{"id":3352,"date":"2016-03-27T09:48:06","date_gmt":"2016-03-27T09:48:06","guid":{"rendered":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/?p=3352"},"modified":"2016-03-27T09:48:06","modified_gmt":"2016-03-27T09:48:06","slug":"forced-convectionparallel-flow-over-flat-plates","status":"publish","type":"post","link":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/forced-convectionparallel-flow-over-flat-plates\/","title":{"rendered":"FORCED CONVECTION:PARALLEL FLOW OVER FLAT PLATES"},"content":{"rendered":"<div class=\"nkyja6a0dae017e1a0\" ><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.nkyja6a0dae017e1a0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.nkyja6a0dae017e1a0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.nkyja6a0dae017e1a0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.nkyja6a0dae017e1a0 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.nkyja6a0dae017e1a0 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<p align=\"justify\"><font size=\"5\"><strong>PARALLEL FLOW OVER FLAT PLATES<\/strong><\/font>  <\/p>\n<p align=\"justify\"><i><font size=\"5\"><\/font><\/i> <\/p>\n<p align=\"justify\"><font size=\"5\">Consider the parallel flow of a fluid over a flat plate of length <i>L <\/i>in the flow direction, as shown in Fig. 19\u20138. The <i>x<\/i>-coordinate is measured along the plate surface from the leading edge in the direction of the flow. The fluid approaches the plate in the <i>x<\/i>-direction with uniform upstream velocity &#8216;V and temperature <i>T<\/i>oo. The flow in the velocity boundary layer starts out as laminar, but if the plate is sufficiently long, the flow will become turbulent at a distance <i>x<\/i>cr from the leading edge where the Reynolds number reaches its critical value for transition.<\/font><\/p>\n<p align=\"justify\"><font size=\"5\">The transition from laminar to turbulent flow depends on the <i>surface geometry, surface roughness, upstream velocity, surface temperature, <\/i>and the <i>type of fluid, <\/i>among other things, and is best characterized by the Reynolds number. The Reynolds number at a distance <i>x <\/i>from the leading edge of a flat plate is expressed as<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0394.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0394\" border=\"0\" alt=\"FORCED CONVECTION-0394\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0394_thumb.jpg\" width=\"185\" height=\"344\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0395.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0395\" border=\"0\" alt=\"FORCED CONVECTION-0395\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0395_thumb.jpg\" width=\"374\" height=\"326\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">in the flow direction. The variation of the boundary layer thickness d and the friction and heat transfer coefficients along an isothermal flat plate are shown <\/font><font size=\"5\">in Fig. 19\u20139. The local friction and heat transfer coefficients are higher in tur- <i>h <\/i>bulent flow than they are in laminar flow. Also, <i>h<\/i><i>x <\/i>reaches its highest values <i>C<\/i><i>f <\/i>when the flow becomes fully turbulent, and then decreases by a factor of <i>x<\/i>-0.2 <\/font><font size=\"5\">in the flow direction, as shown in the figure.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The <i>average <\/i>Nusselt number over the entire plate is determined by substituting the preceding relations into Eq. 19\u20135 and performing the integrations. We get<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0396.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0396\" border=\"0\" alt=\"FORCED CONVECTION-0396\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0396_thumb.jpg\" width=\"364\" height=\"46\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The first relation gives the average heat transfer coefficient for the entire plate <\/font><font size=\"5\">when the flow is <i>laminar <\/i>over the <i>entire <\/i>plate. The second relation gives the average heat transfer coefficient for the entire plate only when the flow is <i>turbulent <\/i>over the <i>entire <\/i>plate, or when the laminar flow region of the plate is too small relative to the turbulent flow region.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">In some cases, a flat plate is sufficiently long for the flow to become turbulent, but not long enough to disregard the laminar flow region. In such cases, the <i>average <\/i>heat transfer coefficient over the entire plate is determined by per- forming the integration in Eq. 19\u20135 over two parts as<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0397.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0397\" border=\"0\" alt=\"FORCED CONVECTION-0397\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0397_thumb.jpg\" width=\"368\" height=\"120\"><\/a><\/font>  <\/p>\n<h5 align=\"justify\"><font size=\"5\">The constants in this relation will be different for different critical Reynolds numbers.<\/font><\/h5>\n<p align=\"justify\"><font size=\"5\"><i>Liqui<\/i><i>d metals <\/i>such as mercury have high thermal conductivities, and are commonly used in applications that require high heat transfer rates. However, they have very small Prandtl numbers, and thus the thermal boundary layer develops much faster than the velocity boundary layer. Then we can assume the velocity in the thermal boundary layer to be constant at the free-stream <\/font><font size=\"5\">value and solve the energy equation. It gives<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0398.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0398\" border=\"0\" alt=\"FORCED CONVECTION-0398\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0398_thumb.jpg\" width=\"356\" height=\"123\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">These relations have been obtained for the case of <i>isotherma<\/i><i>l <\/i>surfaces but could also be used approximately for the case of nonisothermal surfaces by assuming the surface temperature to be constant at some average value. Also, the surfaces are assumed to be <i>smoot<\/i><i>h<\/i>, and the free stream to be <i>turbulen<\/i><i>t free<\/i>. The effect of variable properties can be accounted for by evaluating all properties at the film temperature.<\/font>  <\/p><div class=\"nrfqx6a0dae017e4c1\" ><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.nrfqx6a0dae017e4c1 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.nrfqx6a0dae017e4c1 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.nrfqx6a0dae017e4c1 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.nrfqx6a0dae017e4c1 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.nrfqx6a0dae017e4c1 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n<div class=\"uxlnq6a0dae017e365\" ><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.uxlnq6a0dae017e365 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 993px) and (max-width: 1200px) {\r\n.uxlnq6a0dae017e365 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 769px) and (max-width: 992px) {\r\n.uxlnq6a0dae017e365 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (min-width: 768px) and (max-width: 768px) {\r\n.uxlnq6a0dae017e365 {\r\ndisplay: block;\r\n}\r\n}\r\n@media screen and (max-width: 767px) {\r\n.uxlnq6a0dae017e365 {\r\ndisplay: block;\r\n}\r\n}\r\n<\/style>\r\n\n<p align=\"justify\"><font size=\"5\"><b>Fla<\/b><b>t Plate with Unheated Starting Length<\/b><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">So far we have limited our consideration to situations for which the entire <\/font><font size=\"5\">plate is heated from the leading edge. But many practical applications involve surfaces with an unheated starting section of length j, shown in Fig. 19\u201311, and thus there is no heat transfer for 0 &lt; <i>x <\/i>&lt; j. In such cases, the velocity boundary layer starts to develop at the leading edge (<i>x <\/i>= 0), but the thermal boundary layer starts to develop where heating starts (<i>x <\/i>= j).<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">Consider a flat plate whose heated section is maintained at a constant tem- perature (<i>T <\/i>= <i>T<\/i><i>s <\/i>constant for <i>x <\/i>&gt; j). Using integral solution methods (see Kays and Crawford, 1994), the local Nusselt numbers for both laminar and<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0399.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0399\" border=\"0\" alt=\"FORCED CONVECTION-0399\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0399_thumb.jpg\" width=\"157\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0400.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0400\" border=\"0\" alt=\"FORCED CONVECTION-0400\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0400_thumb.jpg\" width=\"364\" height=\"58\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">for <i>x <\/i>&gt; j. Note that for j = 0, these Nu<i>x <\/i>relations reduce to Nu<i>x <\/i>(for j = 0), which is the Nusselt number relation for a flat plate without an unheated starting length. Therefore, the terms in brackets in the denominator serve as correction factors for plates with unheated starting lengths.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The determination of the average Nusselt number for the heated section of a plate requires the integration of the local Nusselt number relations above, which cannot be done analytically. Therefore, integrations must be done nu- merically. The results of numerical integrations have been correlated for the average convection coefficients [Thomas (1977) as<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0401.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0401\" border=\"0\" alt=\"FORCED CONVECTION-0401\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0401_thumb.jpg\" width=\"354\" height=\"62\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0402.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0402\" border=\"0\" alt=\"FORCED CONVECTION-0402\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0402_thumb.jpg\" width=\"178\" height=\"193\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">The first relation gives the average convection coefficient for the entire heated section of the plate when the flow is laminar over the entire plate. Note that for j = 0 it reduces to <i>h<\/i><i>L <\/i>= 2<i>h<\/i><i>x <\/i>= <i>L <\/i>, as expected. The second relation gives the average convection coefficient for the case of turbulent flow over the en- tire plate or when the laminar flow region is small relative to the turbulent region.<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><b>Unifor<\/b><b>m Heat Flux<\/b><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">When a flat plate is subjected to <i>uniform heat flux <\/i>instead of uniform temper<\/font><font size=\"5\">ature, the local Nusselt number is given by<\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0403.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0403\" border=\"0\" alt=\"FORCED CONVECTION-0403\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0403_thumb.jpg\" width=\"389\" height=\"43\"><\/a><\/font>  <\/p>\n<p align=\"justify\"><font size=\"5\">These relations give values that are 36 percent higher for laminar flow and 4 percent higher for turbulent flow relative to the isothermal plate case. When the plate involves an unheated starting length, the relations developed for the uniform surface temperature case can still be used provided that Eqs. 19\u201324 and 19\u201325 are used for Nu<i>x<\/i>(for j = 0) in Eqs. 19\u201320 and 19\u201321, respectively.<\/font>  <\/p>\n<h5 align=\"justify\"><font size=\"5\">When heat flux is prescribed, the rate of heat transfer to or from the plate and the surface temperature at a distance <i>x <\/i>are determined from<\/font><\/h5>\n<p align=\"justify\"><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0404.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0404\" border=\"0\" alt=\"FORCED CONVECTION-0404\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0404_thumb.jpg\" width=\"518\" height=\"481\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0405.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0405\" border=\"0\" alt=\"FORCED CONVECTION-0405\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0405_thumb.jpg\" width=\"414\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0406.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0406\" border=\"0\" alt=\"FORCED CONVECTION-0406\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0406_thumb.jpg\" width=\"397\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0407.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0407\" border=\"0\" alt=\"FORCED CONVECTION-0407\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0407_thumb.jpg\" width=\"297\" height=\"484\"><\/a><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0408.jpg\"><img decoding=\"async\" loading=\"lazy\" style=\"background-image: none; border-right-width: 0px; margin: 0px auto; padding-left: 0px; padding-right: 0px; display: block; float: none; border-top-width: 0px; border-bottom-width: 0px; border-left-width: 0px; padding-top: 0px\" title=\"FORCED CONVECTION-0408\" border=\"0\" alt=\"FORCED CONVECTION-0408\" src=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-content\/uploads\/2016\/03\/FORCED-CONVECTION-0408_thumb.jpg\" width=\"370\" height=\"166\"><\/a><\/p>\n<p align=\"justify\">\n<p align=\"justify\"><font size=\"5\"><\/font><\/p>\n","protected":false},"excerpt":{"rendered":"<p>PARALLEL FLOW OVER FLAT PLATES Consider the parallel flow of a fluid over a flat plate of length L in the flow direction, as shown in Fig. 19\u20138. The x-coordinate is measured along the plate surface from the leading edge in the direction of the flow. The fluid approaches the plate in the x-direction with [&hellip;]<br \/><a href=\"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/forced-convectionparallel-flow-over-flat-plates\/\" 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\/3352"}],"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=3352"}],"version-history":[{"count":1,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/3352\/revisions"}],"predecessor-version":[{"id":3353,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/posts\/3352\/revisions\/3353"}],"wp:attachment":[{"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/media?parent=3352"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/categories?post=3352"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/machineryequipmentonline.com\/hydraulics-and-pneumatics\/wp-json\/wp\/v2\/tags?post=3352"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}