HEAT TRANSFER EQUATION SHEET - Study and reference

Nov 2, 2026

Uploaded by Muffet

A compact reference sheet compiling core heat transfer governing relations used in thermal analysis. It summarizes conduction, convection, and radiation formulas, including Fourier’s law, Newton’s law of cooling, and blackbody/real-surface radiation with Stefan–Boltzmann effects. 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.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages31

Reading Time1 h 18 min

AccessFree to download

Heat conduction and energy balance

Radiation heat transfer

Thermal circuits and lumped capacitance

Convection heat transfer

External flow correlations (summary table)

Heat equation and temperature distribution

Free convection

Heat exchangers and effectiveness-NTU (ε-NTU)

1 # HEAT TRANSFER EQUATION SHEET Heat Conduction Rate Equations(Fourier's Law) Heat Flux: Heat Rate: W Ac:Cross-Sectional Area Heat Convection Rate Equations(Newton's Law of Cooling) Heat Flux: h:convecton Heat Transfer As:Surface Area m² Heat Rate:q=hA₅(T₅-T)W Heat Raciatonemited udealy bya blackbody surface hasasuface emssve power Heat Flux emitteeE is the emissivity with range of 0≤ε≤1andis the Stefan-Boltzmann constant Iradiation:Gabs=αG but we assume small body in a large enclosure with ε=α so that( Net Radiation heatfux from surface: Net radiation heat exchange rate:( )where for a real surface 0≤ε≤1 This can ALSO be expressed as:qrad=hA(Ts-Tsur)depending on the application where h,is the radiation heat trar TOTAL heat transfer from a surface:( Conservation of Energy(Energy Balance) Ein+Eg一Eout =Est(Control Volume Balance);Ein-Eout =0(Control Surface Balance) where Eg is the conversion of internal energy (chemical,nuclear,electical)to thermal or mechanical energy,and Est=0 for steaystate conditons If no steadystate(ie transient then Heat Equation(used to find the temperature distribution) Heat Equation(Cartesian): ik is consant then te above simpifestowhereis the themal difusviy Heat Equation (Cylindrical): Heat Eqn.(Spherical): Thermal Circuits olimae snhage Plane wall General Lumped Capacitance Analysis Radiation Only Equation Heat Flux,Energy Generation,Convection,and No Radiation Equation Convection Only Equation ;Qmax=pVcθi If there is an additional resistance either in series or in parallel,then replace h with U in all the above lumped capacitanceequaions,where Convection Heat Transfer [Average Nusselt Number][Reynolds Number] where 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 Internal Flow [For Internal Flow in a Pipe of Diameter D] ;where P=Perimeter,L=LengthFor Constant Heat Flux| For Constant Surface Temperature [T=constant]: If there is only convection between the surface temperature,Ts,and the mean fluid temperature,Tm,use If there are multiple resistances between the outermost temperature,T,and the mean fluid temperature,Tm,use Total heat transfer rate over the entire tube length: Qt=m·cp·(Tm,o-Tm,i)=h·A₅·ATim or U·A₅·ATim ;T₅=constant Log mean temperature difference: Free Convection Heat Transfer [Grashof Number [Rayleigh Number] cmo …Vertical Plates: Raz≤10 Popetsvaluatedat iforbeteraecuray oremiar f Inclined 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°. Horizontal Plates:use the following correlations with -Upper surface of Hot Plate or Lower Surface of Cold Plate: -Lower Surface of Hot Plate or Upper Surface of Cold Plate: Vertical Cylinders:the equations for the Vertical Plate can be applied to vertical cylinders of height L if the following criterion is met: o moromuroheRan ≤10-poeouso1 Ran≤10¹.Pr≥07 Poeteseaue a Spheres: Heat Exchangers q=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 [Parallel-Flow Heat Exchanger] Log-Mean Temperature Difference: [Counter-Flow Heat Exchanger] omom obuo ΔTim=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 Effectiveness-NTU Method(E-NTU): ;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] [Heat Capacity Ratio] Note:The condensation orevaporation side of the heat exchanger is assciated with Cmax=○ q=mCp,c(Tc,o-Tc;i)=mnCp,h(Th,i-Tn,

FAQs

What fundamental equation set does the sheet use for heat transfer modeling?

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.

How does the sheet handle transient vs steady-state energy balance?

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.

How are heat exchanger performance and temperature driving force computed?

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.

Nov 2, 2026

Uploaded by Muffet