4.3 Principles of Heat Flow in Fluids
• Heat transfer from a warmer fluid to a cooler fluid, usually through a solid wall separating the two fluids, is common in chemical engineering practice.
mh c ph (T t ) mcc pc (t2 t1 ) (4.3-7)
4.3.3 Heat Flux and HeatTransfer Coefficients
Heat flux
In many types of heat-transfer equipment the transfer surfaces are constructed from tubes.
The two fluids enter at different ends of the exchanger and pass in opposite directions through the unit.
It is called counterflow or countercurrent flow. The temperature-length curves for this case shown in figure.
Temp of condensing vapor T
Δt2 Δt Δt1
Length of tube L
Double-tube heat exchanger
It is assembled of standard metal pipe and standarized return bends and return heads. shown in figure.
• The heat transferred may be latent heat accompanying a phase change such as condensation or vaporization, or
it may be sensible heat from the rise or fall in the temperature of a fluid without any phase chs in total condensers
• For a condenser
mh mcc pc (t2 t1 )
(4.3-7)
Equation (4.3-7) is based on the assumption that the vapor enters the condenser as saturated vapor (no superheat) and the condensate leaves at condensing temperature without being further cooled.
It consists essentially of a bundle of parallel tubes A, the ends of which are expanded into tube sheets B1 and B2.
The tube is inside a cylindrical shell C and is
Single-pass shell-and-tube condenser
If the vapor entering the condenser is not superheated and the condensate is not subcooled, the temperature throughout the shell-side of the condenser is constant.
The temperature of the fluid in the tubes increases continuously as the fluid flows through the tubes.
Temperature ºC
The temperatures of the condensing vapor and of the liquid are plotted against the tube length. The horizontal line represents the temperature of the condensing vapor, and the curved line below it represents the rising temperature of the tube-side fluid.
The temperature plotted figure above are average stream temperatures. The temperature so defined is called the average temperature.
connection G leads to a trap, which is a device that allows flow of liquid but holds back vapor.
The fluid to be heated is pumped through connection H into channel D2.
If the two fluids enter at the same end of the exchanger and flow in the same direction to the other end, the flow is called parallel.
The temperature length curves for parallel flow are shown in Figure
For larger capacities , more elaborate shelland-tube exchangers, containing up to thousand of square meter of area, are used.
Countercurrent and parallel-current flows
For the cold fluid, it can gain heat q=mc(Hc2 - Hc1)
Neglecting the heat transfer with the ambient. The heat lost by the warm fluid is gained by the cold fluid, therefore
show, Parallel flow is not possible to bring
the exit temperature of one fluid nearly to the entrance temperature of the other，
and the heat that can be transferred is less than that possible in countercurrent flow.
The flow type with the counterflow is commonly used. Parallel flow is rarely used in a single-pass exchanger.
As inspection of distribution of temperature
The parallel flow may be used in following situation:
In special situation where it is necessary to limit the maximum temperature of the cooler fluid;
q=mh(Hh1-Hh2)= mc(Hc2 - Hc1)
(4.3-3)
(11-5)
If constant specific heats are assumed, the overall enthalpy balance for a heat exchanger becomes
q=mhCph (Th1-Th2)= mcCpc (tc2 - tc1) (4.3-5)
One fluid flows through the inside pipe and second fluid through the annular space between the outside and inside pipes.
Double-pipe exchanger are useful when not more than 9 to 14 m2 of surface is required.
It is customary to neglect it in comparison with the heat transfer through the wall of the tubes from the warm fluid to the cold fluid.
For the warm fluid, it can lose heat. q=mh(Hh1-Hh2)
If either of these sensible-heat effects is important, it must be accounted for by an added term in the left-hand side of Eq. (4.3-7).
For example, if the condensate leaves at a temperature t that is less than T, the condensing temperature of the vapor, Eq. (4.3-7) must be written