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. |
CONDUCTIONCONVECTIONRADIATION |
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 cylinderrcr = k/h0For a spherercr =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 105for 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/kfluid |
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 = (θmax—θmin)/ ln(θmax/θmin) |
17 |
NTU |
It is number of transfer units. It represents area. |
NTU |
NTU= U A/ Cmin |
18. |
Effectiveness of a HEX |
Ratio of actual RATE of heat transfer to maximum rate of heat transfer.q. actual = mh cph dth = mc cpc dtcq.max = Cmin(thot in – tcold 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 |
ηf = actual q.fin/ q.maxq.max is rate of HT with same base temperature tb all along the fin length |
ηf |
ηf = (Pk/hAc)1/2 |
21. |
FIN EFFECTIVENESS |
Ratio of rate of heat transfer with fin to rate of heat transfer without fin. |
Єf |
Єf = q.with fin/ q.without finЄf=(kP/hAc)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 |
Eλ = C1λ—5/(ec2/λT –1) |
Eλ = C1λ—5/(ec2/λT –1) |
. |
50. ASSUMPTIONS FOR NUMERICAL PROBLEMS
Grey Body Is Take Opaque Hemispherical Body.
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