Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus With Periodic Heat Generation

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Natural Convection ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio ◽  
Periodic Heat

We consider the two-dimensional problem of steady natural convection in a narrow horizontal cylindrical annulus filled with porous medium due to a constant temperature variation on the outer and at the inner boundaries with periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of two, and Rayleigh number. The series is extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small, but Pade approximation leads our results to be good even for much higher value of the similarity parameter.

Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus With Constant Heat Generation

2010 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Natural Convection ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Constant Heat ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow horizontal cylindrical annulus filled with porous medium due to a constant temperature variation on the outer and adiabatic conditions at the inner boundaries with constant volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the gap ratio to the power of two, and Rayleigh number. The series is extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small, but Pade approximation leads our results to be good even for much higher value of the similarity parameter.

Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus With Constant Volumetric Heat Flux

2008 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow Horizontal Cylindrical annulus filled with porous medium due to a constant temperature variation on the outer and adiabatic conditions at the inner boundaries with constant volumetric heat flux The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of two, and Rayleigh number. The series is extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small, but Pade approximation leads our results to be good even for much higher value of the similarity parameter.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Periodic Volumetric Heat Flux

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) Horizontal Cylindrical annulus filled with viscous fluid and periodic volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus With Linear Heat Generation

2011 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Heat Generation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio ◽  
Volumetric Heat Generation

We consider the two-dimensional problem of steady natural convection in a narrow (micro) horizontal cylindrical annulus filled with porous medium due with linear volumetric heat generation. The solution is expanded in powers of a single combined similarity parameter, which is the product of the gap ratio to the power of two, and Rayleigh number. The series is extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small, but pade approximation leads our results to be good even for much higher value of the similarity parameter.

Natural Convection in a Micro Size Horizontal Cylindrical Annulus With Constant Volumetric Heat Flux

2008 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Viscous Fluid ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Grashof Number ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow (Micro size) horizontal cylindrical annulus filled with viscous fluid and constant volumetric heat flux. The solution is expanded in powers of a single combined similarity parameter, which is the product of the gap ratio to the power of four, and Grashof number and the series extended by means of symbolic calculation up to 14 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

The Adiabatic Conditions on Inner Boundary for Natural Convection With Porous Medium in a Narrow Horizontal Cylindrical Annulus

2007 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Adiabatic Conditions ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow Horizontal Cylindrical annulus filled with porous medium due to a cosine temperature variation on the outer and adiabatic conditions at the inner boundaries The solution is expanded in powers of a single combined similarity parameter, which is the product of the Gap ratio to the power of two and Rayleigh number and the series extended by means of symbolic calculation up to 28 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but Pade approximation leads our result to be good even for much higher value of the similarity parameter.

Using Symbolic Calculation for Solving Natural Convection in a Narrow Horizontal Cylindrical Annulus

2005 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Viscous Fluid ◽  
Temperature Variation ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Cylindrical Annulus ◽  
Gap Ratio

We consider the two-dimensional problem of steady natural convection in a narrow Horizontal Cylindrical annulus filled with viscous fluid due to a sine temperature variation on the outer and adiabatic conditions at the inner boundaries. The solution is expanded in powers of a single combined similarity parameter introduced by [1], which is the product of the Gap ratio to the power of four, and Rayleigh number and the series extended by means of symbolic calculation up to 16 terms. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is almost zero but Pade approximation lead our result to be good even for much higher value of the similarity parameter.

Symbolic Calculation for Free Convection in a Circular Cavity With Periodic Heat Generation

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Free Convection ◽  
Heat Generation ◽  
Circular Cavity ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Periodic Heat

We consider the two-dimensional problem of steady natural convection in a circular cavity with periodic heat generation filled with viscous fluid subject to cosine temperature variation on the boundary. The solution is expanded for low Rayleigh number and extended to 16 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but pade approximation leads our result to be good even for higher value of the similarity parameter.

Symbolic Calculation for Free Convection in a Circular Cavity With Porous Material

2009 ◽  
Author(s):  
Kamyar Mansour
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Porous Material ◽  
Dimensionless Parameter ◽  
Circular Cavity ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Similarity Parameter ◽  
Symbolic Calculation ◽  
Darcy Rayleigh Number

We consider the two-dimensional problem of steady natural convection in a circular cavity filled with porous material due to a cosine temperature variation on the boundary. We use Darcy’s law for this cavity filled with porous material. The solution is governed by dimensionless parameter Darcy-Rayleigh number. The solution is expanded for low Darcy-Rayleigh number and extended to 18 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50000 figures. Although the range of the radius of convergence is small but Pade approximation leads our result to be good even for higher value of the similarity parameter.

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