[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-671665-105":59,"doc-detail-671665-en":133},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":126,"head_meta":128,"extra_data":130,"updated_unix":132},105,"en","heat-transfer-key-equations-engineering-notes","Heat-Transfer Key Equations - Engineering Notes","","A compact engineering reference compiling core heat-transfer nomenclature and governing equations across conduction, convection, and radiation. It lists standard definitions for thermal properties such as thermal conductivity, thermal diffusivity, specific heat, and thermal resistance, then summarizes key laws including Fourier’s law, Newton’s cooling law, and Stefan-Boltzmann’s law. It also covers energy balance for control volumes, boundary conditions (Dirichlet, Neumann, insulated), thermal resistance and fin relations, lumped (Lang) capacitance assumptions, and non-dimensional analysis with Biot and Fourier numbers.",{"@graph":69,"@context":125},[70,84,104],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/heat-transfer-key-equations-engineering-notes/671665/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":98,"encodingFormat":97,"isAccessibleForFree":99,"interactionStatistic":100},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/heat-transfer-key-equations-engineering-notes/671665.png","ImageObject",300,407,{"name":92,"@type":93},"Indoniesian Boy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02",true,{"@type":101,"interactionType":102,"userInteractionCount":8},"InteractionCounter",{"@type":103},"ViewAction",{"@type":105,"mainEntity":106},"FAQPage",[107,113,117,121],{"name":108,"@type":109,"acceptedAnswer":110},"What are the key heat-transfer quantities and units summarized in the notes?","Question",{"text":111,"@type":112},"The notes compile nomenclature for power, heat flux, heat, thermal conductivity, convective heat transfer coefficient, thermal diffusivity, thermal resistance, specific heat, and characteristic length with corresponding units.","Answer",{"name":114,"@type":109,"acceptedAnswer":115},"Which governing equations are included for conduction, convection, and radiation?",{"text":116,"@type":112},"Conduction is covered using Fourier’s law and the heat diffusion equation; convection is covered using Newton’s cooling law and convection relations; radiation is covered using Stefan-Boltzmann’s law and emissivity.",{"name":118,"@type":109,"acceptedAnswer":119},"How do boundary conditions differ in the presented framework?",{"text":120,"@type":112},"The notes distinguish Dirichlet conditions (constant surface temperature), Neumann conditions (constant heat flux), and insulated surfaces, and also show how convection combines with boundary behavior through thermal resistance formulations.",{"name":122,"@type":109,"acceptedAnswer":123},"When is lumped (Lang) capacitance valid and which non-dimensional numbers are provided?",{"text":124,"@type":112},"Lumped (Lang) capacitance is stated as valid when the condition involving 0.1 is met. Non-dimensional analysis includes quantities such as the Biot number and Fourier number to characterize conduction and transient behavior.","https://schema.org",{"og:url":83,"og:type":127,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":129,"canonical":83},"index,follow",{"doc_id":131,"site_id":62},671665,1793577992,{"code":4,"msg":5,"data":134},{"doc_id":131,"user_id":135,"nickname":92,"user_avatar":136,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":137,"file_id":138,"file_url":139,"file_type":140,"file_size":141,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":14,"language":142,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":143,"faqs":144,"seo_title":145,"seo_description":67,"update_tm":132,"read_time":24},962090760608,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Heat Transfer Key Equations  \nHere’s a hot nomenclature  \n􀝍 Power (heat transfer per unit time), measured in 􀜹  \n􀝍 ′′ Heat flux (power per unit area), measured in 􀜹 􀝉 −2  \n􀜳 Heat (thermal energy transferred over a time period), measured in 􀜬  \n􀝇 Thermal conductivity (a material property), measured in 􀜹 􀝉−1􀜭 −1 ℎ Convective heat transfer coefficient , measured in 􀜹 􀝉2 􀜭 −2  \n􀟙 Thermal diffusivity , measured in 􀝉 2 􀝏 −1  \n􀜴 􀯧 Thermal resistance , measured in 􀜭 􀜹−1  \n􀜿 Specific heat, measured in 􀜬 􀝇􀝃−1􀜭 −1  \n􀜮 􀮼 Characteristic length , measured in 􀝉  \nConduction  \nFourier’s Law  \nLinear temperature distribution  \nConvection  \nNewton’s Cooling Law  \n􀝍 ′′ = −􀝇 􀝀􀝀􀝐􀝔  \n􀝀􀜶   􀜶2 − 􀜶1 =  \n􀝀􀝔 􀜮  \n􀝍 ′′ = ℎ (􀜶􀯌 − 􀜶∞)  \nHeat Diffusion Equation  \n􀝇 (􀟲􀟲2􀝔􀜶2 + 􀟲􀟲2􀝕􀜶2 + 􀟲􀟲2􀝖􀜶2) + 􀝍̇􀯚 = 􀟩􀜿 􀟲􀟲􀜶􀝐 Steady, 1D, no 􀝍̇􀯚 􀜶 (􀝔) = 􀜿1􀝔  \nEnergy balance of a control volume  \ṅ􀜧􀯜􀯡 − ̇􀜧􀯢􀯨􀯧 + ̇􀜧􀯚 = ̇􀜧􀯦􀯧  \nRadiation  \nStefan-Boltzmann’s Law  \nEmissivity  \n􀜧􀮻 is the emissive power, Boltzmann constant, 5.67  \nHeat Diffusion in 1 dimension Steady, 1D, with 􀝍̇􀯚  \nThermal diffusivity, 􀟙  \n􀝍 ′′ = 􀜧􀯕 = 􀟪􀜶4  \n􀟝 =  \n 􀜧   \n􀜧􀯕  \nand 􀟪 is the Stefan-× 10−8 􀜹 􀝉−2􀜭 −4  \n􀟲 2 􀜶   􀟲􀜶  \n􀝇 􀟲􀝔 2 + 􀝍̇􀯚 = 􀟩􀜿 􀟲􀝐􀜶 (􀝔) = 􀝍̇2􀝔􀝇2 + 􀜿1􀝔 + 􀜿2  \n􀟙 = 􀝇􀟩􀜿  \nDirichlet Condition  \nConstant surface temperature  \n􀜶 (0, 􀝐) = 􀜶􀯦  \nVon  \nConstant heat flux  \n−􀝇  \n􀟲􀟲􀜶􀝔0 = 􀝍􀯦  \nNeumann  \nInsulated surface  \n 􀟲􀜶   \n􀟲􀝔0  \n= 0  \nConvection  \nCombination  \n− 􀝇 􀟲􀟲􀜶􀝔0 = ℎ [􀜶∞ − 􀜶(0, 􀝐)]  \nThermal Resistance  \nThermal resistance Per unit area  \n􀜴 􀯧 =  \nΔ􀜶  \n􀝍  \n􀜴′′􀯧 =  \nΔ􀜶  \n􀝍 ′′  \nFins  \n􀝀􀝀􀝔 (􀜣􀯖􀝀􀝀􀝔􀜶~~ ~~ ) − ℎ􀝇 􀝀􀜣􀝀􀝔􀯦 (􀜶 − 􀜶∞) = 0  \nFor uniform cross-  􀝀 2 􀜶   ℎ􀜲   \nsection 􀝀􀝔2 − 􀝇􀜣􀮼 (􀜶 − 􀜶∞)  \n= 0  \nFor Conduction  \nFor Convection  \n􀜴 􀯧 􀯖􀯢􀯡􀯗 =  \n 􀜮   \n􀝇􀜣  \n􀜴 􀯧 􀯖􀯢􀯡􀯩 = 1ℎ􀜣  \nTotal Heat Transfer Coefficient  \nParametrising  \n􀝉 2 = ℎ􀜲􀝇􀜣~~ ~~􀮼~~ ~~ 􀟠 = 􀜶 − 􀜶∞􀝀􀝀2􀝔􀟠2 − 􀝉2 􀟠 = 0 􀟠 (􀝔)  \n= 􀜥1 􀝁 􀯠􀯫 − 􀜥2 􀝁 −􀯠􀯫  \n􀝍 = 􀜷􀜣Δ􀜶 􀜴 􀯧􀯢􀯧􀯔􀯟 = 1􀜷􀜣  \nLumped (Lang) Capacitance  \nThis assumption is valid when 􀜤􀝅 \u003C 0.1  \n􀝀􀜶  \n􀟩􀜿􀜸 = −ℎ􀜣(􀜶 − 􀜶∞)􀝀􀝐  \nTemperature-time 􀜶 − 􀜶∞ − ℎ􀮺  􀯧  \n~~ ~~ = 􀝁 􀰘􀯖􀯏  \n􀜶􀯜 − 􀜶∞  \nTime constant  \n􀟬􀯧 =  \n􀟩􀜿􀜸  \nℎ􀜣  \nNon-Dimensional Analysis  \nFor when 􀜤􀝅 > 0.1  \n􀝔 ∗ = 􀝔􀜮~~ ~~􀮼~~ ~~ 􀟠 ∗ = 􀟠􀟠􀯜 = 􀜶􀜶􀯜~~ ~~−~~ ~~~~ ~~ 􀝐 ∗ = 􀜨􀝋 = 􀟙􀜮􀝐2􀮼  \n􀟲 2 􀜶   1 􀟲􀜶=  \n􀟲􀝔 2 􀟙 􀟲􀝐  \nbecomes  \n􀟲 2 􀟠 ∗   􀟲􀟠 ∗=  \n􀟲􀝔 ∗2 􀟲􀜨􀝋  \nWhich solves with tabulated constants:  \n􀟠 ∗ ≈ 􀜥1 􀝁 −􀰍21􀮿􀯢 cos (􀟞1􀝔 ∗ )  \nTip Conditions  \nConvection  \nAdiabatic  \nFixed temperature Infinite length (􀝉􀜮 > 2. 65)  \nImportant Quantities  \nBiot Number  \nCharacteristic Length  \nFourier Number  \n−􀝇  \n 􀝀􀟠   \n􀝀􀝔􀯅  \n= ℎ􀟠 (􀜮)  \n 􀝀􀟠   \n􀝀􀝔􀯅  \n= 0  \n􀟠 (􀜮) = 􀟠􀯅  \n􀟠 (􀜮) = 0  \n􀜤􀝅 = ℎ􀜮􀝇􀮼  \n􀜴 􀯖􀯢􀯡􀯗   Δ􀜶􀯦􀯢􀯟􀯜􀯗 􀜤􀝅 = =  \n􀜴 􀯖􀯢􀯡􀯩 Δ􀜶􀯙􀯟􀯨􀯜􀯗􀜮􀯂􀮼 = 􀜸􀜣  \n􀜮􀯂􀯂􀮼 = 􀝔 􀝋􀝂 max Δ􀜶  \n􀜨􀝋 =  \n􀟙􀝐  \n􀜮2􀮼","cbCaic8eTKqTMaTi","https://ap.wps.com/l/cbCaic8eTKqTMaTi","pdf",492593,"English","# Heat Transfer Key Equations\n## Conduction\n## Convection\n## Radiation\n## Boundary Conditions\n## Thermal Resistance and Fins\n## Lumped (Lang) Capacitance\n## Non-Dimensional Analysis\n## Tip Conditions and Important Quantities","[{\"question\":\"What are the key heat-transfer quantities and units summarized in the notes?\",\"answer\":\"The notes compile nomenclature for power, heat flux, heat, thermal conductivity, convective heat transfer coefficient, thermal diffusivity, thermal resistance, specific heat, and characteristic length with corresponding units.\"},{\"question\":\"Which governing equations are included for conduction, convection, and radiation?\",\"answer\":\"Conduction is covered using Fourier’s law and the heat diffusion equation; convection is covered using Newton’s cooling law and convection relations; radiation is covered using Stefan-Boltzmann’s law and emissivity.\"},{\"question\":\"How do boundary conditions differ in the presented framework?\",\"answer\":\"The notes distinguish Dirichlet conditions (constant surface temperature), Neumann conditions (constant heat flux), and insulated surfaces, and also show how convection combines with boundary behavior through thermal resistance formulations.\"},{\"question\":\"When is lumped (Lang) capacitance valid and which non-dimensional numbers are provided?\",\"answer\":\"Lumped (Lang) capacitance is stated as valid when the condition involving 0.1 is met. Non-dimensional analysis includes quantities such as the Biot number and Fourier number to characterize conduction and transient behavior.\"}]","Heat-Transfer Key Equations - Engineering Notes | PDF"]