{"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":"2026-07-12T12:36:08","modified_gmt":"2026-07-12T12:36:08","slug":"heat-exchanger-lmtd","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/hi\/calculators\/heat-exchanger-lmtd\/","title":{"rendered":"Terminal-Temperature LMTD &#038; Area Calculator"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Terminal-Temperature LMTD and Area Calculator\",\"description\":\"Calculate stable LMTD for one documented parallel or counterflow temperature arrangement and area using documented duty, U and correction factor.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/heat-exchanger-lmtd\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web 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id=\"vc-lmtd\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">One documented arrangement and thermal basis<\/p><h1 class=\"vc-header-title\">Terminal-Temperature LMTD &amp; Area Calculator<\/h1><p class=\"vc-header-subtitle\">Calculate a numerically stable log-mean temperature difference for one documented counterflow or parallel-flow arrangement, then apply a documented correction factor, duty and overall U-value.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Stable log1p LMTD<\/span><span class=\"vc-badge\">Q = UAF\u0394Tlm<\/span><span class=\"vc-badge\">No configuration ranking<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-doc-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-id\">Project \/ exchanger identifier<\/label><input class=\"vc-input\" id=\"vc-id\" type=\"text\" maxlength=\"220\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-arr\">Documented idealized arrangement<\/label><select class=\"vc-select\" id=\"vc-arr\"><option value=\"\">Select\u2026<\/option><option value=\"counter\">Counterflow terminal pairing<\/option><option value=\"parallel\">Parallel-flow terminal pairing<\/option><\/select><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-temp-source\">Terminal-temperature source, operating case and revision<\/label><input class=\"vc-input\" id=\"vc-temp-source\" type=\"text\" maxlength=\"400\"><\/div><div class=\"vc-field vc-wide\"><label class=\"vc-label\" for=\"vc-profile\">Stream\/profile basis, including any documented isothermal phase change<\/label><input class=\"vc-input\" id=\"vc-profile\" type=\"text\" maxlength=\"450\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-thi\">Hot inlet T\u2095,\u1d62 <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" id=\"vc-thi\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-tho\">Hot outlet T\u2095,\u2092 <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" id=\"vc-tho\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-tci\">Cold inlet T\ud835\udc84,\u1d62 <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" id=\"vc-tci\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-tco\">Cold outlet T\ud835\udc84,\u2092 <span class=\"vc-label-hint\">(\u00b0C)<\/span><\/label><input class=\"vc-input\" id=\"vc-tco\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-duty\">Documented heat duty Q <span class=\"vc-label-hint\">(kW)<\/span><\/label><input class=\"vc-input\" id=\"vc-duty\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-duty-source\">Duty\/energy-balance source<\/label><input class=\"vc-input\" id=\"vc-duty-source\" type=\"text\" maxlength=\"350\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-u\">Overall U-value <span class=\"vc-label-hint\">(W\/(m\u00b2\u00b7K))<\/span><\/label><input class=\"vc-input\" id=\"vc-u\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-u-source\">U-value, fouling and area-basis source<\/label><input class=\"vc-input\" id=\"vc-u-source\" type=\"text\" maxlength=\"400\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-f\">Documented correction factor F <span class=\"vc-label-hint\">(0&lt;F\u22641)<\/span><\/label><input class=\"vc-input\" id=\"vc-f\" type=\"text\" inputmode=\"decimal\" maxlength=\"80\"><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-f-source\">F source \/ configuration basis<\/label><input class=\"vc-input\" id=\"vc-f-source\" type=\"text\" maxlength=\"400\"><\/div><\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Applicability gate:<\/strong> terminal temperatures must belong to the same documented steady case; hot temperature must not increase and cold temperature must not decrease unless a different signed convention\/model is explicitly developed. Both paired terminal differences must remain strictly positive.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Documented LMTD result<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Terminal difference \u0394T\u2081<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dt1\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Terminal difference \u0394T\u2082<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dt2\">\u2014<\/div><\/div><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Log-mean difference \u0394Tlm<\/div><div class=\"vc-rcard-value\" id=\"vc-r-lmtd\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Corrected driving force F\u0394Tlm<\/div><div class=\"vc-rcard-value\" id=\"vc-r-corrected\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Area from entered Q,U,F<\/div><div class=\"vc-rcard-value\" id=\"vc-r-area\">\u2014<\/div><\/div><\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><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\">Equations and design boundary<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><h3>Implemented terminal pairings<\/h3><div class=\"vc-formula-box\">Counterflow: \u0394T\u2081=T\u2095,\u1d62\u2212T\ud835\udc84,\u2092 ; \u0394T\u2082=T\u2095,\u2092\u2212T\ud835\udc84,\u1d62<br>Parallel flow: \u0394T\u2081=T\u2095,\u1d62\u2212T\ud835\udc84,\u1d62 ; \u0394T\u2082=T\u2095,\u2092\u2212T\ud835\udc84,\u2092<br>\u0394T<sub>lm<\/sub>=(\u0394T\u2081\u2212\u0394T\u2082)\/ln(\u0394T\u2081\/\u0394T\u2082)<br>A=Q\/(UF\u0394T<sub>lm<\/sub>)<\/div><p>Temperature differences in kelvins and degrees Celsius have the same numerical magnitude. The implementation uses log1p for close terminal differences and the exact continuous limit \u0394Tlm=\u0394T when \u0394T\u2081=\u0394T\u2082.<\/p><h3>Source and scope<\/h3><p>A NASA heat-exchanger design report uses the general relation q=UA\u0394Tlm and defines the terminal log-mean temperature difference. This page adds a user-documented correction factor F for arrangements where the chosen idealized pairing does not alone represent the actual geometry. F=1 is not assumed; it must be entered with its source.<\/p><h3>Why the former comparison was removed<\/h3><p>The former page computed counterflow and parallel-flow results from the same four outlet temperatures and announced that counterflow was more efficient and always preferred. Changing arrangement generally changes outlet temperatures, duty, U and feasible construction, so those two arithmetic pairings were not a controlled design comparison. The page also estimated both areas with no correction factor or Q\/U provenance.<\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Not exchanger design approval:<\/strong> verify stream energy balance, phase\/property changes, pressure drop, fouling, U\/area definition, correction-factor method, minimum approach, flow distribution, transient\/off-design cases and mechanical\/process-code requirements.<\/p><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Documented terminal-temperature LMTD arithmetic only. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var map={lm_id:'vc-id',lm_arr:'vc-arr',lm_temp_source:'vc-temp-source',lm_profile:'vc-profile',lm_thi:'vc-thi',lm_tho:'vc-tho',lm_tci:'vc-tci',lm_tco:'vc-tco',lm_duty:'vc-duty',lm_duty_source:'vc-duty-source',lm_u:'vc-u',lm_u_source:'vc-u-source',lm_f:'vc-f',lm_f_source:'vc-f-source'};function num(raw){var s=String(raw).trim().replace(',','.');if(s.length>80||!\/^[-+]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;return Number(s)}function fmt(v){if(!Number.isFinite(v))return'\u2014';if(v===0)return'0';return Number(v.toPrecision(12)).toString()}function clear(){['vc-r-dt1','vc-r-dt2','vc-r-lmtd','vc-r-corrected','vc-r-area'].forEach(function(i){$(i).textContent='\u2014'});$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function fail(m){clear();$('vc-error').textContent=m}function setUrl(){var u=new URL(location);Object.keys(map).forEach(function(q){var v=$(map[q]).value.trim();if(v)u.searchParams.set(q,v);else u.searchParams.delete(q)});history.replaceState(null,'',u.toString())}function lmean(a,b){if(a===b)return a;var x=(a-b)\/b;return(a-b)\/Math.log1p(x)}function calc(){setUrl();var x={};Object.keys(map).forEach(function(q){x[q]=$(map[q]).value.trim()});var any=Object.keys(x).some(function(q){return x[q]});if(!any){$('vc-error').textContent='';clear();return}if(!Object.keys(map).every(function(q){return x[q]})){fail('Enter every arrangement, temperature, duty, U, F and provenance field.');return}if(x.lm_arr!=='counter'&&x.lm_arr!=='parallel'){fail('Select a valid documented arrangement.');return}var thi=num(x.lm_thi),tho=num(x.lm_tho),tci=num(x.lm_tci),tco=num(x.lm_tco),qkw=num(x.lm_duty),u=num(x.lm_u),f=num(x.lm_f);if(![thi,tho,tci,tco,qkw,u,f].every(Number.isFinite)){fail('All numerical fields must be complete finite decimal numbers.');return}if(thi<tho){fail('Hot outlet must not exceed hot inlet for this model.');return}if(tco<tci){fail('Cold outlet must not be below cold inlet for this model.');return}if(qkw<=0||u<=0){fail('Duty and U-value must be strict positive numbers.');return}if(f<=0||f>1){fail('Correction factor F must be greater than 0 and no greater than 1.');return}if(![thi,tho,tci,tco,qkw,u,f].every(function(v){return Math.abs(v)<=1e30})){fail('Normalized inputs must not exceed 10\u00b3\u2070 in magnitude.');return}var dt1=x.lm_arr==='counter'?thi-tco:thi-tci,dt2=x.lm_arr==='counter'?tho-tci:tho-tco;if(!(dt1>0&&dt2>0)){fail('Both paired terminal temperature differences must be strict positive numbers; check crossing\/pinch and arrangement.');return}var lm=lmean(dt1,dt2),corrected=f*lm,q=qkw*1000,area=q\/(u*corrected);if(![lm,corrected,q,area].every(Number.isFinite)||Math.max(lm,corrected,q,area)>1e100){fail('LMTD\/area result exceeds the finite numerical range.');return}$('vc-error').textContent='';$('vc-r-dt1').textContent=fmt(dt1)+' K';$('vc-r-dt2').textContent=fmt(dt2)+' K';$('vc-r-lmtd').textContent=fmt(lm)+' K';$('vc-r-corrected').textContent=fmt(corrected)+' K';$('vc-r-area').textContent=fmt(area)+' m\u00b2';$('vc-r-note').textContent='Exchanger: '+x.lm_id+' | Arrangement: '+x.lm_arr+' | Temperatures: '+x.lm_temp_source+' | Profile: '+x.lm_profile+' | Duty: '+x.lm_duty_source+' | U: '+x.lm_u_source+' | F: '+x.lm_f_source+'.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var q=new URLSearchParams(location.search);Object.keys(map).forEach(function(x){if(q.has(x))$(map[x]).value=q.get(x)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Calculate stable LMTD for one documented counterflow or parallel-flow terminal pairing and area using documented duty, U-value and correction factor F.<\/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\/hi\/wp-json\/wp\/v2\/calculator\/100128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator\/100128\/revisions"}],"predecessor-version":[{"id":102447,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/calculator\/100128\/revisions\/102447"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/media?parent=100128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/categories?post=100128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/hi\/wp-json\/wp\/v2\/tags?post=100128"}],"curies":[{"name":"\u0921\u092c\u094d\u0932\u094d\u092f\u0942\u092a\u0940","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}