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 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 dtc
q.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.max
q.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 fin
 
Єf=(kP/hAc)1/2  
22.
Dimensional analysis
It is a process to develop an equation between dimensionless numbers based on dimensional homogeneity
23
Buckingham
Theorem
Let total number of variables =n
Total no. of dimensions = m
Number 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)

Sr.

No.

Item or quantity

definition

Symbol

Formula

Units

25.

Stefan’s Boltzmann Law

Gives total emissive power of a black body

E total =σ T4   

T is the absolute temperature

E total =σ T4   

W/m2

26.

WIEN’S DISPLACEMENT LAW

The wavelength for maximum emissive power decreases with increase in absolute temperature

λmaxT =289 μm

λmaxT =289 μm

μm

27.

 Reflectivity

 Reflected radiations/incident radiation

ρ

ρ = Reflected radiations/incident radiation

No units

28.

 Absorptivity

 Absorbed radiations/incident radiation

α = Absorbed radiations/incident radiation

α = Absorbed radiations/incident radiation

No units

29.

Transmissivity

 Transmitted radiations/incident radiation

 

τ

 

τ = Transmitted radiations/incident radiation

No units

30.

 Emissivity

 Emissivity

Ratio of emissive power of a grey body to the emissive power of a black body at the same temperature

Emissivity Є                      

Emissivity Є =(Eg/Eb) at the same temperature

No Units

31.

Kirchhoff Law

Kirchhoff Law

ϵ = α,

emissivity = absorptivity

Kirchhoff Law

ϵ = α,

Kirchhoff Law

ϵ = α,

emissivity = absorptivity

No units

32.

Lambert’s Cosine Law

Lambert’s Cosine Law

Iϴ = In cosϴ

Where Iϴ is intensity in ϴ direction

In is intensity in the normal direction

Lambert’s Cosine Law

Iϴ = In cosϴ

Where Iϴ is intensity in ϴ direction

In is intensity in the normal direction

Lambert’s Cosine Law

Iϴ = In cosϴ

Where Iϴ is intensity in ϴ direction

In is intensity in the normal direction

W/m2

33.

. Shape factor

. Shape factor

F12 = q.1-2/q.1 = (Radiations incident on body 2)/( radiations emitted from body 1)

. Shape factor

F12 = q.1-2/q.1 = (Radiations incident on body 2)/( radiations emitted from body 1)

. Shape factor

F12 = q.1-2/q.1 = (Radiations incident on body 2)/( radiations emitted from body 1)

No units

34.

 Radiosity

 Radiosity

Sum of reflected and emitted radiation

 Radiosity, J

Sum of reflected and emitted radiation

34. Radiosity

Sum of reflected and emitted radiation

J = ρG + Є  W/m

W/m

35.

Radiation Shield

Radiation Shield

A device to protect from the radiations.

Radiation Shield

. UMBRELLA

Radiation Shield

A device too product from the radiations. UMBRELLA

No units

36.

Hydrodynamic boundary layer

Hydrodynamic boundary layer

It has velocity variation.               

Hydrodynamic boundary layer

Hydrodynamic boundary layer

It has velocity variation.               

NA

37.

Thermal boundary layer

It has both temperature and velocity variation

Thermal boundary layer has both temperature and velocity variation

Thermal boundary layer has both temperature and velocity variation

NA

38.

Pool boiling

Pool boiling

Heating Process of conversion of a stationary liquid into vapor at the saturation temperature

Pool boiling

Heating Process of conversion of a stationary liquid into vapor at the saturation temperature

Pool boiling

Heating Process of conversion of a stationary liquid into vapor at the saturation temperature

NA

39.

Forced convection boiling

Forced convection boiling

Heat the moving liquid to convert into vapor at the saturation temperature. In this, move the liquid with a pump& Gas with a blower.

Forced convection boiling

Forced convection boiling

Heat the moving liquid to convert into vapor at the saturation temperature. In this, move the liquid with a pump& Gas with a blower.

NA

40.

Condensation

Condensation

Cooling vapors to covert into liquid at the saturation temperature. Cool with a surface maintained at a temperature much lower than the saturation temperature.

Condensation

Condensation

Cooling vapors to covert into liquid at the saturation temperature. Cool with a surface maintained at a temperature much lower than the saturation temperature.

NA

41.

Drop-wise condensation

Drop-wise condensation

When vapors changes into drops of liquid on cooling. It is possible on an oily surface.

Drop-wise condensation

Drop-wise condensation

When vapors changes into drops of liquid on cooling. It is possible on an oily surface.

NA

42.

Film-wise condensation

O

Film-wise condensation

On cooling, when vapors changes into a film of liquid. It is on a finished surface

Film-wise condensation

Film-wise condensation

On cooling, when vapors changes into a film of liquid. It is on a finished surface

NA

43.

Radiation density

Radiation density = Eb

Radiosity density = J / π

Radiation density = Eb

Radiosity density = J / π

Radiation density = Eb

Radiosity density = J / π

W/m2

44.

OVERALL HEAT TRANSFER COEFFICIENT

OVERALL HEAT TRANSFER COEFFICIENT ‘U’

U  (accounts for convection + conduction +convection) in a heat exchanger

OVERALL HEAT TRANSFER COEFFICIENT ‘U’

EQUATION OF ‘U’ FOR A PLAIN WAL

1/UA =1/hi Ai  + x/kA +1/ho Ao

For a wall Ao=Ai=A

FORMULA OF ‘U’ FOR A PIPE

1/UA =1/hiAi  + ln (r2/r1)/2πk L +1/hoAo

W/m2

45.

CONDITIONS FOR LAMINAR AND TURBULENT FLOW

CONDITIONS FOR LAMINAR AND TURBULENT FLOW IN FREE CONVECTION

Free Convection

Gr Pr  10      Laminar flow

 Gr Pr >10      Turbulent flow

CONDITIONS FOR LAMINAR AND TURBULENT FLOW

Free Convection

Gr Pr 

CONDITIONS FOR LAMINAR AND TURBULENT FLOW

Free Convection

Gr Pr  10      Laminar flow

 Gr Pr >10      Turbulent flow

NA

46.

Conditions For Forced convection over a flat plat

Forced convection over a flat plat

Re≤ 5 lacs Laminar flow

Re> 7 lac Turbulent flow

Forced convection over a flat plat

Re

Forced convection over a flat plat

Re≤ 5 lacs Laminar flow

Re> 7 lac Turbulent flow

NA

47.

Condition for Pipe Forced convection

Pipe Forced convection

Re ≤ 2000 Laminar Flow

Re>4000 Turbulent flow

Pipe Forced convection

Re

Pipe Forced convection

Re ≤ 2000 Laminar Flow

Re>4000 Turbulent flow

NA

48.

RELATION BETWEEN δth  and δ

RELATION BETWEEN δth  and δ

δth = δ Pr-1/3

RELATION BETWEEN δth  and δ

δth = δ Pr-1/3

RELATION BETWEEN δth  and δ

δth = δ Pr-1/3

mm

49.

black body

Opaque body

Grey body

White body

Transparent body

black body

α =1, ρ =0 and τ=0

Opaque body

α+ρ =1  and τ =0

Grey body

α +ρ+τ =1

White body

α=0,ρ=1 and τ =0

Transparent body

τ =1, ρ=0 and α =0

black body

α =1, ρ =0 and τ=0

Opaque body

α+ρ =1  and τ =0

Grey body

α +ρ+τ =1

White body

α=0,ρ=1 and τ =0

Transparent body

τ =1, ρ=0 and α =0

black body

α =1, ρ =0 and τ=0

Opaque body

α+ρ =1  and τ =0

Grey body

α +ρ+τ =1

White body

α=0,ρ=1 and τ =0

Transparent body

τ =1, ρ=0 and α =0

NA

.

50. ASSUMPTIONS FOR NUMERICAL PROBLEMS

Grey Body Is Take Opaque Hemispherical Body.

 

https://www.mesubjects.net/wp-admin/post.php?post=645&action=edit    Steady &Unsteady State H. Con

https://www.mesubjects.net/wp-admin/post.php?post=630&action=edit     CONVECTION HEAT TRANSFER

https://www.mesubjects.net/wp-admin/post.php?post=63&action=edit                  Radiation Introduction