard formulas for simple systems are easily combined to obtain formulas which are valid for complicated systems.

Compact Modeling of Forced Flow in Longitudinal Fin Heat Sinks With Tip Bypass

2003 ◽  
Vol 125 (3) ◽  
pp. 319-324 ◽  
Author(s):  
C. B. Coetzer ◽  
J. A. Visser
Keyword(s):  
Pressure Drop ◽  
Heat Sink ◽  
Heat Sinks ◽  
Compact Model ◽  
Forced Flow ◽  
Compact Modeling ◽  
Transfer Coefficients ◽  
Wide Range ◽  
Laminar And Turbulent Flow ◽  
Improved Accuracy

This paper introduces a compact model to predict the interfin velocity and the resulting pressure drop across a longitudinal fin heat sink with tip bypass. The compact model is based on results obtained from a comprehensive study into the behavior of both laminar and turbulent flow in longitudinal fin heat sinks with tip bypass using CFD analysis. The new compact flow prediction model is critically compared to existing compact models as well as to the results obtained from the CFD simulations. The results indicate that the new compact model shows at least a 4.5% improvement in accuracy predicting the pressure drop over a wide range of heat sink geometries and Reynolds numbers simulated. The improved accuracy in velocity distribution between the fins also increases the accuracy of the calculated heat transfer coefficients applied to the heat sinks.

scholarly journals Two conjugate convection boundary-layers of counter forced flow

2018 ◽  
Vol 22 (2) ◽  
pp. 835-846
Author(s):  
Mohamed Mosaad
Keyword(s):  
Heat Transfer ◽  
Boundary Layers ◽  
Conjugate Heat Transfer ◽  
Transfer Problem ◽  
Forced Flow ◽  
Relative Importance ◽  
Counter Flow ◽  
Wide Range ◽  
Convection Boundary ◽  
Laminar Forced Convection

In this study, the conjugate heat transfer problem of two laminar forced convection boundary-layers of counter flow on the opposite sides of a conductive wall is analyzed by employing the integral method. The analysis is conducted in a dimensionless framework to generalize the solution. The dimensionless parameters affecting the thermal interaction between the two convection layers are deduced from the analysis. These parameters give a measure of the relative importance of interactive heat transfer modes. Mean Nusselt number data are obtained for a wide range of the main affecting parameters.

scholarly journals The first boundary value problem of the dynamics of an anisotropic elastic half-space under the action of subsonic transport loads

2020 ◽  
Vol 4 (78) ◽  
pp. 45-52
Author(s):  
G. K. ZAKIR’YANOVA ◽  
◽  
L. A. ALEXEYEVA ◽  
Keyword(s):  
Rock Mass ◽  
Boundary Value Problem ◽  
Half Space ◽  
Wide Class ◽  
Boundary Value ◽  
Operator Method ◽  
Elastic Half Space ◽  
Theory Of Elasticity ◽  
Wide Range ◽  
Anisotropic Elastic

The first boundary value problem of the theory of elasticity for an anisotropic elastic half-space is solved when a transport load moves along its surface. The subsonic Raleigh case is considered, when the velocity of motion is less than the velocity of propagation of bulk and surface elastic waves. The Green’s tensor of the transport boundary value problem is constructed and on its basis the solution of boundary value problems for a wide class of distributed traffic loads is given. To solve the problem, the methods of tensor and linear algebra, integral Fourier transform, and operator method for solving systems of differential equations were used. The obtained solution makes it possible to investigate the dynamics of the rock mass for a wide class of transport loads, in a wide range of velocities, both low velocities and high velocities, and to evaluate the strength properties of the rock mass under the influence of road transport. In particular, determine the permissible velocities of its movement and carrying capacity. In addition, a investigation on its basis of the movement of the day surface along the route will make it possible to establish criteria for the seismic resistance of ground structures and the permissible distances of their location from the route.

scholarly journals Interpolation of Boundary Condition at Time-Interval of Unknown Lenghth for the Problem of Convective Diffusion in a Three-Layered Water Filter

2019 ◽  
pp. 25-28
Author(s):  
Olha Chernukha ◽  
Yurii Bilushchak
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Mass Transfer ◽  
Boundary Condition ◽  
Boundary Value Problem ◽  
Convective Diffusion ◽  
Lower Boundary ◽  
Time Interval ◽  
Water Filter ◽  
The Right

On the basis of mathematical model of convectivediffusion in a three-layered filter it is formulated a contactinitial-boundary value problem for description of mass transferof pollution accompanying the sorption processes. It is proposedthe algorithm for establishing the estimation of values of soughtfunction (concentration of pollution) at the lower boundary of thefilter on the basis of the interpolation of experimental data. It istaken into account that the right end of the interpolation segmentis unknown. It is determined the exact solutions of contact-initialboundaryvalue problems of mass transfer with provision forboth diffusive and convective mechanisms of transfer as well assorption processes, which is based on integral transformationsover space variables in the contacting regions. Is it designedsoftware and established regularities of convective diffusionprocess in the three-layered filter.

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