{"id":100128,"date":"2026-02-15T20:19:16","date_gmt":"2026-02-15T20:19:16","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100128"},"modified":"2026-04-05T15:43:00","modified_gmt":"2026-04-05T15:43:00","slug":"heat-exchanger-lmtd","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/heat-exchanger-lmtd\/","title":{"rendered":"LMTD Calculator \u2014 Counter &#038; Parallel Flow Heat Exchanger"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Heat Exchanger LMTD Calculator\",\"description\":\"LMTD calculator for parallel and counter flow heat exchangers. Includes Q=U\u00b7A\u00b7LMTD.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/heat-exchanger-lmtd\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is LMTD?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"LMTD (Log Mean Temperature Difference) is the effective average temperature driving force for heat transfer in a heat exchanger. It accounts for the varying temperature difference between hot and cold fluids along the exchanger length using a logarithmic mean.\"}},\n{\"@type\":\"Question\",\"name\":\"How is LMTD calculated?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"LMTD = (\u0394T\u2081 \u2212 \u0394T\u2082) \/ ln(\u0394T\u2081\/\u0394T\u2082). For counter flow: \u0394T\u2081 = T_h,in \u2212 T_c,out and \u0394T\u2082 = T_h,out \u2212 T_c,in. For parallel flow: \u0394T\u2081 = T_h,in \u2212 T_c,in and \u0394T\u2082 = T_h,out \u2212 T_c,out.\"}},\n{\"@type\":\"Question\",\"name\":\"Why is counter flow more efficient than parallel flow?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Counter flow produces a higher LMTD for the same inlet\/outlet temperatures, meaning less heat transfer area is needed. The cold fluid can also be heated closer to the hot fluid inlet temperature, which is impossible in parallel flow.\"}},\n{\"@type\":\"Question\",\"name\":\"When is LMTD undefined?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"When \u0394T\u2081 = \u0394T\u2082 (equal temperature differences at both ends), the formula gives 0\/0. In this special case, LMTD simply equals \u0394T\u2081 = \u0394T\u2082 (arithmetic mean equals log mean when both are equal).\"}},\n{\"@type\":\"Question\",\"name\":\"What is Q = U \u00d7 A \u00d7 LMTD?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"This is the basic heat exchanger design equation. Q is heat duty (W), U is overall heat transfer coefficient (W\/m\u00b2K), A is heat transfer area (m\u00b2), and LMTD is the log mean temperature difference (K). Given any three, you can find the fourth.\"}}\n]}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Heat Exchanger LMTD Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/heat-exchanger-lmtd\/\"}]}<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" 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.15s}.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none;white-space:nowrap;transition:background .15s}.vc-promo-link:hover{background:var(--vc-accent-hover)}.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\n.vc-viz{margin:20px 0;background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px;overflow:hidden}.vc-viz svg{width:100%;height:auto;display:block}.vc-viz-title{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:0.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:12px}<\/style>\n\n<div class=\"vc-calculator\">\n<header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p><h1 class=\"vc-header-title\">Heat Exchanger LMTD Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate Log Mean Temperature Difference for parallel and counter flow heat exchangers. Optional Q=U\u00b7A\u00b7LMTD sizing.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">LMTD<\/span><span class=\"vc-badge\">Counter &amp; Parallel<\/span><span class=\"vc-badge\">#181<\/span><\/div><\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Thi\">Hot Inlet <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Thi\" step=\"any\" value=\"120\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Tho\">Hot Outlet <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Tho\" step=\"any\" value=\"80\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Tci\">Cold Inlet <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Tci\" step=\"any\" value=\"20\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Tco\">Cold Outlet <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Tco\" step=\"any\" value=\"60\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-U\">Overall U <span class=\"vc-label-hint\">(W\/m\u00b2\u00b7K) \u2014 optional<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-U\" step=\"any\" min=\"0\" value=\"500\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-Q\">Heat Duty Q <span class=\"vc-label-hint\">(kW) \u2014 optional<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-Q\" step=\"any\" min=\"0\" value=\"100\"><\/div>\n        <\/div>\n        <div class=\"vc-presets\"><div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-Thi=\"120\" data-Tho=\"80\" data-Tci=\"20\" data-Tco=\"60\">Water-Water 120\u219280 \/ 20\u219260<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-Thi=\"150\" data-Tho=\"90\" data-Tci=\"25\" data-Tco=\"85\">Steam-Water 150\u219290 \/ 25\u219285<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-Thi=\"200\" data-Tho=\"120\" data-Tci=\"30\" data-Tco=\"70\">Oil Cooler 200\u2192120 \/ 30\u219270<\/button>\n        <\/div>\n    <\/form>\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Results<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button><\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Counter Flow LMTD<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lmtd-cf\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Parallel Flow LMTD<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lmtd-pf\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Counter Flow Area (if U &amp; Q given)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area-cf\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Parallel Flow Area (if U &amp; Q given)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area-pf\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Hot Side \u0394T<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dTh\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Cold Side \u0394T<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dTc\">\u2014<\/div><\/div>\n        <\/div>\n        <div class=\"vc-note\" id=\"vc-note\"><\/div>\n        <div class=\"vc-viz\" id=\"vc-viz\"><div class=\"vc-viz-title\">Temperature Profile (Counter Flow)<\/div><div id=\"vc-viz-svg\"><\/div><\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>LMTD Formula<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div><h3>Counter Flow<\/h3><p>\u0394T\u2081 = T_h,in \u2212 T_c,out &nbsp;&nbsp;|&nbsp;&nbsp; \u0394T\u2082 = T_h,out \u2212 T_c,in<\/p><h3>Parallel Flow<\/h3><p>\u0394T\u2081 = T_h,in \u2212 T_c,in &nbsp;&nbsp;|&nbsp;&nbsp; \u0394T\u2082 = T_h,out \u2212 T_c,out<\/p><h3>Design Equation<\/h3><div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div><p>Counter flow always produces a higher LMTD than parallel flow for the same temperatures, meaning less area is needed.<\/p><\/div><\/div><\/div>\n<div class=\"vc-section\" id=\"vc-sec-related\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\"><a class=\"vc-related-link\" href=\"\/calculators\/heater-power-calculator\/\">Heater Power<\/a><a class=\"vc-related-link\" href=\"\/calculators\/heat-loss-wall\/\">Heat Loss Wall<\/a><a class=\"vc-related-link\" href=\"\/calculators\/insulation-thickness-calculator\/\">Insulation Thickness<\/a><\/div><\/div><\/div><\/div>\n<div class=\"vc-section\" id=\"vc-sec-faq\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div><\/div>\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Professional instruments. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n<footer class=\"vc-footer\"><p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p><div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div><\/footer>\n<\/div>\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n'use strict';var SLUG='heat-exchanger-lmtd';function $(id){return document.getElementById(id)}function fmt(n,d){if(isNaN(n)||!isFinite(n))return'\u2014';return n.toFixed(d===undefined?2:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\nfunction calcLMTD(dT1,dT2){if(dT1<=0||dT2<=0)return NaN;if(Math.abs(dT1-dT2)<0.001)return dT1;return(dT1-dT2)\/Math.log(dT1\/dT2)}\nfunction calculate(){var Thi=parseFloat($('vc-Thi').value),Tho=parseFloat($('vc-Tho').value),Tci=parseFloat($('vc-Tci').value),Tco=parseFloat($('vc-Tco').value);if(isNaN(Thi)||isNaN(Tho)||isNaN(Tci)||isNaN(Tco)){$('vc-results').classList.remove('vc-visible');return}\nvar dT1_cf=Thi-Tco,dT2_cf=Tho-Tci;var dT1_pf=Thi-Tci,dT2_pf=Tho-Tco;var lmtd_cf=calcLMTD(dT1_cf,dT2_cf);var lmtd_pf=calcLMTD(dT1_pf,dT2_pf);\n$('vc-r-lmtd-cf').innerHTML=fmt(lmtd_cf,2)+' <span class=\"vc-rcard-unit\">\u00b0C<\/span>';\n$('vc-r-lmtd-pf').innerHTML=fmt(lmtd_pf,2)+' <span class=\"vc-rcard-unit\">\u00b0C<\/span>';\n$('vc-r-dTh').innerHTML=fmt(Thi-Tho,1)+' <span class=\"vc-rcard-unit\">\u00b0C<\/span>';\n$('vc-r-dTc').innerHTML=fmt(Tco-Tci,1)+' <span class=\"vc-rcard-unit\">\u00b0C<\/span>';\nvar U=parseFloat($('vc-U').value),Q=parseFloat($('vc-Q').value)*1000;\nif(!isNaN(U)&&!isNaN(Q)&&U>0&&Q>0){if(!isNaN(lmtd_cf)&&lmtd_cf>0){var A_cf=Q\/(U*lmtd_cf);$('vc-r-area-cf').innerHTML=fmt(A_cf,2)+' <span class=\"vc-rcard-unit\">m\u00b2<\/span>'}else{$('vc-r-area-cf').innerHTML='\u2014'}\nif(!isNaN(lmtd_pf)&&lmtd_pf>0){var A_pf=Q\/(U*lmtd_pf);$('vc-r-area-pf').innerHTML=fmt(A_pf,2)+' <span class=\"vc-rcard-unit\">m\u00b2<\/span>'}else{$('vc-r-area-pf').innerHTML='\u2014'}}else{$('vc-r-area-cf').innerHTML='<span class=\"vc-rcard-unit\">enter U & Q<\/span>';$('vc-r-area-pf').innerHTML='<span class=\"vc-rcard-unit\">enter U & Q<\/span>'}\nvar notes=[];if(!isNaN(lmtd_cf)&&!isNaN(lmtd_pf)&&lmtd_cf>0&&lmtd_pf>0){var pct=((lmtd_cf-lmtd_pf)\/lmtd_pf*100);notes.push('Counter flow LMTD is '+fmt(pct,1)+'% higher than parallel flow.')}\nif(dT1_pf<=0||dT2_pf<=0)notes.push('\u26a0 Parallel flow: temperature cross detected \u2014 not feasible.');if(dT1_cf<=0||dT2_cf<=0)notes.push('\u26a0 Counter flow: temperature cross detected \u2014 check temperatures.');\n$('vc-note').innerHTML=notes.join('<br>');$('vc-note').style.display=notes.length?'':'none';\n$('vc-results').classList.add('vc-visible');drawTempProfile(Thi,Tho,Tci,Tco);saveHistory({Thi:Thi,Tho:Tho,Tci:Tci,Tco:Tco,lmtd_cf:lmtd_cf,_summary:'LMTD(CF)='+fmt(lmtd_cf,1)+'\u00b0C'})}\n\nfunction drawTempProfile(Thi,Tho,Tci,Tco){var el=$('vc-viz-svg');if(!el)return;var W=500,H=200,mx=60,my=30,pw=W-2*mx,ph=H-2*my;var allT=[Thi,Tho,Tci,Tco];var Tmin=Math.min.apply(null,allT)-5,Tmax=Math.max.apply(null,allT)+5;function yT(T){return my+ph-(T-Tmin)\/(Tmax-Tmin)*ph}\nvar s='<svg viewBox=\"0 0 '+W+' '+H+'\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\">';s+='<rect width=\"'+W+'\" height=\"'+H+'\" fill=\"var(--vc-surface)\" rx=\"4\"\/>';\n\/\/ Axes\ns+='<line x1=\"'+mx+'\" y1=\"'+my+'\" x2=\"'+mx+'\" y2=\"'+(my+ph)+'\" stroke=\"var(--vc-border)\" stroke-width=\"1\"\/>';s+='<line x1=\"'+mx+'\" y1=\"'+(my+ph)+'\" x2=\"'+(mx+pw)+'\" y2=\"'+(my+ph)+'\" stroke=\"var(--vc-border)\" stroke-width=\"1\"\/>';\ns+='<text x=\"'+(mx+pw\/2)+'\" y=\"'+(H-5)+'\" text-anchor=\"middle\" font-size=\"9\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-muted)\">Exchanger Length \u2192<\/text>';\n\/\/ Hot stream (counter flow: left=Thi, right=Tho)\ns+='<line x1=\"'+mx+'\" y1=\"'+yT(Thi).toFixed(1)+'\" x2=\"'+(mx+pw)+'\" y2=\"'+yT(Tho).toFixed(1)+'\" stroke=\"var(--vc-red,#b91c1c)\" stroke-width=\"2.5\"\/>';\ns+='<circle cx=\"'+mx+'\" cy=\"'+yT(Thi).toFixed(1)+'\" r=\"4\" fill=\"var(--vc-red,#b91c1c)\"\/>';s+='<circle cx=\"'+(mx+pw)+'\" cy=\"'+yT(Tho).toFixed(1)+'\" r=\"4\" fill=\"var(--vc-red,#b91c1c)\"\/>';\ns+='<text x=\"'+(mx-5)+'\" y=\"'+(yT(Thi)-6).toFixed(1)+'\" text-anchor=\"end\" font-size=\"10\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-red,#b91c1c)\">'+Thi+'\u00b0<\/text>';\ns+='<text x=\"'+(mx+pw+5)+'\" y=\"'+(yT(Tho)-6).toFixed(1)+'\" font-size=\"10\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-red,#b91c1c)\">'+Tho+'\u00b0<\/text>';\n\/\/ Cold stream (counter flow: left=Tco, right=Tci)\ns+='<line x1=\"'+mx+'\" y1=\"'+yT(Tco).toFixed(1)+'\" x2=\"'+(mx+pw)+'\" y2=\"'+yT(Tci).toFixed(1)+'\" stroke=\"var(--vc-blue)\" stroke-width=\"2.5\"\/>';\ns+='<circle cx=\"'+mx+'\" cy=\"'+yT(Tco).toFixed(1)+'\" r=\"4\" fill=\"var(--vc-blue)\"\/>';s+='<circle cx=\"'+(mx+pw)+'\" cy=\"'+yT(Tci).toFixed(1)+'\" r=\"4\" fill=\"var(--vc-blue)\"\/>';\ns+='<text x=\"'+(mx-5)+'\" y=\"'+(yT(Tco)+14).toFixed(1)+'\" text-anchor=\"end\" font-size=\"10\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-blue)\">'+Tco+'\u00b0<\/text>';\ns+='<text x=\"'+(mx+pw+5)+'\" y=\"'+(yT(Tci)+14).toFixed(1)+'\" font-size=\"10\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-blue)\">'+Tci+'\u00b0<\/text>';\n\/\/ Legend\ns+='<line x1=\"'+(mx+pw\/2-50)+'\" y1=\"14\" x2=\"'+(mx+pw\/2-30)+'\" y2=\"14\" stroke=\"var(--vc-red,#b91c1c)\" stroke-width=\"2\"\/>';s+='<text x=\"'+(mx+pw\/2-27)+'\" y=\"17\" font-size=\"9\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-secondary)\">Hot<\/text>';\ns+='<line x1=\"'+(mx+pw\/2+10)+'\" y1=\"14\" x2=\"'+(mx+pw\/2+30)+'\" y2=\"14\" stroke=\"var(--vc-blue)\" stroke-width=\"2\"\/>';s+='<text x=\"'+(mx+pw\/2+33)+'\" y=\"17\" font-size=\"9\" font-family=\"var(--vc-mono)\" fill=\"var(--vc-ink-secondary)\">Cold<\/text>';\ns+='<\/svg>';el.innerHTML=s;}\ndocument.querySelectorAll('.vc-preset-btn').forEach(function(btn){btn.addEventListener('click',function(e){e.preventDefault();$('vc-Thi').value=this.getAttribute('data-Thi');$('vc-Tho').value=this.getAttribute('data-Tho');$('vc-Tci').value=this.getAttribute('data-Tci');$('vc-Tco').value=this.getAttribute('data-Tco');calculate()})});\n$('vc-form').addEventListener('input',calculate);$('vc-form').addEventListener('change',calculate);\n$('vc-copy-btn').addEventListener('click',function(){var t='Heat Exchanger LMTD\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nCounter Flow LMTD: '+$('vc-r-lmtd-cf').textContent+'\\nParallel Flow LMTD: '+$('vc-r-lmtd-pf').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu';if(navigator.clipboard)navigator.clipboard.writeText(t).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'},2000)})});\ndocument.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\nvar faqData=[{q:'What is LMTD?',a:'<p>Log Mean Temperature Difference \u2014 the effective average driving force for heat transfer. Accounts for varying \u0394T along the exchanger using a logarithmic mean.<\/p>'},{q:'How is LMTD calculated?',a:'<p>LMTD = (\u0394T\u2081 \u2212 \u0394T\u2082) \/ ln(\u0394T\u2081\/\u0394T\u2082). Counter flow: \u0394T\u2081 = Th,in\u2212Tc,out, \u0394T\u2082 = Th,out\u2212Tc,in. Parallel flow swaps accordingly.<\/p>'},{q:'Why is counter flow more efficient?',a:'<p>Higher LMTD = less area needed. Cold fluid can approach hot inlet temp (impossible in parallel flow). Always preferred when mechanically feasible.<\/p>'},{q:'When is LMTD undefined?',a:'<p>When \u0394T\u2081 = \u0394T\u2082 exactly, the formula gives 0\/0. In this case, LMTD = \u0394T\u2081 = \u0394T\u2082 (the special case is handled in this calculator).<\/p>'},{q:'What is Q = U \u00d7 A \u00d7 LMTD?',a:'<p>Basic heat exchanger design equation. Q = heat duty (W), U = overall heat transfer coefficient (W\/m\u00b2K), A = area (m\u00b2), LMTD = driving force (K).<\/p>'}];\nvar fl=$('vc-faq-list');faqData.forEach(function(f){fl.innerHTML+='<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>'+f.q+'<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">'+f.a+'<\/div><\/div><\/div>'});fl.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(!b)return;b.closest('.vc-faq-item').classList.toggle('vc-open')});\nfunction saveHistory(e){var k='vc_history_'+SLUG;var a=[];try{a=JSON.parse(localStorage.getItem(k))||[]}catch(x){}e._ts=new Date().toISOString();a.unshift(e);if(a.length>10)a=a.slice(0,10);try{localStorage.setItem(k,JSON.stringify(a))}catch(x){}}\nfunction renderFormulas(){try{katex.render('\\\\text{LMTD}=\\\\frac{\\\\Delta T_1-\\\\Delta T_2}{\\\\ln\\\\!\\\\left(\\\\dfrac{\\\\Delta T_1}{\\\\Delta T_2}\\\\right)}',$('vc-katex-1'),{displayMode:true,throwOnError:false});katex.render('Q = U \\\\cdot A \\\\cdot \\\\text{LMTD}',$('vc-katex-2'),{displayMode:true,throwOnError:false})}catch(e){}}\nfunction init(){renderFormulas();$('vc-note').style.display='none';calculate()}if(document.readyState==='loading')document.addEventListener('DOMContentLoaded',init);else init();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Free LMTD calculator for heat exchangers. Enter hot\/cold inlet and outlet temperatures to calculate log mean temperature difference for parallel and counter flow configurations.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100128","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100128\/revisions"}],"predecessor-version":[{"id":100953,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100128\/revisions\/100953"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}