HEAT TRANSFER SYMBOLS AND FORMULAS CLASS NOTES
_{HEAT TRANSFER SYMBOLS }
_{AND FORMULAS CLASS NOTES}
_{Heat transfer symbols and formula are }_{very helpful }
_{understanding the topic in great depth with lot of}
_{ ease. }_{These make the learning simple and convenient.}
_{Symbols also reduce the learning time. }
Fig. Conduction through a Composite Wall (linear Temperature Variation)
Fig. Conduction through a Cylinder (Logarithmic Temperature Variation)
_{Sr. No.} 
_{Item or quantity} 
_{Definition} 
_{Symbol} 
_{Formula} 
_{Units} 
_{1.} 
_{Thermal conductivity} 
_{Rate of heat transfer per unit area per unit temperature difference and per unit wall thickness.}_{k=q. For A= 1m2 , dt=10c and dx=1m} 
_{k} 
_{Q=kA∂t/∂x} 
_{W/m0C} 
_{2.} 
_{Thermal diffusivity} 
_{Ratio of thermal conductivity to heat capacity per unit volume} 
_{α} 
_{Α =k/ρcp} 
_{m2/s} 
_{3.} 
_{Temperature gradient} 
_{Change of temperature with respect to x,}_{it is NEGATIVE as x increases, t decreases.} 
_{∂t/∂x,.} 
_{∂t/∂x,.} 
_{0C/m} 
_{4.} 
_{Fourier equation} 
_{Gives rate of heat transfer in conduction.} 
_{q. = k A dt/dx} 
_{q. = k A dt /dx} 
_{WATTS} 
_{5.} 
_{Fourier Law} 
_{(i) q. A}_{(ii) q. dt}_{(iii) q. A dt}_{(iv) q. =h A dt} 
_{q. =h A dt} 
_{q. =h A dt} 
_{W} 
_{6.} 
_{CONDUCTION}_{CONVECTION}_{RADIATION} 
_{Fourier equation is conduction equation.}_{Newton’s Law of cooling is convection equation.}_{Stephen’s Boltzmann Law is radiation equation.} 

_{7.} 
_{CRITICAL RADIUS OF INSULATION} 
_{It is a radius of insulation at which the rate of heat transfer is maximum} 
_{rcr} 
_{For a cylinder}_{rcr = k/h0}_{For a sphere}_{rcr =2 k/h0} 
_{mm} 
_{8.} 
_{Biot number} 
_{internal resistance/external resistance}_{=Conductive resistance/Convective resistance} 
_{Bi} 
_{Bi =hx/ksolid} 
_{No units} 
_{9.} 
_{Steady state} 
_{Temperature does change with time. Human body} 
_{∂t/∂time=0} 
_{∂t/∂time=0} 
_{0C/s} 
_{10.} 
_{Unsteady state} 
_{Temperature changes with time. Atmospheric temp} 
_{∂t/∂time} 
_{∂t/∂time} 
_{0C/s} 
_{11.} 
_{FREE OR NATURAL CONVECTION} 
In free or natural convection, density difference causes bulk motion of the fluid. Product of Grashoff’s number and Prandtl number governs free convection. In nature, all processes are of free convection. 
q^{.} = h A dt 
q^{.} = h A dt 
12. 
FORCED CONVECTION 
Pump moves a liquid & a blower moves a gas over the heated surface. I Reynolds number and Prandtl number governs forced convection. 
q^{.} = h A dt 
q^{.} = h A dt 
13 
CRITICAL REYNOLD NUMBER 
Value of Reynolds number where the laminar region ends.(a)Its value is 5 x 10^{5}for a flat horizontal plate.(b) It is 2100 for flow through a pipe. 
Re 
Re = ρVD/μ 
14 
Nusselt number 
It helps to find ‘h’ 
Nu 
Nu= hl/k_{fluid} 
15 
Overall heat transfer coefficient 
It accounts for convection +conduction +convection 
U 

16 
LMTD 
It is a mean temperature DIFFERENCE for a heat exchanger 
LMTD 
LMTD = (θ_{max}—θ_{min})/ ln(θmax/θ_{min}) 
17 
NTU 
It is number of transfer units. It represents area. 
NTU 
NTU= U A/ C_{min} 
18. 
Effectiveness of a HEX 
Ratio of actual RATE of heat transfer to maximum rate of heat transfer.q^{. }_{actual} = m_{h} c_{ph} dt_{h} = m_{c} c_{pc} dt_{c}q^{.}_{max} = C_{min}(t_{hot in} – t_{cold in}) 
Є 
Є = q^{.}_{actual }/q^{.}_{max} 
19. 
FIN 
Fin is an extended surface. It increases surface and rate of heat transfer economically. 
— 
— 
20. 
FIN EFFICIENCY 
η_{f }= actual q^{.}_{fin}/ q^{.}_{max}q^{.}_{max } is rate of HT with same base temperature t_{b} all along the fin length 
η_{f } 
η_{f }= (Pk/hA_{c})^{1/2} 
21. 
FIN EFFECTIVENESS 
Ratio of rate of heat transfer with fin to rate of heat transfer without fin. 
Є_{f} 
Є_{f} = q^{.}_{with fin}/ q^{.}_{without fin}_{ }Є_{f}_{=}(kP/hA_{c})^{1/2} _{ } 
22. 
Dimensional analysis 
It is a process to develop an equation between dimensionless numbers based on dimensional homogeneity 
– 
– 
23 
BuckinghamTheorem 
Let total number of variables =nTotal no. of dimensions = mNumber of 
– 
– 
24. 
Planck’s Law 
Gives emissive power of a black body FOR A SINGLE WAVELENGTH 
E_{λ} = C_{1}λ^{—5}/(e^{c2/λT} –1) 
E_{λ} = C_{1}λ^{—5}/(e^{c2/λT} –1) 
. 
50. ASSUMPTIONS FOR NUMERICAL PROBLEMS
Grey Body Is Take Opaque Hemispherical Body.
https://www.mesubjects.net/wpadmin/post.php?post=645&action=edit Steady &Unsteady State H. Con
https://www.mesubjects.net/wpadmin/post.php?post=630&action=edit CONVECTION HEAT TRANSFER
https://www.mesubjects.net/wpadmin/post.php?post=63&action=edit Radiation Introduction