scale up of heat transfer equipments

8/3/2019 Scale Up of Heat Transfer Equipments

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SCALE UP OF HEAT TRANSFER EQUIPMENTS

What is Heat Transfer?

Energy (heat) is transit due to temperature difference. In simple words, we can

say that heat is transported from high temperature to low temperature area in

physical systems.

Heat transfer tells us:

How (with what modes) dQ is transferred

At what rate dQ is transferred

Temperature distribution inside the body

Modes of Heat Transfer

Heat, a form of kinetic energy, is transferred in three ways:

Conduction

Convection and

Radiation.

Conduction: An energy transfer across a system boundary due to a temperature

difference by the mechanism of intermolecular interactions. Conduction needs

matter and does not require any bulk motion of matter.

Where: q = heat flow vector

k = thermal conductivity, a thermodynamic property of the material

A = Cross sectional area in direction of heat flow

= Gradient of temperature


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Convection: An energy transfer across a system boundary due to a temperature

difference by the combined mechanisms of intermolecular interactions and bulk

transport. Convection needs fluid matter.

Newtons Law of Cooling:

q = h As

Where: q = heat flow from surface, a scalar

h = heat transfer coefficient

As = Surface area from which convection is occurring

= TS - TTemperature Difference between surface and coolant

Free or natural convection

(Induced by buoyancy forces)

Convection

Forced convection (induced by

External means)

Radiation: Radiation heat transfer involves the transfer of heat by

electromagnetic radiation that arises due to the temperature of the body.Radiation does not need matter.

Emissive power of a surface:

E = TS4

Where: e = emissivity

= Steffan Boltzman constant

Ts = Absolute temperature of the surface

May occur

with phase

change

(Boiling, condensation)


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The above equation is derived from Stefan Boltzman law, which describes a

gross heat emission rather than heat transfer. The rate of radiation heat

exchange between a small surface and a large surrounding is given by the

following expression:

q = A (Ts4 T4sur)

Where: = Surface EmissivityA= Surface Area

Ts = Absolute temperature of surface

Tsur = Absolute temperature of surroundings

What is Heat exchanger?

A heat exchanger is a device designed to perform heat transfers from one

medium to another.

Heat exchangers are used to transfer heat from one substance to either itssurroundings or another substance. Heat exchangers are important

components for the operational reliability of most process plants.

Purpose of heat exchangers:

Heat exchangers are used to transfer heat from a fluid on a side of a barrier

to a fluid on the other side without allowing the fluids to mix together.

Heat exchangers maximize the surface area of a wall that is used between the

two fluids while minimizing any resistance to the flow of a fluid through the

exchanger.

Types of heat exchangers

Heat exchangers are classified on the basis of flow arrangements,

Parallel flow or Counter flow arrangement

Shell and tube arrangement

Cross flow arrangement


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Parallel-flow

A major type of heat exchangers, allow two fluids to enter the exchanger

at the same end. The two fluids then travel in parallel to the other side of the exchanger.

The hot fluid transfers heat to the wall via convection.

Parallel-flow heat exchangers are often used when two fluids must be

brought to close to the same temperature.

Counter-flow

The fluids enter the exchanger from opposite ends.

As the two flows move toward each other from opposite directions, the

system is able to maintain almost a constant gradient between the two

liquid flows as they travel the length of the exchanger.

This enables nearly all the heat properties from one flow to be transferred

to the other flow.

Shell and tube arrangement:


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As its name implies, this type of heat exchanger consists of a shell (a largepressure vessel) with a bundle of tubes inside it. One fluid runs through the

tubes, and another fluid flows over the tubes (through the shell) to transfer heat

between the two fluids. The set of tubes is called a tube bundle, and may be

composed by several types of tubes: plain, longitudinally finned, etc.

Cross flow arrangement:

In a cross-flow heat exchanger the direction of fluids are perpendicular to each

other.

Scale up of heat exchangers:

Dimensional analysis:

Heat transfer processes are described by physical properties and process

parameters, the dimensions of which not only include the basic dimensionsmass (M), length (L) and time (T) but also Temperature () as the fourth one.


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Dimensionless Numbers

The major dimensionless groups employed for heat exchanger design or scale

up are;

Reynolds Number

The Reynolds number represents the ratio of the applied to the opposing

viscous drag forces.

Where, Re - Reynolds number

- Fluid density

v- Velocity

D - Tube diameter

- Fluid viscosity

Nusselt Number

Nusselt number is the ratio of convective to conductive heat transfer across

(normal to) the boundary

Stanton Number

The Stanton number is a dimensionless number that measures the ratio of

heat transferred into a fluid to the thermal capacity of fluid. It is used to

characterize heat transfer in forced convection flows.

Where, h = convection heat transfer coefficient

= density of the fluid

cp = specific heat of the fluid

V= velocity of the fluid

It can also be represented in terms of the fluid's Nusselt, Reynolds, and Prandtl

numbers:


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Colburnj-Factor for Heat Transfer,jH

Where, St - Stanton number

Pr - Prandtl number

(w/) Sieder Tate term

Prandtl Number

The Prandtl number Pr the ratio of momentum diffusivity (kinematic

viscosity) to thermal diffusivity.

Where, - kinematic viscosity, = /

- thermal diffusivity, = k/ (cp)

- Dynamic viscosity

k- Thermal conductivitycp - specific heat

Density

Graetz Number

The Graetz number, Gz is a dimensionless number that characterizes laminar

flow in a conduit. The number is defined as

Where,DH - hydraulic diameter

L - Length

Re - Reynolds number

Pr - Prandtl number.

Peclet Number

The Peclet number reflects the ratio of heat transferred by convection to that

transferred by conduction and is most commonly found in applications inlaminar flow or with liquid metals.


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= Re. Pr

Where, Cp - Heat capacity DensityD - Characteristic length V - Velocity

k - Thermal Conductivity

Grashof Number

Grashof number is a dimensionless number in fluid dynamics and heat

transfer which approximates the ratio of the buoyancy to viscous force acting

on a fluid. It frequently arises in the study of situations involving natural

convection.

Where, g - acceleration due to Earth's gravity

- Volumetric thermal expansion coefficient

- Temperature gradient

L - Length

- Kinematic viscosity

- dynamic viscosity

The product of the Grashof number and the Prandtl number gives the Rayleigh

number, a dimensionless number that characterizes convection problems in

heat transfer.

Biot number

Biot number is the ratio of the heat transfer resistances inside of and at the

surface of a body.

Where, Bi Biot number

h = heat transfer coefficient or convective heat transfer coefficient


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LC = characteristic length, which is commonly defined as Lc=Vbody/Asufrace

kb = Thermal conductivity of the body

Scale up procedure:

In most heat transfer processes, it includes not only the fluid mechanics but also

the mass transfer processes. And mass transfer is subject to phase equilibria

which are not scale dependent. Hence the scale up procedure is a bit difficult to

frame since each process obey different laws.

However, we can generalize the steps involved in design or scale up of heat

exchangers as;

1. Geometry calculations

2. Heat transfer correlations

3. Pressure drop correlations

Geometry calculations:

The area available for heat transfer plays a vital role in the design or scale up.

Area can be given as,

Where, Q heat transfer rate,

U Overall heat transfer coefficient, GTD LTD / ln (GTD/LTD) {GTD, LTD = greater, lower temp. diff}

Number of transfer units:

Where, U overall heat transfer coefficient

A Area available for heat transfer

Cpmin heat capacity

The effectiveness of the heat transfer is the function of (NTU and Cpmin/Cpmax)


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Heat transfer correlations:

DittusBoelter correlation

A common and particularly simple correlation useful for many applications is

the DittusBoelter heat transfer correlation for fluids in turbulent flow. This

correlation is applicable when forced convection is the only mode of heat

transfer.

Pr- Prandtl number

Re - Reynolds number

n = 0.4 for heating (wall hotter than the bulk fluid)

0.33 for cooling (wall cooler than the bulk fluid)

Heat transfer coefficient:

The heat transfer coefficient is the proportionality coefficient between the

heat flux that is a heat flow per unit area and the driving force for the flow of

heat (i.e., the temperature difference,T).

The heat transfer coefficient is often calculated from the Nusselt number.

For a liquid flowing in a straight circular pipe with a Reynolds number

between 10 000 and 120 000 (in the turbulent pipe flow range), when the


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liquid's Prandtl number is between 0.7 and 120, the heat transfer coefficient

between the bulk of the fluid and the pipe surface can be expressed as:

Where

h heat transfer coefficient

kw - thermal conductivity of the fluid

DH - Hydraulic diameter

Nu - Nusselt number

For finned tubes, the coefficient h cannot be found by the use of equations

normally used in bare tube tubes.

An correlation for longitudinal finned tubes is given below.

Overall heat transfer coefficient:

The overall heat transfer coefficient U is a measure of the overall ability of a

series of conductive and convective barriers to transfer heat.

Where, U = the overall heat transfer coefficient

A = the contact area for each fluid side

hw = conductance per unit area of wall

hI, ho = conductance at inner side and outer side of the tube


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In heat transfer unit there are three successive steps at work;

1) Convection from the hot fluid to metal wall

2) Conduction through the wall

3) Convection from wall to cold fluid

In the above process, 2nd step depends on the thermal conductivity of metals and

the presence of scale and fouling.

Hence the other two steps, by means of convection are considered invariably in

the scale up of heat transfer equipments.

As we studied earlier, convection may be forced convection or natural

convection.

Forced convection:

In any system under forced convection, the Nusselt number in general is

expressed as a function of the Reynolds number and the Prandtl number. The

correlation is called Nusselt equation.

Nu = f (Re, Pr)

Free convection:

In any system under free convection, an equation similar to forced convection

can be derived. The correlation is given as a function of Grashof number and

Prandtl number.

Nu = f (Gr, Pr)

Pressure drop calculations:

Determining pressure drop in single pass pipe in tube heat exchanger is

relatively easy or extremely difficult in shell and tube exchanger.

The pressure drop in a straight run pipe is given as,

Where, L length of pipe,

uav avg. velocity

Dh hydraulic diameter

f darcys friction factor


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The pressure drop calculation helps in pumping power determination;

Pumping power =

m Mass flow rate

Pressure drop

- Density

scale up of heat transfer equipments

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