# Heat Transfer by Convection

Topics: Heat transfer, Log mean temperature difference, Trigraph Pages: 12 (1071 words) Published: June 26, 2013
Heat Transfer by Convection
Ch.E. 324 Based on the lecture notes of Prof. Alberto Laurito

Learning Objectives
At the end of the discussion you should be able to: • differentiate convection from conduction • identify whether a heat transfer by convection is forced or natural • solve individual film coefficients(h) and overall heat transfer coefficients(U) in a double pipe heat exchanger.

Convection
- heat is transferred due to a mixing process between cold and hot portions of a fluid. Two Types of Convection 1. Forced convection - mixing is due to mechanical means such as pumps, compressors, agitators. 2. Natural convection - mixing is due to density difference arising from temperature gradient.

Convection
APPLICATIONS: 1. Double pipe heat exchanger* 2. Shell and tube heat exchanger 3. Bank of tubes 4. Film type condensation

Film Concept
Metal wall

Ti
Cold fluid Tb To Ta Hot fluid

• When a rapidly moving fluid comes in contact with a stationary phase, a thin film is formed.

q
Inner film

•The thin film acts as a boundary layer between the moving fluid and the wall. •The thin film contributes an additional resistance to heat flow.

outer film

Temperature profile for heat transfer by

convection from one fluid to another

Film Concept
Metal wall Air 25oC Cold fluid

Ti
Cold fluid Tb To Ta Hot fluid

100oC Water

Hot fluid

q
Inner film

outer film

Temperature profile for heat transfer by

convection from one fluid to another

Heat Transfer Equation
Resistances in Series: q = qi = qw = qo
Metal wall Ti Cold fluid

RT = Ri + Rw + Ro
Hot fluid

Ta
Tb

Inner film:

qi

Ti Ta Ri
Ta Tb Rw Tb To Ro

Ri

xi kiAi xw kwAw xo koAo

To

q
Metal wall: q w

Rw

outer film

Inner film

o – outside i – inside

w – metal wall

Outer film: qo

Ro

Individual Heat transfer Coefficient (h)
• x i and xo are not measurable

x k

1 h

xi ki

1 hi

xo ko

1 ho

hi - inside film coefficient or heat transfer coefficient

ho - outside film coefficient or heat-transfer coefficient

RT

Ri R w R o
Ri 1 hi A i Rw xw kwAw

Ro

1 ho A o

Convection Conduction Convection

RT

1 hi A i

xw kwAw

1 ho A o

Individual Heat transfer Coefficient (h)
Recall: Fourier’s Law

T q kA x

or: q

T A xk

x but: k
Tb To

1 h
Ti Ta

T therefore: q A 1h finally: q hA T
Inner film: qi

hi Ai Ti

Ti
To

Ti Ta
outer film

outer film: qo = ho A o ΔTo overall:

Tb To

Inner film

q UA Tlm

Overall Heat Transfer Coefficient (U)
Thus,

q

Tlm RT

UATlm

q Ui A i Tlm q Uo A o Tlm

Note: The values of hi,ho are dependent on the properties of the fluid and the type of flow.

1 RT = UA

1 1 = = Ui A i Uo A o

Overall Heat Transfer Coefficient (U)
RT 1 UA 1 Ui A i 1 Uo A o

but: R T

1 hi A i

xw kwAw

1 ho A o

1 Ui A i
1 Ui A i 1 Ui 1 hi A i 1 hi

1 Uo A o
xw kwAw

1 hi A i

xw kwAw
1 Uo A o 1 Uo
Uo

1 ho A o
1 hi A i Ao hi A i
Ao hi A i

1 ho A o Ai ho A o

xw kwAw xw Ao kwAw
1 xw Ao kwAw

1 ho A o 1 ho
1 ho

x w Ai kwAw

Ui

1 hi

1 xw Ai kwAw

Ai ho A o

Heat Transfer Areas (Ao & Ai)
For a single pipe:

Di

Ao and Ai are lateral surface area of the pipe.

Do

Ao

DoL

Ai

DiL

A w Am

LDlm (mean area of cylindrica l sec tion)

Heat Transfer Areas (Ao & Ai)
1 Ui 1 hi x w Ai kwAw Ai ho A o 1 Uo Ao hi A i xw Ao kwAw 1 ho AW LDlm

Substituting in the above formulas: A i
Where:

DiL

Ao

DoL

Di = inside diameter of inner tube.

Do = outside diameter of tube.

1 Ui

1 hi

x w DiL k w LDlm

DiL ho DoL

1 Uo

DoL hi DiL

x w DoL k w LDlm

1 ho

1 Ui

1 hi

x wDi k wDlm

Di hoDo

1 Uo

Do hiDi

x w Do k wDlm

1 ho

Heat Transfer Coefficient (hi and ho)
MAIN PROBLEM: Finding h (hi and ho) • hi and ho are needed to find Ui or Uo • hi - heat transfer coefficient of the inner film. •...