Heat Transfer (Q)is the movement of heat from one body to another.

In heat transfer two (min.) different fluids (gas or liquid) are involved as mentioned below:

Source (S): The hotter body, usually product or process (liquid, gas or steam) being cooled.

Receiver (R): The cooling water, which we are treating with chemicals.

In cooling water systems, heat transfer is usually called as indirect heat transfer. Cooling water (Receiver) does not have contact with the source. A good conductor of heat separates the receiver and the source usually a metal wall.

Q. Quantity of heat transferred, usually expressed in BTU or Kcal.

- Heat transfer rate (q): The heat transfer (Q) per unit time (t) units is:

q = Q (Btu)

t (hr)

- Heat transfer surface (A): the barrier (metal) that allows heat to pass from source to receiver.

- Heat exchanger (H.E.): The assembly (arrangement) of barrier (metal) in a containment vessel. In this both, the source and receiver can be liquid or gas.

Condenser (H.E.): This is also a heat exchanger, but those heat exchangers are specifically called as condensers wherein the source is steam or any vapour and the receiver is a liquid (cooling water).

Evaporator (E): This is also a heat exchanger, but those heat exchangers are specifically called as evaporators wherein the receiver is a liquid (low boiling point) which gets vaporized.

The source is also a liquid (cooling water).

Usually found in refrigeration circuit or Air cooler circuit.

Thermal Conductivity (K):

This is the coefficient for conduction of heat through solid, liquid and gaseous material. It is a function of the molecular state of the medium.

K has standard values for individual materials (standard values mentioned in TABLE-1).

Units of (K) are as:

K = -q/a = (Btu/hr ft²) = Btu

dt/dn ( ^oF/ft ) hr ft ^oF

Where K = Thermal Conductivity

q = Rate of heat transfer

a = Area of heat transfer

dt = Differential Temp.

dn = Wall thickness

TABLE 1

Standard Values of (K)

Heat Transfer Coefficient (h) HTC:

This is the coefficient of conduction of heat through individual materials in which turbulent systems are involved. ‘h” has standard values for systems which are mentioned in TABLE 2. This is also called as individual Heat Transfer Coefficient and Film Coefficient.

Units of (h) are as:

H = q = (Btu/hr)

A. Del.T (ft2 ^oF )

TABLE 2

Approximate range of individual HTC (h)

Overall heat transfer coefficient: (U)

This is the sum of the individual heat transfer coefficients. Usually this is encountered in H.E. in which heat flows from a fluid at a bulk temperature (t₁) through the pipe wall, through a layer of insulation and finally into a fluid at bulk temperature t₅. The interfacial temperatures being t₂, t₃ and t₄ are as shown in Figure.

TABLE 3

Standard overall coefficient of heat transfer (U)

Calculation of overall H.T.C. (U) Related to C.W.T.)

Data required:

Formulae reqd. Notations used

1. q = mx l m: mass Flow rate (kg/hr)

2. l= h_G – h_L

3. m = G d l : latent heat of condensation (KCals)/kg

h_G: heat cap. of gas

h_L: heat cap. of liquid

G: Gas flow rate

d : Density of gas

m: Mass flow rate of gas (kgs/hr)

Latent Heat Calculations:

(Refer Perry’s Handbook Section 3 Physical Chemical Data Subsection Thermodynamic Properties)

Reference Temperature is 42.2 (T₁)

42.2^oC + 273 = 315^oK

(For h_G – h_L values refer heat capacity chart

Latest Heat l = hG- hL from Perry at specified temperature and

= 936 – 638.35 presence of process fluid)

= 298.6 KJ/kg

lin Kcal/kg = 298.6

4.2

= 71.1 KCals/kgs —————–Equation 1

Density Calculations (Kg/m³): (Refer Density chart from Perry’s)

Process I/L Temp. (T₁) = 315oK

Density of Propylene =

Basis: 1 kg of Liq Propylene = 2.094 x 10^-3m³

Density = _1__ = 0.47 x 10³ Kg/m³ ———— Equation 2

2.094 x 10^-3

Mass Flow rate of process (M) = Volumetric Flow rate y Density

= 195 x 0.47 x 10³

= 91650 Kg/hr———————————————— Equation 3

LMTD = DT₁ – DT₂ (LMTDt1 Log Mean Temp Difference)

In (DT₁ / DT₂)

Solution

1. q = m x l

= 91650 x 71.1 (Ref. Equation)

= 6516315

U_A = ____q___ = 6516315

Area x LMTD 1877 x 6

= 578 KCals/hr m^{2 o}C

U_A is the actual overall H.T.C.

U_D The design H.T.C. is to be obtained from client

Fouling or Dirt H.T.C. (hd)

1__ = __1__ - _1___

hd U_Actual U_Design

U_(Actual) is 578 KCals/hr m^{2 o}C

U_(Design) is 800 KCals/hr m^{2 o}C

hd, The Dirt Factor, is (2082) KCals/hr m^{2 o}C

TABLE 4

Standard range of fouling factors (hd) for H.Exchangers are given : Fluids

Definitions :

Co Current Flow : If the receiver (R ) and the Source (S) flow in the same direction through the H.E. The graphical representation required for concurrent calculations of L.M.T.D. is as mentioned below :

T₁ – Inlet temp. of source (hot fluid)

T₂ – Outlet temp. of source (hot fluid)

t₁ – Inlet temp. of receiver (cold fluid)

t₂ – Outlet temp. of receiver (cold fluid)

For LMTD Calculations DT₁ = (T₁ - t₁)

DT₂ = (T₂ - t₂)

Counter Current Flow :

If the receiver (R) and source (S) flow in the opposite direction through heat exchanger.

The graphical representation of counter current flow required for LMTD calculations is mentioned below.

For LMTD Calculations DT₁ = (T₁ - t₂)

DT₂ = (T₂ - t₁)

Heat of Fusion (Hf) : This is the heat required for solid phase to change to liquid phase.

Heat of Vaporization (Hv) : This is the heat required for liquid phase to change to vapour phase.

Heat of Condensation (Hc) : This is the heat required for vapour phase to change to liquid phase.

Latent heat (l) : This is the amount of heat required during phase change.

Heat Flux (Æ) : Heat transfer per unit area is called as heat flux.

Heat Duty : Heat transfer per unit area per ^oC is called as heat duty.

Sensible heat : This is the amount of heat required during the particular phase till the phase change occurs.

Approach temp. : Difference between hot fluid inlet and cold fluid outlet (T₁ – t₂) & (T₂ – t₁).

Range : Actual temp. rise or fall i.e. for hot fluid (T₁ – T₂) and for cold fluid (T₁ – T₂) and for cold fluid (t₁ – t₂).

Reference chart for conversions :

HEAT TRANSFER COEFFICIENT CALCULATIONS

I. Heat Exchanger Details Required :

A. From Client : (I) Surface area of process heat transfer (A) in m2

(ii) Design fouling factor of the heat exchange (U_Design)

(iii) Flow pattern in the Heat Exchanger with a co-current

or counter current.

(iv) Density of process fluid (d) in Kgs/m³

B. From Perry’s (I) Latent Heat of the Process Fluid (A) Handbook :

II. Formulae :

1. Mass flow Rate (M) = Volume flow rate x Density of Process Fluid

2. Heat Flux q = M x l

3. DLMTD = DT₁ – DT₂

in DT₁DT₂

Note : Values of DT₁ will depend on the flow pattern (in Heat Exchanger) of process and cooling water :

For Co-current = DT₁ = (T₁ – t₁)

DT₂ = (T₂ – t₂)

Counter Co-current = DT₁ = (T₁ – t₂)

DT₂ = (T₂ – t₁)

4. HTC (U) = q

A x DLMTD

5. Fouling Factor (h_d) : __1__ = __1____ – 1____

h_d U _(actual) U_(design)