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It further covers energy balance and the heat equation for temperature distribution, thermal circuit and lumped-capacitance approaches, log-mean temperature difference, free convection correlations, and the ε–NTU method for heat exchangers.",{"@graph":14,"@context":71},[15,34,54],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/heat-transfer-equation-sheet-study-and-reference/671664/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":48,"encodingFormat":47,"isAccessibleForFree":49,"interactionStatistic":50},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/heat-transfer-equation-sheet-study-and-reference/671664.png","ImageObject",300,407,{"name":42,"@type":43},"Muffet","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-02",true,{"@type":51,"interactionType":52,"userInteractionCount":26},"InteractionCounter",{"@type":53},"ViewAction",{"@type":55,"mainEntity":56},"FAQPage",[57,63,67],{"name":58,"@type":59,"acceptedAnswer":60},"What fundamental equation set does the sheet use for heat transfer modeling?","Question",{"text":61,"@type":62},"It compiles Fourier’s law for conduction, Newton’s law of cooling for convection, and radiation relations based on blackbody emission and Stefan–Boltzmann behavior, combined with energy balance for consistent heat rates.","Answer",{"name":64,"@type":59,"acceptedAnswer":65},"How does the sheet handle transient vs steady-state energy balance?",{"text":66,"@type":62},"It states steady-state uses Est = 0 in the control-volume energy balance, while transient situations require the heat equation to determine temperature distribution over time.",{"name":68,"@type":59,"acceptedAnswer":69},"How are heat exchanger performance and temperature driving force computed?",{"text":70,"@type":62},"It provides log-mean temperature difference formulas and the ε–NTU method, including definitions of heat capacity rates and the heat exchanger effectiveness relation using Cmin and correction factors.","https://schema.org",{"og:url":32,"og:type":73,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":75,"canonical":32},"index,follow",{"doc_id":77,"site_id":7},671664,1793577987,{"code":4,"msg":80,"data":81},"success",[82,86,90,94,99,103,108,113,118,121,125],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":83,"show_sort_weight":84,"slug":85},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":87,"show_sort_weight":88,"slug":89},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":91,"show_sort_weight":92,"slug":93},"Exam",70,"exam",{"id":95,"doc_module":4,"doc_module_name":25,"category_name":96,"show_sort_weight":97,"slug":98},5,"Comic",60,"comic",{"id":100,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":101,"slug":102},6,50,"technology",{"id":104,"doc_module":4,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},7,"Healthcare",40,"healthcare",{"id":109,"doc_module":4,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},8,"Research & Report",30,"research-report",{"id":114,"doc_module":4,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},9,"Religion & Spirituality",20,"religion-spirituality",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":119,"show_sort_weight":116,"slug":120},"World Cup","world-cup",{"id":122,"doc_module":4,"doc_module_name":25,"category_name":123,"show_sort_weight":122,"slug":124},10,"Lifestyle","lifestyle",{"id":126,"doc_module":4,"doc_module_name":25,"category_name":127,"show_sort_weight":95,"slug":128},19,"General","general",{"code":4,"msg":80,"data":130},{"doc_id":77,"user_id":131,"nickname":42,"user_avatar":132,"doc_module":4,"category_id":100,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":26,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":138,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":78,"read_time":143},962090768927,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","1  \n# HEAT TRANSFER EQUATION SHEET\n\nHeat Conduction Rate Equations(Fourier's Law)  \nHeat Flux:  \nHeat Rate:  \nW  \nAc:Cross-Sectional Area  \nHeat Convection Rate Equations(Newton's Law of Cooling)  \nHeat Flux:  \nh:convecton Heat Transfer  \nAs:Surface Area m²  \nHeat Rate:q=hA₅(T₅-T)W  \nHeat Raciatonemited udealy bya blackbody surface hasasuface emssve power  \nHeat Flux emitteeE is the emissivity with range of 0≤ε≤1andis the Stefan-Boltzmann constant  \nIradiation:Gabs=αG but we assume small body in a large enclosure with ε=α so that(  \nNet Radiation heatfux from surface:  \nNet radiation heat exchange rate:(  \n)where for a real surface 0≤ε≤1  \nThis can ALSO be expressed as:qrad=hA(Ts-Tsur)depending on the application  \nwhere h,is the radiation heat trar  \nTOTAL heat transfer from a surface:(  \n   \nConservation of Energy(Energy Balance)  \nEin+Eg一Eout =Est(Control Volume Balance);Ein-Eout =0(Control Surface Balance)  \nwhere Eg is the conversion of internal energy (chemical,nuclear,electical)to thermal or mechanical energy,and  \nEst=0 for steaystate conditons If no steadystate(ie transient then  \nHeat Equation(used to find the temperature distribution)  \nHeat Equation(Cartesian):  \nik is consant then te above simpifestowhereis the themal difusviy  \nHeat Equation (Cylindrical):  \nHeat Eqn.(Spherical):  \nThermal Circuits  \nolimae  \nsnhage  \nPlane wall  \nGeneral Lumped Capacitance Analysis  \nRadiation Only Equation  \nHeat Flux,Energy Generation,Convection,and No Radiation Equation  \nConvection Only Equation  \n;Qmax=pVcθi  \nIf there is an additional resistance either in series or in parallel,then replace h with U in all the above lumped capacitanceequaions,where  \nConvection Heat Transfer  \n[Average Nusselt Number][Reynolds Number]  \nwhere p is the density,V is the velocity,Lc is the characteristic length,μ is the dynamic viscosity,V is the kinematic viscosity,m is the mas flowrate,h is the average convection coeficent,and k iste fluid thermal conductvity  \nInternal Flow  \n[For Internal Flow in a Pipe of Diameter D]  \n;where P=Perimeter,L=LengthFor Constant Heat Flux|  \nFor Constant Surface Temperature [T=constant]:  \nIf there is only convection between the surface temperature,Ts,and the mean fluid temperature,Tm,use  \nIf there are multiple resistances between the outermost temperature,T,and the mean fluid temperature,Tm,use  \nTotal heat transfer rate over the entire tube length:  \nQt=m·cp·(Tm,o-Tm,i)=h·A₅·ATim or U·A₅·ATim ;T₅=constant  \nLog mean temperature difference:  \nFree Convection Heat Transfer  \n[Grashof Number  \n[Rayleigh Number]  \ncmo   …Vertical Plates:  \nRaz≤10 Popetsvaluatedat iforbeteraecuray oremiar f  \nInclined Plates:for the top and bottom surfaces of cooledand heated inclined plates,respectively,the equations of the verticalplate can be used by replacing(g)with(g cosθ)in Ra for 0≤θ≤60°.  \nHorizontal Plates:use the following correlations with  \n-Upper surface of Hot Plate or Lower Surface of Cold Plate:  \n-Lower Surface of Hot Plate or Upper Surface of Cold Plate:  \nVertical Cylinders:the equations for the Vertical Plate can be applied to vertical cylinders of height L if the following criterion is  \nmet:  \no moromuroheRan ≤10-poeouso1  \nRan≤10¹.Pr≥07 Poeteseaue a  \nSpheres:  \nHeat Exchangers  \nq=mcp(T。-Ti)=UAs△Tim;where U is the overall heat transferHeat Gain/Loss Equations:coefficient and Ag is the total heat exchanger surface area  \n[Parallel-Flow Heat Exchanger]  \nLog-Mean Temperature Difference:  \n[Counter-Flow Heat Exchanger]  \nomom obuo  \nΔTim=F△Tim,CF;where F is a correction factorFor Cross-Flow and Shell-and-Tube Heat Exchangers:obtained from the figures by calculating P&R values  \nEffectiveness-NTU Method(E-NTU):  \n;where Cmin isthe minimum heat apacty rate n IWK]Number of Transfer Units(NTU):Heat Capacity Rates:Cc=mc Cp,c [Cold Fluid];Cn=mh Cp,h [Hot Fluid]  \n[Heat Capacity Ratio]  \nNote:The condensation orevaporation side of the heat exchanger is assciated with Cmax=○  \n   \nq=mCp,c(Tc,o-Tc;i)=mnCp,h(Th,i-Tn,","cbCaiphE5AKNFAIZ","https://ap.wps.com/l/cbCaiphE5AKNFAIZ","pdf",4257451,31,"English","# Heat conduction and energy balance\n# Radiation heat transfer\n# Thermal circuits and lumped capacitance\n# Convection heat transfer\n## External flow correlations (summary table)\n# Heat equation and temperature distribution\n# Free convection\n# Heat exchangers and effectiveness-NTU (ε-NTU)","[{\"question\":\"What fundamental equation set does the sheet use for heat transfer modeling?\",\"answer\":\"It compiles Fourier’s law for conduction, Newton’s law of cooling for convection, and radiation relations based on blackbody emission and Stefan–Boltzmann behavior, combined with energy balance for consistent heat rates.\"},{\"question\":\"How does the sheet handle transient vs steady-state energy balance?\",\"answer\":\"It states steady-state uses Est = 0 in the control-volume energy balance, while transient situations require the heat equation to determine temperature distribution over time.\"},{\"question\":\"How are heat exchanger performance and temperature driving force computed?\",\"answer\":\"It provides log-mean temperature difference formulas and the ε–NTU method, including definitions of heat capacity rates and the heat exchanger effectiveness relation using Cmin and correction factors.\"}]","HEAT TRANSFER EQUATION SHEET - Study and reference | PDF",78]