{"id":3116,"date":"2016-03-22T18:38:51","date_gmt":"2016-03-22T18:38:51","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=3116"},"modified":"2016-03-22T18:38:51","modified_gmt":"2016-03-22T18:38:51","slug":"heat-exchangersthe-log-mean-temperature-difference-method","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/heat-exchangersthe-log-mean-temperature-difference-method\/","title":{"rendered":"HEAT EXCHANGERS:THE LOG MEAN TEMPERATURE DIFFERENCE METHOD"},"content":{"rendered":"<div class=\"iktpb6a0dd9b7c2b0c\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '61e5902552e2353963d8d2f1bd1f4a8f',\n\t\t'format' : 'iframe',\n\t\t'height' : 250,\n\t\t'width' : 300,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/61e5902552e2353963d8d2f1bd1f4a8f\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.iktpb6a0dd9b7c2b0c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.iktpb6a0dd9b7c2b0c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.iktpb6a0dd9b7c2b0c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.iktpb6a0dd9b7c2b0c {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.iktpb6a0dd9b7c2b0c {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\">\u25a0 <b>TH<\/b><b>E LOG MEAN TEMPERATURE<\/b><b> <\/b><b>DIFFERENC<\/b><b>E METHOD<\/b><\/font> <\/p>\n<p align=\"justify\">\n<h6 align=\"justify\"><font size=\"5\"><\/font><\/h6>\n<p><font size=\"5\">Earlier, we mentioned that the temperature difference between the hot and <\/font><font size=\"5\">cold fluids varies along the heat exchanger, and it is convenient to have a <\/font><font size=\"5\"><i>mea<\/i><i>n temperature difference <\/i>\/},<i>T<\/i><i>m <\/i>for use in the relation <i>Q <\/i>= <i>U<\/i><i>A<\/i><i>s <\/i>\/},<i>T<\/i><i>m<\/i>.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">In order to develop a relation for the equivalent average temperature differ<\/font><font size=\"5\">ence between the two fluids, consider the <i>parallel-flow double-pipe <\/i>heat ex- changer shown in Fig. 23\u201314. Note that the temperature difference \/},<i>T <\/i>between the hot and cold fluids is large at the inlet of the heat exchanger but decreases exponentially toward the outlet. As you would expect, the temperature of the hot fluid decreases and the temperature of the cold fluid increases along the heat exchanger, but the temperature of the cold fluid can never exceed that of the hot fluid no matter how long the heat exchanger is.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Assuming the outer surface of the heat exchanger to be well insulated so that any heat transfer occurs between the two fluids, and disregarding any<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">changes in kinetic and potential energy, an energy balance on each fluid in a differential section of the heat exchanger can be expressed as<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0107.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0107\" border=\"0\" alt=\"HEAT EXCHANGERS-0107\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0107_thumb.jpg\" width=\"436\" height=\"484\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">at the two ends (inlet and outlet) of the heat exchanger. It makes no difference which end of the heat exchanger is designated as the <i>inle<\/i><i>t <\/i>or the <i>outlet <\/i>(Fig. 23\u201315).<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The temperature difference between the two fluids decreases from \/},<i>T<\/i>1 at <\/font><font size=\"5\">the inlet to \/},<i>T<\/i>2 at the outlet. Thus, it is tempting to use the arithmetic mean temperature \/},<i>T<\/i>am = 1 (\/},<i>T<\/i>1 + \/},<i>T<\/i>2) as the average temperature difference. The <\/font><font size=\"5\">logarithmic mean temperature difference \/},<i>T<\/i>lm is obtained by tracing the ac- tual temperature profile of the fluids along the heat exchanger and is an <i>exact <\/i><\/font><font size=\"5\">representation of the <i>average temperature difference <\/i>between the hot and <\/font><font size=\"5\">cold fluids. It truly reflects the exponential decay of the local temperature difference.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">Note that \/},<i>T<\/i>lm is always less than \/},<i>T<\/i>am. Therefore, using \/},<i>T<\/i>am in calculations instead of \/},<i>T<\/i>lm will overestimate the rate of heat transfer in a heat ex- changer between the two fluids. When \/},<i>T<\/i>1 differs from \/},<i>T<\/i>2 by no more than 40 percent, the error in using the arithmetic mean temperature difference is less than 1 percent. But the error increases to undesirable levels when \/},<i>T<\/i>1 differs from \/},<i>T<\/i>2 by greater amounts. Therefore, we should always use the <\/font><font size=\"5\"><i>logarithmi<\/i><i>c mean temperature difference <\/i>when determining the rate of heat transfer in a heat exchanger.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0108.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0108\" border=\"0\" alt=\"HEAT EXCHANGERS-0108\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0108_thumb.jpg\" width=\"194\" height=\"354\"><\/a><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><strong>Counter-Flow Heat Exchangers<\/strong><\/font> <\/p>\n<h5 align=\"justify\"><font size=\"5\">The variation of temperatures of hot and cold fluids in a counter-flow heat ex<\/font><font size=\"5\">changer is given in Fig. 23\u201316. Note that the hot and cold fluids enter the heat exchanger from opposite ends, and the outlet temperature of the <i>cold fluid <\/i>in this case may exceed the outlet temperature of the <i>hot fluid. <\/i>In the limiting case, the cold fluid will be heated to the inlet temperature of the hot fluid. However, the outlet temperature of the cold fluid can <i>never <\/i>exceed the inlet temperature of the hot fluid, since this would be a violation of the second law of thermodynamics.<\/font><\/h5>\n<p align=\"justify\"><font size=\"5\">The relation already given for the log mean temperature difference is developed using a parallel-flow heat exchanger, but we can show by repeating the analysis for a counter-flow heat exchanger that is also applicable to counter- flow heat exchangers. But this time, \/},<i>T<\/i>1 and \/},<i>T<\/i>2 are expressed as shown in Fig. 23\u201315.<\/font> <\/p><div class=\"fpfbw6a0dd9b7c2ca8\" ><script type=\"text\/javascript\">\n\tatOptions = {\n\t\t'key' : '0c1eb4c533eaedb7b996f49a5a4983a9',\n\t\t'format' : 'iframe',\n\t\t'height' : 300,\n\t\t'width' : 160,\n\t\t'params' : {}\n\t};\n<\/script>\n<script type=\"text\/javascript\" src=\"\/\/www.highperformanceformat.com\/0c1eb4c533eaedb7b996f49a5a4983a9\/invoke.js\"><\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.fpfbw6a0dd9b7c2ca8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.fpfbw6a0dd9b7c2ca8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.fpfbw6a0dd9b7c2ca8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.fpfbw6a0dd9b7c2ca8 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.fpfbw6a0dd9b7c2ca8 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"yglgw6a0dd9b7c2bd9\" ><script async src=\"https:\/\/pagead2.googlesyndication.com\/pagead\/js\/adsbygoogle.js?client=ca-pub-0778475562755157\"\n     crossorigin=\"anonymous\"><\/script>\n<!-- 300x600 hydraulics-and-pneumatics -->\n<ins class=\"adsbygoogle\"\n     style=\"display:inline-block;width:300px;height:600px\"\n     data-ad-client=\"ca-pub-0778475562755157\"\n     data-ad-slot=\"3735577695\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script><\/div><style type=\"text\/css\">\r\n@media screen and (min-width: 1201px) {\r\n.yglgw6a0dd9b7c2bd9 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.yglgw6a0dd9b7c2bd9 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.yglgw6a0dd9b7c2bd9 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.yglgw6a0dd9b7c2bd9 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.yglgw6a0dd9b7c2bd9 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\">For specified inlet and outlet temperatures, the log mean temperature difference for a <i>counter-flow <\/i>heat exchanger is always <i>greater <\/i>than that for a parallel-flow heat exchanger. That is, \/},<i>T<\/i>lm, CF &gt; \/},<i>T<\/i>lm, PF, and thus a smaller surface area (and thus a smaller heat exchanger) is needed to achieve a specified heat transfer rate in a counter-flow heat exchanger. Therefore, it is common practice to use counter-flow arrangements in heat exchangers.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">In a counter-flow heat exchanger, the temperature difference between the hot and the cold fluids will remain constant along the heat exchanger when the <i>heat capacity rates <\/i>of the two fluids are <i>equal <\/i>(that is, \/},<i>T <\/i>= constant <\/font><font size=\"5\">when <i>C<\/i><i>h <\/i>= <i>C<\/i><i>c <\/i>or <i>m<\/i><i>h<\/i><i>C<\/i><i>ph <\/i>= <i>m<\/i><i>c<\/i><i>C<\/i><i>pc<\/i>). Then we have \/},<i>T<\/i>1 = \/},<i>T<\/i>2, and the last log <\/font><font size=\"5\">mean temperature difference relation gives \/},<i>T<\/i>lm = 0 , which is indeterminate.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">It can be shown by the application of l\u2019H\u00f4pital\u2019s rule that in this case we have <\/font><font size=\"5\"> as expected.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">A <i>condenser <\/i>or a <i>boiler <\/i>can be considered to be either a parallel- or counter <\/font><font size=\"5\">flow heat exchanger since both approaches give the same result.<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Multipas<\/b><b>s and Cross-Flow Heat Exchangers:<\/b><b> <\/b><b>Us<\/b><b>e of a Correction Factor<\/b><\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">The log mean temperature difference \/},<i>T<\/i>lm relation developed earlier is limited<\/font> <\/p>\n<p align=\"justify\"><font size=\"5\">to parallel-flow and counter-flow heat exchangers only. Similar relations are <\/font><font size=\"5\">also developed for <i>cross-flow <\/i>and <i>multipass shell-and-tube <\/i>heat exchangers, but the resulting expressions are too complicated because of the complex flow conditions.<\/font> <\/p>\n<h5 align=\"justify\"><font size=\"5\">In such cases, it is convenient to relate the equivalent temperature dif- ference to the log mean temperature difference relation for the counter-flow case as<\/font><\/h5>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0109.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0109\" border=\"0\" alt=\"HEAT EXCHANGERS-0109\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0109_thumb.jpg\" width=\"225\" height=\"36\"><\/a><\/p>\n<p align=\"justify\"><font size=\"5\">where <i>F <\/i>is the <b>cor<\/b><b>r<\/b><b>ectio<\/b><b>n factor, <\/b>which depends on the <i>geometr<\/i><i>y <\/i>of the heat exchanger and the inlet and outlet temperatures of the hot and cold fluid streams. The \/},<i>T<\/i>lm, CF is the log mean temperature difference for the case of a <i>counte<\/i><i>r<\/i><i>-flo<\/i><i>w <\/i>heat exchanger with the same inlet and outlet temperatures and is determined from Eq. 23\u201325 by taking \/},<i>T<\/i>l = <i>T<\/i><i>h<\/i>, in &#8211; <i>T<\/i><i>c<\/i>, out and <\/font><font size=\"5\">The correction factor is less than unity for a cross-flow and multipass shell-and-tube heat exchanger. That is, <i>F <\/i>:s 1. The limiting value of <i>F <\/i>= 1 corresponds to the counter-flow heat exchanger. Thus, the correction factor <i>F <\/i>for a heat exchanger is <i>a measure of deviation of the <\/i>\/},<i>T<\/i>lm <i>f<\/i><i>r<\/i><i>o<\/i><i>m the corresponding values for the counter-flow case.<\/i><\/font> <\/p>\n<h5 align=\"justify\"><font size=\"5\">The correction factor <i>F <\/i>for common cross-flow and shell-and-tube heat ex- changer configurations is given in Fig. 23\u201318 versus two temperature ratios <i>P <\/i>and <i>R <\/i>defined as<\/font><\/h5>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0110.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0110\" border=\"0\" alt=\"HEAT EXCHANGERS-0110\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0110_thumb.jpg\" width=\"369\" height=\"280\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0111.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0111\" border=\"0\" alt=\"HEAT EXCHANGERS-0111\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0111_thumb.jpg\" width=\"154\" height=\"484\"><\/a><\/p>\n<p align=\"justify\"><font size=\"5\">where the subscripts 1 and 2 represent the <i>inle<\/i><i>t <\/i>and <i>outlet<\/i><i>, <\/i>respectively. Note <\/font><font size=\"5\">that for a shell-and-tube heat exchanger, <i>T <\/i>and <i>t <\/i>represent the <i>shell- <\/i>and <\/font><font size=\"5\"><i>tube-sid<\/i><i>e <\/i>temperatures, respectively, as shown in the correction factor <\/font><font size=\"5\">charts. It makes no difference whether the hot or the cold fluid flows <\/font><font size=\"5\">through the shell or the tube. The determination of the correction factor <i>F <\/i>requires the availability of the <i>inle<\/i><i>t <\/i>and the <i>outle<\/i><i>t <\/i>temperatures for both the cold and hot fluids.<\/font><\/p>\n<p align=\"justify\"><font size=\"5\">Note that the value of <i>P <\/i>ranges from 0 to 1. The value of <i>R<\/i>, on the other hand, ranges from 0 to infinity, with <i>R <\/i>= 0 corresponding to the phase-change <\/font><font size=\"5\">(condensation or boiling) on the shell-side and <i>R <\/i>\u2192 oc to phase-change on the tube side. The correction factor is <i>F <\/i>= 1 for both of these limiting cases. Therefore, the correction factor for a <i>condenser <\/i>or <i>boiler <\/i>is <i>F <\/i>= 1, regardless of the configuration of the heat exchanger.<a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0112.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0112\" border=\"0\" alt=\"HEAT EXCHANGERS-0112\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0112_thumb.jpg\" width=\"429\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0113.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0113\" border=\"0\" alt=\"HEAT EXCHANGERS-0113\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0113_thumb.jpg\" width=\"425\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0114.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0114\" border=\"0\" alt=\"HEAT EXCHANGERS-0114\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0114_thumb.jpg\" width=\"419\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0115.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0115\" border=\"0\" alt=\"HEAT EXCHANGERS-0115\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0115_thumb.jpg\" width=\"410\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0116.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0116\" border=\"0\" alt=\"HEAT EXCHANGERS-0116\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0116_thumb.jpg\" width=\"291\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0117.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-bottom: 0px; border-left: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top: 0px; border-right: 0px; padding-top: 0px\" title=\"HEAT EXCHANGERS-0117\" border=\"0\" alt=\"HEAT EXCHANGERS-0117\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/HEAT-EXCHANGERS-0117_thumb.jpg\" width=\"394\" height=\"484\"><\/a><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u25a0 THE LOG MEAN TEMPERATURE DIFFERENCE METHOD Earlier, we mentioned that the temperature difference between the hot and cold fluids varies along the heat exchanger, and it is convenient to have a mean temperature difference \/},Tm for use in the relation Q = UAs \/},Tm. In order to develop a relation for the equivalent average [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/heat-exchangersthe-log-mean-temperature-difference-method\/\" class=\"more-link\" >Continue reading&#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/3116"}],"collection":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/comments?post=3116"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/3116\/revisions"}],"predecessor-version":[{"id":3117,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/3116\/revisions\/3117"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=3116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=3116"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=3116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}