Heat transfer within cooling system (heat exchanger)

The process represented in the above figure (1.1) is one in which hot fluid is cooled by water, which itself heated without any loss of exchanged heat. Industrial heat exchangers consist of a number of tubes enclose in a shell. Exchangers with cooling water in the tubes, and hot product in the shell are the most satisfactory. Fouling often occurs if water is circulated through the shell, because the velocity of the water stream is lower in this design. Tubes are much easier to clean than the shell. Matters are also so arranged that the pressure of the product being cooled is higher than that of cooling water, so that the water cannot leak into the hot product, and damage the equipment.

In the figure (t1) temperature of CW inlet; (t2) temperature of CW outlet; (T1) temperature of process inlet; (T2) Temperature of process outlet. Here we will consider CW as cooling water and Process as P.

Now  U = ΔHp/ΔtmA                                                                                                (eq-1.0)

Where:             U = net effective overall heat transfer coefficient (Kcal/0C-h-m2)

ΔH = difference in enthalpy of P at T1 and T2 (Kcal/kg)

P = flow rate of the product (m3/h)

A = area of heat transfer surface (m2)

Δtm = the average of the temperature differences at both ends of the exchanger (0C)

Δtm = (T1-t2) +(T2-t1)                                     (eq – 1.5)

2

Here it is assumed that the temperature of the fluid is in the shell falls continuously and uniformly from T1 to T2, while that of the water inside the tubes rises similarly from t1 to t2. With this assumption it is permissible to use the average of the terminal differences for the mean temperature difference. In more complicated heat exchangers, however, it is necessary to use the log mean temperature difference, and when calculation the value for multipass exchangers correction factors also must be applied to (Δtm).

(Δt)log e =     (Δt)max – (Δt)min                        = (T2-t1) – (T1 – t2)                (eq – 1.6)

log e [(Δt)max/(Δt)min]                    log e [(T2-t1)/(T1-t2)]

(see topic LMTD for detailed description)

In a water-tube exchanger U is likely to decrease gradually because of accumulating deposits, or because of scale formation on the tubes. Referring to the figure, the effect of these events on the heat transfer coefficient can be predicted qualitatively. If a thin layer of insulating scale forms on either side of the tube T2 rises and t2 falls as less heat passes from P to CW through the insulating layer. Thus ΔH decreases, and as both t1 and T1 are unaffected by conditions within the heat exchanger, Δtm increases. The net result is that the heat transfer coefficient becomes smaller.

If deposits slow the flow of water, t2 and T2 both rise. In this event, however, Δtm    may increase and ΔH may decrease by such small amounts that the effect on U may not be significant.

The reciprocal of the heat transfer coefficient is called the “fouling resistance,” this number multiplied by one thousand is the “fouling factor.” Except in unusual circumstances the effect of fouling resistances can never be exactly known, as fouling within an actual heat exchanger is seldom uniform, and also the net effect is a combination of conditions on both sides of the heat transfer surface.