Convective Thermal Flow - Revision history

Saak at 08:23, 3 July 2025

2025-07-03T08:23:42Z

← Older revision		Revision as of 08:23, 3 July 2025
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	\|noutputs = 5		\|noutputs = 5
	\|nparameters = 0		\|nparameters = 0
	\|components = A, B, C		\|components = A, B, C, E
	\|License = NA		\|License = NA
	\|Creator = ~~[[User:Himpe]]~~		\|Creator = C. Moosmann, E.B. Rudnyi, A. Greiner, J.G. Korvink
	\|Editor =		\|Editor =
	* [[User:Himpe]]		* [[User:Himpe]]

Schuetz2 at 05:26, 12 June 2025

2025-06-12T05:26:55Z

← Older revision		Revision as of 05:26, 12 June 2025
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	title = {Convective Thermal Flow},		title = {Convective Thermal Flow},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Convection}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Convection}</nowiki>,
	year = {2018}		year = {2018}
	}		}

Saak at 15:31, 10 September 2024

2024-09-10T15:31:14Z

← Older revision		Revision as of 15:31, 10 September 2024
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	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{http://modelreduction.org/index.php/Convection}</nowiki>,		url = <nowiki>{http://modelreduction.org/index.php/Convection}</nowiki>,
	year = {~~20XX~~}		year = {2018}
	}		}

Malhotra: infobox string

2023-11-30T09:29:32Z

infobox string

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 [[Category:MIMO]]
 [[Category:sparse]]
 ==Description: Convective Thermal Flow Problems==

Mlinaric: Add categories, small fixes

2023-09-01T18:26:16Z

Add categories, small fixes

← Older revision		Revision as of 18:26, 1 September 2023
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	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:Oberwolfach]]		[[Category:Oberwolfach]]
			[[Category:linear]]
			[[Category:time invariant]]
			[[Category:first differential order]]
			[[Category:MIMO]]
			[[Category:sparse]]

	==Description: Convective Thermal Flow Problems==		==Description: Convective Thermal Flow Problems==
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	Triangular <tt>PLANE55</tt> elements have been used for meshing and discretizing by the finite element method, resulting in 19282 elements and 9710 nodes.		Triangular <tt>PLANE55</tt> elements have been used for meshing and discretizing by the finite element method, resulting in 19282 elements and 9710 nodes.
	The second design is a 3D model of a chip cooled by forced convection (Fig. 2) <ref name="harper1997"/>.		The second design is a 3D model of a chip cooled by forced convection (Fig. 2) <ref name="harper1997"/>.
	In this case the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.		In this case, the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.
	Since the implementation of the convective term in ANSYS does not allow defining the fluid speed on a per element basis but on a per region one, the flow profile has to be approximated by piece-wise step functions.		Since the implementation of the convective term in ANSYS does not allow defining the fluid speed on a per-element basis but on a per-region one, the flow profile has to be approximated by piece-wise step functions.
	The approximation used for these benchmarks is shown in Fig. 1.		The approximation used for these benchmarks is shown in Fig. 1.

	The Dirichlet boundary conditions are applied to the original system.		The Dirichlet boundary conditions are applied to the original system.
	In both models the reference temperature is set to <math>300 K</math>, Dirichlet boundary conditions as well as initial conditions are set to <math>0</math> with respect to the reference.		In both models, the reference temperature is set to <math>300 \, \text{K}</math>, and Dirichlet boundary conditions as well as initial conditions are set to <math>0</math> with respect to the reference.
	The specified Dirichlet boundary conditions are in both cases the inlet of the fluid and the outer faces of the solids. Matrices are supplied for the symmetric case (fluid speed is zero; no convection), and the non-symmetric case (with forced convection).		The specified Dirichlet boundary conditions are in both cases the inlet of the fluid and the outer faces of the solids. Matrices are supplied for the symmetric case (fluid speed is zero; no convection), and the non-symmetric case (with forced convection).
	Table 1 shows the output nodes specified for the two benchmarks, Table 2 links the filenames according to the different cases.		Table 1 shows the output nodes specified for the two benchmarks, Table 2 links the filenames according to the different cases.
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	:<math>		:<math>
	\begin{align}		\begin{align}
	E \dot{x}(t) &= Ax(t) + Bu(t) \\		E \dot{x}(t) &= A x(t) + B u(t) \\
	y(t) &= Cx(t)		y(t) &= C x(t)
	\end{align}		\end{align}
	</math>		</math>
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	System dimensions:		System dimensions:

	<math>E \in \mathbb{R}^{N \times N}</math>,		<math>E \in \mathbb{R}^{n \times n}</math>,
	<math>A \in \mathbb{R}^{N \times N}</math>,		<math>A \in \mathbb{R}^{n \times n}</math>,
	<math>B \in \mathbb{R}^{N \times 1}</math>,		<math>B \in \mathbb{R}^{n \times 1}</math>,
	<math>C \in \mathbb{R}^{5 \times N}</math>.		<math>C \in \mathbb{R}^{5 \times n}</math>.

	System variants:		System variants:

	<tt>flow_v0</tt>: <math>N = 9669</math>,		<tt>flow_v0</tt>: <math>n = 9669</math>,
	<tt>flow_v0.5</tt>: <math>N = 9669</math>,		<tt>flow_v0.5</tt>: <math>n = 9669</math>,
	<tt>chip_v0</tt>: <math>N = 20082</math>,		<tt>chip_v0</tt>: <math>n = 20082</math>,
	<tt>chip_v0.1</tt>: <math>N = 20082</math>.		<tt>chip_v0.1</tt>: <math>n = 20082</math>.

	==Citation==		==Citation==

Mitchell: typo

2022-03-14T15:12:16Z

typo

← Older revision		Revision as of 15:12, 14 March 2022
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	In this case the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.		In this case the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.
	Since the implementation of the convective term in ANSYS does not allow defining the fluid speed on a per element basis but on a per region one, the flow profile has to be approximated by piece-wise step functions.		Since the implementation of the convective term in ANSYS does not allow defining the fluid speed on a per element basis but on a per region one, the flow profile has to be approximated by piece-wise step functions.
	The approximation used for ~~this~~ benchmarks is shown in Fig. 1.		The approximation used for these benchmarks is shown in Fig. 1.

	The Dirichlet boundary conditions are applied to the original system.		The Dirichlet boundary conditions are applied to the original system.

Mitchell: grammar

2022-03-14T15:10:52Z

grammar

← Older revision		Revision as of 15:10, 14 March 2022
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	The second design is a 3D model of a chip cooled by forced convection (Fig. 2) <ref name="harper1997"/>.		The second design is a 3D model of a chip cooled by forced convection (Fig. 2) <ref name="harper1997"/>.
	In this case the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.		In this case the tetrahedral element type <tt>SOLID70</tt> was used, resulting in 107989 elements and 20542 nodes.
	Since the implementation of the convective term in ANSYS does not allow ~~for definition of~~ the fluid speed on a per element, but on a per region ~~basis~~, the flow profile has to be approximated by piece-wise step functions.		Since the implementation of the convective term in ANSYS does not allow defining the fluid speed on a per element basis but on a per region one, the flow profile has to be approximated by piece-wise step functions.
	The approximation used for this benchmarks is shown in Fig. 1.		The approximation used for this benchmarks is shown in Fig. 1.

Mitchell: errant comma

2022-03-14T15:09:05Z

errant comma

← Older revision		Revision as of 15:09, 14 March 2022
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	An intermediate level is to include a flow region with a given velocity profile that adds convective transport to the model.		An intermediate level is to include a flow region with a given velocity profile that adds convective transport to the model.
	Compared to convection boundary conditions this approach has the advantage that the film coefficient does not need to be specified and that information about the heat profile in the flow can be obtained.		Compared to convection boundary conditions this approach has the advantage that the film coefficient does not need to be specified and that information about the heat profile in the flow can be obtained.
	A drawback of the method is the greatly increased number of elements needed to perform a physically valid simulation, because the solution accuracy when employing upwind finite element schemes depends on the element size.		A drawback of the method is the greatly increased number of elements needed to perform a physically valid simulation because the solution accuracy when employing upwind finite element schemes depends on the element size.
	While this problem still is linear, due to the forced convection, the conductivity matrix changes from a symmetric matrix to an un-symmetric one.		While this problem still is linear, due to the forced convection, the conductivity matrix changes from a symmetric matrix to an un-symmetric one.
	So this problem type can be used as a benchmark for problems containing un-symmetric matrices.		So this problem type can be used as a benchmark for problems containing un-symmetric matrices.

Mitchell: grammar

2022-03-14T15:08:14Z

grammar

← Older revision		Revision as of 15:08, 14 March 2022
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	However, caution has to be taken to select the [[wikipedia:Heat_transfer_coefficient\|film coefficient]].		However, caution has to be taken to select the [[wikipedia:Heat_transfer_coefficient\|film coefficient]].

	An intermediate level is to include a flow region with a given velocity profile, that adds convective transport to the model.		An intermediate level is to include a flow region with a given velocity profile that adds convective transport to the model.
	Compared to convection boundary conditions this approach has the advantage that the film coefficient ~~has~~ not to be specified and that information about the heat profile in the flow can be obtained.		Compared to convection boundary conditions this approach has the advantage that the film coefficient does not need to be specified and that information about the heat profile in the flow can be obtained.
	A drawback of the method is the greatly increased number of elements needed to perform a physically valid simulation, because the solution accuracy when employing upwind finite element schemes depends on the element size.		A drawback of the method is the greatly increased number of elements needed to perform a physically valid simulation, because the solution accuracy when employing upwind finite element schemes depends on the element size.
	While this problem still is linear, due to the forced convection, the conductivity matrix changes from a symmetric matrix to an un-symmetric one.		While this problem still is linear, due to the forced convection, the conductivity matrix changes from a symmetric matrix to an un-symmetric one.

Himpe: /* Citation */ update part 2

2021-11-19T08:18:34Z

Citation: update part 2

← Older revision		Revision as of 08:18, 19 November 2021
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''~~Convection~~'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/~~Convection~~		::The MORwiki Community, '''Convective Thermal Flow'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Convective_Thermal_Flow

	@MISC{morwiki_convection,		@MISC{morwiki_convection,