Analytical methods for heat transfer and fluid flow problems:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 247 - 256 |
| Physical Description: | XX, 258 S. graph. Darst. |
| ISBN: | 3540222472 |
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| 245 | 1 | 0 | |a Analytical methods for heat transfer and fluid flow problems |c Bernhard Weigand |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2004 | |
| 300 | |a XX, 258 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 500 | |a Literaturverz. S. 247 - 256 | ||
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| 650 | 4 | |a Heat |x Transmission | |
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Record in the Search Index
| _version_ | 1804135051716198400 |
|---|---|
| adam_text | CONTENTS LIST OF
SYMBOLS....................................................................................................
XV LIST OF COPYRIGHTED FIGURES
.............................................................................XIX
1
INTRODUCTION.....................................................................................................
.. ..1
PROBLEMS.........................................................................................................
9 2 LINEAR PARTIAL DIFFERENTIAL EQUATIONS
............................................................. 11 2.1
CLASSIFICATION OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS
.................. 11 2.2 CHARACTER OF THE SOLUTIONS FOR THE PARTIAL
DIFFERENTIAL EQUATIONS .............. 19 2.2.1 PARABOLIC SECOND-ORDER
EQUATIONS ..................................................... 19 2.2.2
ELLIPTIC SECOND-ORDER EQUATIONS
........................................................ 21 2.2.3
HYPERBOLIC SECOND-ORDER EQUATIONS
.................................................. 23 2.3 SEPARATION OF
VARIABLES
..............................................................................
24 2.3.1 ONE-DIMENSIONAL TRANSIENT HEAT CONDUCTION IN A FLAT
PLATE............. 24 2.3.2 STEADY-STATE HEAT CONDUCTION IN A
RECTANGULAR PLATE........................ 31 2.3.3 SEPARATION OF
VARIABLES FOR THE GENERAL CASE OF A LINEAR SECOND- ORDER PARTIAL
DIFFERENTIAL
EQUATION..............................................................
37
PROBLEMS.......................................................................................................
39 3 HEAT TRANSFER IN PIPE AND CHANNEL FLOWS (PARABOLIC PROBLEMS)
................ 43 3.1 HEAT TRANSFER IN PIPE AND CHANNEL FLOWS WITH
CONSTANT WALL
TEMPERATURE......................................................................................................
43 3.1.1 VELOCITY DISTRIBUTION OF HYDRODYNAMICALLY FULLY DEVELOPED PIPE
AND CHANNEL
FLOWS..............................................................................................
44 3.1.2 THERMAL ENTRANCE SOLUTIONS FOR CONSTANT WALL TEMPERATURE
............ 46 PROPERTIES OF THE STURM-LIOUVILLE
SYSTEM.................................................... 50 3.2
THERMAL ENTRANCE SOLUTIONS FOR AN ARBITRARY WALL TEMPERATURE
DISTRIBUTION
.......................................................................................................
66 3.3 FLOW AND HEAT TRANSFER IN AXIALLY ROTATING PIPES WITH CONSTANT
WALL HEAT FLUX
...................................................................................................................
69 3.3.1 VELOCITY DISTRIBUTION FOR THE HYDRODYNAMICALLY FULLY DEVELOPED
FLOW IN AN AXIAL ROTATING
PIPE....................................................................
72 3.3.2 THERMAL ENTRANCE SOLUTION FOR CONSTANT WALL HEAT
FLUX................... 75
PROBLEMS.......................................................................................................
83 XII CONTENTS 4 ANALYTICAL SOLUTIONS FOR STURM - LIOUVILLE SYSTEMS
WITH LARGE EIGENVALUES
...........................................................................................................
87 4.1 HEAT TRANSFER IN TURBULENT PIPE FLOW WITH CONSTANT WALL
TEMPERATURE 103 4.2 HEAT TRANSFER IN AN AXIALLY ROTATING PIPE WITH
CONSTANT WALL
TEMPERATURE....................................................................................................
109 4.3 ASYMPTOTIC EXPRESSIONS FOR OTHER THERMAL BOUNDARY CONDITIONS
.......... 113
PROBLEMS.....................................................................................................
115 5 HEAT TRANSFER IN DUCT FLOWS FOR SMALL PECLET NUMBERS (ELLIPTIC
PROBLEMS)..............................................................................................
117 5.1 HEAT TRANSFER FOR CONSTANT WALL TEMPERATURES FOR X * 0 AND X
0 ........ 120 5.1.1 HEAT TRANSFER IN LAMINAR PIPE AND CHANNEL FLOWS FOR
SMALL PECLET NUMBERS
.....................................................................................................
131 5.1.2 HEAT TRANSFER IN TURBULENT PIPE AND CHANNEL FLOWS FOR SMALL
PECLET NUMBERS
.....................................................................................................
138 5.2 HEAT TRANSFER FOR CONSTANT WALL HEAT FLUX FOR X * 0 AND X 0
................ 142 5.2.1 HEAT TRANSFER IN LAMINAR PIPE AND CHANNEL
FLOWS FOR SMALL PECLET NUMBERS
.....................................................................................................
147 5.2.2 HEAT TRANSFER IN TURBULENT PIPE AND CHANNEL FLOWS FOR SMALL
PECLET NUMBERS
.....................................................................................................
150 5.3 RESULTS FOR HEATING SECTIONS WITH A FINITE
LENGTH................................... 153 5.3.1 PIECEWISE CONSTANT
WALL TEMPERATURE ............................................. 154 5.3.1
PIECEWISE CONSTANT WALL HEAT
FLUX.................................................. 157 5.4
APPLICATION OF THE SOLUTION METHOD TO RELATED PROBLEMS
....................... 159
PROBLEMS.....................................................................................................
161 6 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
..................................................... 165 6.1 THE
METHOD OF SEPARATION OF VARIABLES
................................................... 165 6.2
TRANSFORMATIONS RESULTING IN LINEAR PARTIAL DIFFERENTIAL EQUATIONS
....... 172 6.3 FUNCTIONAL RELATIONS BETWEEN DEPENDENT VARIABLES
............................... 174 6.3.1 INCOMPRESSIBLE FLOW OVER A
HEATED FLAT PLATE ................................. 174 6.3.2
COMPRESSIBLE FLOW OVER A FLAT, HEATED
PLATE................................... 177 6.4 SIMILARITY
SOLUTIONS..................................................................................
179 6.4.1 SIMILARITY SOLUTIONS FOR A TRANSIENT HEAT CONDUCTION
PROBLEM....... 179 6.4.2 SIMILARITY SOLUTIONS OF THE BOUNDARY LAYER
EQUATIONS FOR LAMINAR FREE CONVECTION FLOW ON A VERTICAL FLAT
PLATE.......................................... 186 6.4.3 SIMILARITY
SOLUTIONS OF THE COMPRESSIBLE BOUNDARY LAYER
EQUATIONS....................................................................................................
192
PROBLEMS.....................................................................................................
198 APPENDIX A: THE FULLY DEVELOPED VELOCITY PROFILE FOR TURBULENT DUCT
FLOWS....................................................................................................................
203 APPENDIX B: THE FULLY DEVELOPED VELOCITY PROFILE IN AN AXIALLY
ROTATING PIPE
......................................................................................................................
215 CONTENTS XIII APPENDIX C: A NUMERICAL SOLUTION METHOD FOR
EIGENVALUE PROBLEMS ........ 227 C.1 NUMERICAL
TOOLS.......................................................................................
229 APPENDIX D: DETAILED DERIVATION OF CERTAIN PROPERTIES OF THE METHOD
FOR SOLVING THE EXTENDED GRAETZ
PROBLEMS............................................................ 235
D.1 SYMMETRY OF THE MATRIX OPERATOR L %
..................................................... 235 D.2 THE
EIGENFUNCTIONS CONSTITUTE A SET OF ORTHOGONAL FUNCTIONS..............
236 D.3 A DETAILED DERIVATION OF EQ. (5.31) AND EQ.
(5.61)................................ 237 D.4 SIMPLIFICATION OF THE
EXPRESSION FOR THE TEMPERATURE DISTRIBUTION (FOR CONSTANT WALL
TEMPERATURE)
..........................................................................
239 D.5 SIMPLIFICATION OF THE EXPRESSION FOR THE TEMPERATURE
DISTRIBUTION (FOR CONSTANT WALL HEAT FLUX)
...............................................................................
240 D.6 THE VECTOR NORM 2 J * R
..........................................................................
243 REFERENCES
...........................................................................................................
247 INDEX
....................................................................................................................
257
|
| adam_txt |
CONTENTS LIST OF
SYMBOLS.
XV LIST OF COPYRIGHTED FIGURES
.XIX
1
INTRODUCTION.
. .1
PROBLEMS.
9 2 LINEAR PARTIAL DIFFERENTIAL EQUATIONS
. 11 2.1
CLASSIFICATION OF SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS
. 11 2.2 CHARACTER OF THE SOLUTIONS FOR THE PARTIAL
DIFFERENTIAL EQUATIONS . 19 2.2.1 PARABOLIC SECOND-ORDER
EQUATIONS . 19 2.2.2
ELLIPTIC SECOND-ORDER EQUATIONS
. 21 2.2.3
HYPERBOLIC SECOND-ORDER EQUATIONS
. 23 2.3 SEPARATION OF
VARIABLES
.
24 2.3.1 ONE-DIMENSIONAL TRANSIENT HEAT CONDUCTION IN A FLAT
PLATE. 24 2.3.2 STEADY-STATE HEAT CONDUCTION IN A
RECTANGULAR PLATE. 31 2.3.3 SEPARATION OF
VARIABLES FOR THE GENERAL CASE OF A LINEAR SECOND- ORDER PARTIAL
DIFFERENTIAL
EQUATION.
37
PROBLEMS.
39 3 HEAT TRANSFER IN PIPE AND CHANNEL FLOWS (PARABOLIC PROBLEMS)
. 43 3.1 HEAT TRANSFER IN PIPE AND CHANNEL FLOWS WITH
CONSTANT WALL
TEMPERATURE.
43 3.1.1 VELOCITY DISTRIBUTION OF HYDRODYNAMICALLY FULLY DEVELOPED PIPE
AND CHANNEL
FLOWS.
44 3.1.2 THERMAL ENTRANCE SOLUTIONS FOR CONSTANT WALL TEMPERATURE
. 46 PROPERTIES OF THE STURM-LIOUVILLE
SYSTEM. 50 3.2
THERMAL ENTRANCE SOLUTIONS FOR AN ARBITRARY WALL TEMPERATURE
DISTRIBUTION
.
66 3.3 FLOW AND HEAT TRANSFER IN AXIALLY ROTATING PIPES WITH CONSTANT
WALL HEAT FLUX
.
69 3.3.1 VELOCITY DISTRIBUTION FOR THE HYDRODYNAMICALLY FULLY DEVELOPED
FLOW IN AN AXIAL ROTATING
PIPE.
72 3.3.2 THERMAL ENTRANCE SOLUTION FOR CONSTANT WALL HEAT
FLUX. 75
PROBLEMS.
83 XII CONTENTS 4 ANALYTICAL SOLUTIONS FOR STURM - LIOUVILLE SYSTEMS
WITH LARGE EIGENVALUES
.
87 4.1 HEAT TRANSFER IN TURBULENT PIPE FLOW WITH CONSTANT WALL
TEMPERATURE 103 4.2 HEAT TRANSFER IN AN AXIALLY ROTATING PIPE WITH
CONSTANT WALL
TEMPERATURE.
109 4.3 ASYMPTOTIC EXPRESSIONS FOR OTHER THERMAL BOUNDARY CONDITIONS
. 113
PROBLEMS.
115 5 HEAT TRANSFER IN DUCT FLOWS FOR SMALL PECLET NUMBERS (ELLIPTIC
PROBLEMS).
117 5.1 HEAT TRANSFER FOR CONSTANT WALL TEMPERATURES FOR X * 0 AND X
0 . 120 5.1.1 HEAT TRANSFER IN LAMINAR PIPE AND CHANNEL FLOWS FOR
SMALL PECLET NUMBERS
.
131 5.1.2 HEAT TRANSFER IN TURBULENT PIPE AND CHANNEL FLOWS FOR SMALL
PECLET NUMBERS
.
138 5.2 HEAT TRANSFER FOR CONSTANT WALL HEAT FLUX FOR X * 0 AND X 0
. 142 5.2.1 HEAT TRANSFER IN LAMINAR PIPE AND CHANNEL
FLOWS FOR SMALL PECLET NUMBERS
.
147 5.2.2 HEAT TRANSFER IN TURBULENT PIPE AND CHANNEL FLOWS FOR SMALL
PECLET NUMBERS
.
150 5.3 RESULTS FOR HEATING SECTIONS WITH A FINITE
LENGTH. 153 5.3.1 PIECEWISE CONSTANT
WALL TEMPERATURE . 154 5.3.1
PIECEWISE CONSTANT WALL HEAT
FLUX. 157 5.4
APPLICATION OF THE SOLUTION METHOD TO RELATED PROBLEMS
. 159
PROBLEMS.
161 6 NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
. 165 6.1 THE
METHOD OF SEPARATION OF VARIABLES
. 165 6.2
TRANSFORMATIONS RESULTING IN LINEAR PARTIAL DIFFERENTIAL EQUATIONS
. 172 6.3 FUNCTIONAL RELATIONS BETWEEN DEPENDENT VARIABLES
. 174 6.3.1 INCOMPRESSIBLE FLOW OVER A
HEATED FLAT PLATE . 174 6.3.2
COMPRESSIBLE FLOW OVER A FLAT, HEATED
PLATE. 177 6.4 SIMILARITY
SOLUTIONS.
179 6.4.1 SIMILARITY SOLUTIONS FOR A TRANSIENT HEAT CONDUCTION
PROBLEM. 179 6.4.2 SIMILARITY SOLUTIONS OF THE BOUNDARY LAYER
EQUATIONS FOR LAMINAR FREE CONVECTION FLOW ON A VERTICAL FLAT
PLATE. 186 6.4.3 SIMILARITY
SOLUTIONS OF THE COMPRESSIBLE BOUNDARY LAYER
EQUATIONS.
192
PROBLEMS.
198 APPENDIX A: THE FULLY DEVELOPED VELOCITY PROFILE FOR TURBULENT DUCT
FLOWS.
203 APPENDIX B: THE FULLY DEVELOPED VELOCITY PROFILE IN AN AXIALLY
ROTATING PIPE
.
215 CONTENTS XIII APPENDIX C: A NUMERICAL SOLUTION METHOD FOR
EIGENVALUE PROBLEMS . 227 C.1 NUMERICAL
TOOLS.
229 APPENDIX D: DETAILED DERIVATION OF CERTAIN PROPERTIES OF THE METHOD
FOR SOLVING THE EXTENDED GRAETZ
PROBLEMS. 235
D.1 SYMMETRY OF THE MATRIX OPERATOR L %
. 235 D.2 THE
EIGENFUNCTIONS CONSTITUTE A SET OF ORTHOGONAL FUNCTIONS.
236 D.3 A DETAILED DERIVATION OF EQ. (5.31) AND EQ.
(5.61). 237 D.4 SIMPLIFICATION OF THE
EXPRESSION FOR THE TEMPERATURE DISTRIBUTION (FOR CONSTANT WALL
TEMPERATURE)
.
239 D.5 SIMPLIFICATION OF THE EXPRESSION FOR THE TEMPERATURE
DISTRIBUTION (FOR CONSTANT WALL HEAT FLUX)
.
240 D.6 THE VECTOR NORM 2 J * R
.
243 REFERENCES
.
247 INDEX
.
257 |
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| author | Weigand, Bernhard 1962- |
| author_GND | (DE-588)115406662 |
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| author_sort | Weigand, Bernhard 1962- |
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| building | Verbundindex |
| bvnumber | BV021271626 |
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| callnumber-raw | QC320 |
| callnumber-search | QC320 |
| callnumber-sort | QC 3320 |
| callnumber-subject | QC - Physics |
| classification_rvk | UG 2500 |
| classification_tum | MTA 700f MTA 309f MTA 330f |
| ctrlnum | (OCoLC)56492273 (DE-599)BVBBV021271626 |
| dewey-full | 536/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 536 - Heat |
| dewey-raw | 536/.2 |
| dewey-search | 536/.2 |
| dewey-sort | 3536 12 |
| dewey-tens | 530 - Physics |
| discipline | Maschinenbau / Maschinenwesen Physik Mathematik |
| discipline_str_mv | Maschinenbau / Maschinenwesen Physik Mathematik |
| format | Book |
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| id | DE-604.BV021271626 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:44:37Z |
| indexdate | 2024-07-09T20:34:22Z |
| institution | BVB |
| isbn | 3540222472 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014592739 |
| oclc_num | 56492273 |
| open_access_boolean | |
| owner | DE-703 DE-573 DE-1050 DE-91G DE-BY-TUM DE-634 DE-83 DE-92 |
| owner_facet | DE-703 DE-573 DE-1050 DE-91G DE-BY-TUM DE-634 DE-83 DE-92 |
| physical | XX, 258 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| spelling | Weigand, Bernhard 1962- Verfasser (DE-588)115406662 aut Analytical methods for heat transfer and fluid flow problems Bernhard Weigand Berlin [u.a.] Springer 2004 XX, 258 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 247 - 256 Fluid mechanics Heat Transmission Mechanics, Analytic Separation of variables Wärmeübertragung (DE-588)4064211-2 gnd rswk-swf Kanalströmung (DE-588)4137410-1 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Rohrströmung (DE-588)4050412-8 gnd rswk-swf Analytische Lösung (DE-588)4313842-1 gnd rswk-swf Rohrströmung (DE-588)4050412-8 s Kanalströmung (DE-588)4137410-1 s Wärmeübertragung (DE-588)4064211-2 s Partielle Differentialgleichung (DE-588)4044779-0 s Analytische Lösung (DE-588)4313842-1 s 1\p DE-604 DE-604 SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014592739&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Weigand, Bernhard 1962- Analytical methods for heat transfer and fluid flow problems Fluid mechanics Heat Transmission Mechanics, Analytic Separation of variables Wärmeübertragung (DE-588)4064211-2 gnd Kanalströmung (DE-588)4137410-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Rohrströmung (DE-588)4050412-8 gnd Analytische Lösung (DE-588)4313842-1 gnd |
| subject_GND | (DE-588)4064211-2 (DE-588)4137410-1 (DE-588)4044779-0 (DE-588)4050412-8 (DE-588)4313842-1 |
| title | Analytical methods for heat transfer and fluid flow problems |
| title_auth | Analytical methods for heat transfer and fluid flow problems |
| title_exact_search | Analytical methods for heat transfer and fluid flow problems |
| title_exact_search_txtP | Analytical methods for heat transfer and fluid flow problems |
| title_full | Analytical methods for heat transfer and fluid flow problems Bernhard Weigand |
| title_fullStr | Analytical methods for heat transfer and fluid flow problems Bernhard Weigand |
| title_full_unstemmed | Analytical methods for heat transfer and fluid flow problems Bernhard Weigand |
| title_short | Analytical methods for heat transfer and fluid flow problems |
| title_sort | analytical methods for heat transfer and fluid flow problems |
| topic | Fluid mechanics Heat Transmission Mechanics, Analytic Separation of variables Wärmeübertragung (DE-588)4064211-2 gnd Kanalströmung (DE-588)4137410-1 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Rohrströmung (DE-588)4050412-8 gnd Analytische Lösung (DE-588)4313842-1 gnd |
| topic_facet | Fluid mechanics Heat Transmission Mechanics, Analytic Separation of variables Wärmeübertragung Kanalströmung Partielle Differentialgleichung Rohrströmung Analytische Lösung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014592739&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT weigandbernhard analyticalmethodsforheattransferandfluidflowproblems |