Heat transfer fundamentals (1/5)
Introduction
A large number of production facilities in many industries use processes in which heat is transferred between different fluids. The basic principle of heat transfer
is extremely simple, two fluids at different temperatures are placed in contact with a conductive barrier (the tube wall) and heat is transferred from the hotter
fluid to the colder fluid until they reach the same temperature level. In industrial processes this is carried out in heat exchangers of various types and styles
usually purpose built for the process and site conditions of the application.
The driving force for heat transfer is the difference in temperature levels between the hot and cold fluids, the greater the difference the higher the rate at which
the heat will flow between them. With complex processing sequences the designer must optimise the temperature levels at each stage to maximise the total rate of
heat flow.
A second factor controlling the transfer of heat is the area of the conductive barrier provided for heat flow. The greater the area the larger the amount of heat
that will flow in a given time with a given temperature difference. The designer has to minimise this area to provide cost effective solutions to his client and
with skill the amount of area can be minimised and configured to reduce the containment volume and overall cost.
The third and perhaps the most important factor controlling the transfer of heat is the rate at which the heat flows into or out from each of the fluids. A high
resistance to heat flow in either fluid will produce a slow overall rate of transfer. The level of resistance to heat flow results from many different factors including
the inherent thermal characteristics of the fluids but can be influenced by the designer in a very positive way by the generation of turbulence within the fluids
to prevent the creation of a thermally resistant static ‘boundary layer’ of fluid in contact with the heat transfer surface.
The fourth factor, also under the control of the designer, is the flow of heat through the conductive barrier between the fluids. The material chosen has to be
compatible with the fluids of the process, it must not corrode or contaminate a food product, it must have an appropriate level of mechanical strength to withstand
working temperatures and pressures and it must have a low resistance to heat flow so that it does not become the overriding factor in the heat transfer process.
The mathematical equations which describe the process of heat transfer are fairly simple:
Q = K.S.Dt
Where:
- Q = Amount of heat transferred
- S = Area for heat transfer
- Dt = Effective temperature difference
- K = A factor which describes the rate of heat transfer
The value of K is slightly more complex to calculate:
K = 1 / [ (1/a1) (1/a2) ( Ltw/ltw) (f1)
(f2) ]
Where:
- a = the partial heat transfer coefficients (1 and 2)
- ltw = thermal conductivity of the metal
- Ltw = the thickness of the metal
- f = the fouling factor for each fluid (1 and 2)
While the values for 'f' are usually specified by the client, the values of 'a' & 'Ltw' can be influenced directly
by the designer by the choice of tube size and thickness and the materials of construction. The values for 'a', the partial
heat transfer coefficients depend greatly on the nature of the fluids but also, crucially, on the geometry of the heat transfer surfaces they are in contact with.
Importantly the final values are heavily influenced by what happens at the level of the boundary layers, the fluid actually in contact with the heat transfer surface.
Heat Transfer Processes
Most of the academic research taking place into heat transfer processes concentrates on ways of predicting with accuracy the precise values of the boundary layer
resistance and on ways of affecting the values without paying too high a penalty in terms of increased pressure losses.
Many techniques to reduce the tubeside boundary layer resistance have been tried including various styles of tube ‘inserts’ which take the form of complex wire
shapes or flat twisted strips fitted inside the tubes and various styles of tube deformation. Most have the disadvantage of increasing the resistance to fluid flow,
the pressure loss, at a rate which increases more rapidly than the decrease in boundary layer resistance. One technique which does not have this disadvantage however
is that of deforming the tube with either a continuous spiral indentation or an intermittent spot indentation. Our own research has shown that by choosing the depth,
angle and width of the indentation carefully, the rate of decrease in boundary layer resistance can exceed the rate of increase in pressure loss. This is the form
chosen for HRS SPIRATUBE units.
The continuous disturbance of the boundary layer of the tubeside fluid increases the amount of turbulence within the fluid as described mathematically by the ‘Nusselt
number’ and, providing the tubeside fluid has the higher resistance to heat flow, will increase the overall rate at which heat is transferred.
Fouling Factors
These are normally specified by the client based on his experience of running his plant or process but if not restricted to proper levels can totally negate any
benefits generated by skilful design. They represent the theoretical resistance to heat flow due to a build up of a layer of dirt or other fouling substance on
one or both of the tube surfaces but are often overstated by the end user in an attempt to minimise the frequency of cleaning. In reality they can, if badly chosen,
lead to increased cleaning frequency.
Fouling mechanisms vary with the application but can be broadly classified into four common and readily identifiable types.
Types of Fouling
- Chemical fouling where chemical changes within the fluid cause a fouling layer to be deposited. A common example of this phenomenon is scaling in a kettle or boiler
caused by calcium salts depositing onto the heating elements as the solubility of the salts reduce with increasing temperature. This is outside the control of the
heat exchanger designer but can be minimised by careful control of the tube wall temperature in contact with the fluid.
- Biological fouling caused by the growth of organisms within the fluid which deposit out onto the surface. This is outside the control of the heat exchanger designer
but it can be influenced by the choice of materials as some, notably the non-ferrous brasses, are poisonous to some organisms.
- Deposition fouling where particles within the fluid settle out onto the surface when the velocity falls below a critical level. This is to a large extent within
the control of the designer as the critical velocity for any fluid/particle combination can be calculated to allow a design to be drawn up with minimum velocity
levels higher than the critical level. Mounting the heat exchanger vertically can also minimise the effect as gravity would tend to pull the particles out of the
heat exchanger away from the heat transfer surface.
- Corrosion fouling where a layer of corrosion products builds up on the surface of the tube forming an extra layer of, usually, high thermal resistance material.
By careful choice of materials of construction the effects can be minimised as a wide range of corrosion resistant materials based on stainless steel are now available
to the heat exchanger manufacturer.