Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions
Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for...
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| Veröffentlicht in: | International journal of heat and mass transfer 2010-10, Vol.53 (21), p.4885-4898 |
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| container_title | International journal of heat and mass transfer |
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| creator | Vera, Marcos Liñán, Amable |
| description | Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes. |
| doi_str_mv | 10.1016/j.ijheatmasstransfer.2010.06.004 |
| format | Article |
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The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.</description><identifier>ISSN: 0017-9310</identifier><identifier>EISSN: 1879-2189</identifier><identifier>DOI: 10.1016/j.ijheatmasstransfer.2010.06.004</identifier><identifier>CODEN: IJHMAK</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Applied sciences ; Computational fluid dynamics ; Counterflow ; Devices using thermal energy ; Eigenfunction expansions ; Eigenfunctions ; Energy ; Energy. 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The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.</description><subject>Applied sciences</subject><subject>Computational fluid dynamics</subject><subject>Counterflow</subject><subject>Devices using thermal energy</subject><subject>Eigenfunction expansions</subject><subject>Eigenfunctions</subject><subject>Energy</subject><subject>Energy. Thermal use of fuels</subject><subject>Exact sciences and technology</subject><subject>Fluid flow</subject><subject>Fluids</subject><subject>Heat exchangers</subject><subject>Heat exchangers (included heat transformers, condensers, cooling towers)</subject><subject>Heat transfer</subject><subject>Laminar</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Parallel-plate</subject><issn>0017-9310</issn><issn>1879-2189</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNqNkE9P3DAQxa2KSl1ov0MulbhkseP87YkK0QJaiQP0bE0m4-KVNwkeb1m-fR0t6qUXTqPR_PTemyfEuZJrJVV9sV277RNB3AFzDDCypbAuZDrLei1l-UGsVNt0eaHa7kSspFRN3mklP4lT5u2yyrJeiYcN7NwIIcNpP0YK1k8v2QwBvCefzx4iZYtNRgd8gvE3Bf6WXR8AYwbjkME8h-ngdgvGk99HN438WXy04Jm-vM0z8evH9ePVTb65_3l79X2TY1nrmNclEkBldV1WNOi-ArTSNihVQWShATnY1uqeirbHDmxfWLQVQl9hayWV-kycH3VThuc9cTQ7x0jew0jTno2qG1VUWqsioZdHFMPEHMiaOaTU4dUoaZY-zdb836dZ-jSyNqnPJPH1zQ0YwdvEoON_OoVWXVc1VeLujhyl1_-4pMLoaEQaXCCMZpjc-03_AgYcm-A</recordid><startdate>20101001</startdate><enddate>20101001</enddate><creator>Vera, Marcos</creator><creator>Liñán, Amable</creator><general>Elsevier Ltd</general><general>Elsevier</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20101001</creationdate><title>Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions</title><author>Vera, Marcos ; Liñán, Amable</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c463t-64ceaa5f3645ed3b5acf0f7c012eefa7a0df8f3be28bc9afb2fcf5cab5c8f0e43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applied sciences</topic><topic>Computational fluid dynamics</topic><topic>Counterflow</topic><topic>Devices using thermal energy</topic><topic>Eigenfunction expansions</topic><topic>Eigenfunctions</topic><topic>Energy</topic><topic>Energy. Thermal use of fuels</topic><topic>Exact sciences and technology</topic><topic>Fluid flow</topic><topic>Fluids</topic><topic>Heat exchangers</topic><topic>Heat exchangers (included heat transformers, condensers, cooling towers)</topic><topic>Heat transfer</topic><topic>Laminar</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Parallel-plate</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Vera, Marcos</creatorcontrib><creatorcontrib>Liñán, Amable</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>International journal of heat and mass transfer</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Vera, Marcos</au><au>Liñán, Amable</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions</atitle><jtitle>International journal of heat and mass transfer</jtitle><date>2010-10-01</date><risdate>2010</risdate><volume>53</volume><issue>21</issue><spage>4885</spage><epage>4898</epage><pages>4885-4898</pages><issn>0017-9310</issn><eissn>1879-2189</eissn><coden>IJHMAK</coden><abstract>Multilayered, counterflow, parallel-plate heat exchangers are analyzed numerically and theoretically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects longitudinal conduction both in the fluid and in the plates. The solution for the temperature field involves eigenfunction expansions that can be solved in terms of Whittaker functions using standard symbolic algebra packages, leading to analytical expressions that provide the eigenvalues numerically. It is seen that the approximate solution obtained by retaining the first two modes in the eigenfunction expansion provides an accurate representation for the temperature away from the entrance regions, specially for long heat exchangers, thereby enabling simplified expressions for the wall and bulk temperatures, local heat-transfer rate, overall heat-transfer coefficient, and outlet bulk temperatures. The agreement between the numerical and theoretical results suggests the possibility of using the analytical solutions presented herein as benchmark problems for computational heat-transfer codes.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.ijheatmasstransfer.2010.06.004</doi><tpages>14</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | International journal of heat and mass transfer, 2010-10, Vol.53 (21), p.4885-4898 |
| issn | 0017-9310 1879-2189 |
| language | eng |
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| source | Elsevier ScienceDirect Journals |
| subjects | Applied sciences Computational fluid dynamics Counterflow Devices using thermal energy Eigenfunction expansions Eigenfunctions Energy Energy. Thermal use of fuels Exact sciences and technology Fluid flow Fluids Heat exchangers Heat exchangers (included heat transformers, condensers, cooling towers) Heat transfer Laminar Mathematical analysis Mathematical models Parallel-plate |
| title | Laminar counterflow parallel-plate heat exchangers: Exact and approximate solutions |
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