**1. Definition of plate heat exchangers**

### What is a plate heat exchanger?

Plate and frame heat exchangers have a very specific design compared to other heat exchangers: the liquid is divided into wide but narrow channels between thin plates. This allows for a very high heat exchange coefficient and consequently a fairly compact heat exchanger compared to other designs, which can make them an interesting proposition when space or costs are limited. However, such a design leads to a high pressure drop, which limits its application at high flow rates.

This type of heat exchanger was particularly popularized by the Alfa Laval company, sometimes referred to as the "Alfa Laval Plate Heat Exchanger". The most common construction is to press the plates against each other with gaskets in between. Such a design allows very easy opening and cleaning of the heat exchanger, which is important in situations where heavy pollution is expected or when regular cleaning is required for hygienic reasons (food industry). The use of gaskets limits the operating pressure and temperature, so other welded plate designs exist (brazed plate heat exchangers). They can operate in more extreme conditions, but cannot be opened for inspection and cleaning.

## 2. Calculation method: dimensioning of the plate heat exchanger

### How to design a plate heat exchanger?

### 2.1 STEP 1: Obtain the design data

To dimension a plate and frame heat exchanger, the following data must be defined:

- Fluid properties (viscosity, specific heat... as a function of temperature if possible)
- Inlet and outlet temperature of each fluid (note: the procedure here is to size a heat exchanger knowing this data, but it can be adjusted afterwards with Excel to calculate the outlet temperature if for example the characteristics of the heat exchanger are known)
- inlet pressure of liquids
- Permissible pressure drop

### 2.2 STEP 2: Calculate the required heat flow

Heat flux can be calculated when the flow rate, the entering and leaving temperatures, and the specific heat of the fluid on either the hot or cold side are known.

With

M_{C}= mass flow cold side (kg/s)

See_{C}= specific heat of cold liquid

T_{co}= outlet temperature cold side (K)

T_{day}= cold liquid inlet temperature (K)

M_{H}= mass flow hot side (kg/s)

See_{H}= specific heat of hot liquid (J/kg/K)

T_{To}= outlet temperature hot side (K)

T_{Hi}= inlet temperature of the hot medium (K)

It is then possible to approximate the size of the heat exchanger by estimating the overall heat transfer coefficient H.

H for plate heat exchangers is often between 2 and 7 kW.m^{2}.K^{-1}.

H = total heat exchange coefficient (kW.m^{2}.K-1)

S = area of the heat exchanger (m^{2})

ΔTml (K)

The value of S can thus be calculated as a 1st approximation of the heat exchanger size.

### 2.3 STEP 3: Calculate the number of panels required

This phase requires some references from suppliers, specifically the size of the plates they can supply, the maximum size of the heat exchanger when using a specific plate, the design of the plate, as well as the maximum flow that the heat exchanger can handle.

From there the engineer can select a panel size and design and calculate the number of panels required.

N = S/s

With

N = number of plates required

S = total heat exchange surface (m^{2})

s = size of a single disk (m^{2})

It is also possible to calculate the number of channels: n = (N-1)/2

### 2.4 STEP 4: Confirm heat exchanger size

After a rough design of the plate and frame heat exchanger has been made, it is necessary to explain in detail the many options available for the plates and to use correlations that allow to recalculate the heat transfer coefficient and then a required exchange area . The calculation then proceeds iteratively until the calculated heat exchange area equals the assumed area.

A correlation giving the Nusselt number can be used:

With

Nu = Nusselt number (-) = h.D_{H}/M

Re = Reynolds number (-) = ρ.u.D_{H}/M

a = coefficient depending on the corrugation of the plates (-)

b = coefficient depending on the corrugation of the plates (-)

Pr = Prandtl number = μ.Cp/λ

Pr_{w}= Prandtl number under plate (wall) conditions

And

h = thermal transmittance (W.m^{-2}.K^{-1})

μ = viscosity of the liquid (Pa.s)

ρ = density of the liquid (kg/m^{3})

u = velocity of the liquid between 2 plates (m/s)

Cp = specific heat of the liquid (J/kg/K)

λ = thermal conductivity (W/m/K)

D_{H}= hydraulic diameter = [4*l*d_{Platte}] / [2*(l+d_{Platte})] (M)

l = width of panels (m)

D_{Platte}= distance between 2 panels (m)

a and b depend on α, the angle of the waves on the plates. The table below is from [Aydin], who takes her source from [Kakac].

shaft angle in ° | Regarding | A | B |

<30 | <10 | 0,718 | 0,349 |

<30 | >10 | 0,348 | 0,663 |

45 | <10 | 0,718 | 0,349 |

45 | 10-100 | 0,400 | 0,598 |

45 | >100 | 0,300 | 0,663 |

50 | <20 | 0,630 | 0,333 |

50 | 20-300 | 0,291 | 0,591 |

50 | >300 | 0,130 | 0,732 |

60 | <20 | 0,562 | 0,326 |

60 | 20-400 | 0,306 | 0,529 |

60 | >400 | 0,108 | 0,703 |

>65 | <20 | 0,562 | 0,326 |

>65 | 20-500 | 0,331 | 0,503 |

>65 | >500 | 0,087 | 0,718 |

It is then possible to calculate the overall heat transfer coefficient h on both the hot and cold side and then calculate the overall heat transfer coefficient H.

H = overall heat transfer coefficient (W.m^{-2}.K^{-1})

H_{C}= heat transfer coefficient on the cold side (W.m^{-2}.K^{-1})

R_{FC}= fouling resistance on the cold side (K.W^{-1}.M^{-2})

H_{H}= heat transfer coefficient on the hot side (W.m^{-2}.K^{-1})

R_{fh}= fouling resistance on the hot side (K.W^{-1}.M^{-2})

e = thickness of panels (m)

λ = thermal conductivity of the plate (W.m^{-1}.K^{-1})

It is then necessary to compare the calculated H with the assumed H.

if h_{calculated}= H_{supposed}If the calculation is valid, the size of the heat exchanger with the total heat exchange area S is correct.

if h_{calculated}≠H_{supposed}, then the calculation must be performed again, this time with H_{supposed}as a starting point, or if the values are very far apart, change the design of the heat exchanger (plate size...) and run again.

### 2.5 STEP 5: Calculate the pressure drop

The design determined in step 4 is only valid if the pressure drop on both sides is less than the permissible pressure drop. If yes, the design can be kept, if not, some design options like plate size, corrugation, number of plates... Checking the pressure drop is especially important for gasketed plate heat exchangers which have limited pressure resistance compared to brazed plate heat exchangers.

### 2.6 STEP 6: Optimization and detailed design

Even if the finished design meets the process conditions, it may be possible to improve the design by making it less costly and more compact... the design procedure can then be repeated for the basic design calculated by changing the plate type. size, number of panels...etc...

The above procedure is helpful to get an idea, but cannot be used for such detail. It should be done with a specialized company. Detailed planning and construction drawings must always be created with the support of such a company.

Those

[Aydin] Bericht an das Department of Chemical Engineering, Middle East Technical University, Plate Heat Exchanger design, Aydin et al., 2016, https://www.slideshare.net/ervaldi/plate-type-heat-exchanger-design-62443113

[Kakac] Heat Exchangers, Selection, Rating and Thermal Design, Kakac et al, CRC Press

## FAQs

### How is heat exchanger design calculated? ›

Solution: The surface area per tube will be: **Sa = πDL = π (3/12) (10) ft² = 7.854 ft² - (D – tube diameter in ft)**. The number of tubes required would thus be: n = 178.7 ft² = 22.7 tubes (23 or 24 tubes).

**What is the correct calculation of effectiveness of heat exchanger? ›**

How do I determine the effectiveness of a heat exchanger? From fluid's properties, calculate the maximum (q_{max}) and actual heat transfer (q). Determine the ratio between the heat capacities of the fluids, C_{r} = C_{min} / C_{máx}. Calculate the effectiveness as the ratio of the heats, **ε = q/q _{max}**.

**What is the basic heat exchanger design equation? ›**

**Q = UA(FΔTlm)**

In this equation, U is the overall heat transfer coefficient, A is the total area of heat transfer, ΔTlm is the log-mean temperature difference, and F is the log-mean temperature difference correction factor.

**What is 2/3 rule in heat exchanger? ›**

The “two-thirds rule” from API RP 521 states: For relatively low-pressure equipment, complete tube failure is not a viable contingency when the design pressure of the low-pressure side is equal to or greater than two-thirds the design pressure of the high-pressure side.

**How do you calculate total heat required? ›**

The equation for the amount of heat, Q , required to change the temperature of an object in a single phase is **Q=mcΔT** Q = m c Δ T , where m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature of the substance.

**How do you calculate design flow rate? ›**

The actual (design) flow rate can be calculated by **dividing the peak hour volume by the PHF**, 464/0.86 = 540 pcu/hr, or by multiplying the peak 15 minute volume by four, 4 * 135 = 540 pcu/hr.

**How do you calculate heat loss in design? ›**

The formula is: **Room volume x Delta T x Air Changes per Hour x .** **018**.

**How is design current calculated? ›**

First we must calculate the Design Current. Applying equation, **P=I x V** for 8.7kW @ 240v, you get the following: Therefore if the voltage is 240 the shower will draw a current of 36.25 Amps. We can now decide on the size of fuse.

**How do you calculate effectiveness? ›**

We can calculate the efficiency of anything by **dividing the energy input and the energy output by 100%**.

**How do you calculate heat quality? ›**

We wish to determine the value of Q - the quantity of heat. To do so, we would use the equation **Q = m•C•ΔT**. The m and the C are known; the ΔT can be determined from the initial and final temperature. With three of the four quantities of the relevant equation known, we can substitute and solve for Q.

### How do you calculate heat transfer coefficient of heat exchanger? ›

To calculate heat transfer coefficient: Divide the thickness of the first layer with the thermal conductivity of the medium.

**What is the 10 13 rule for exchangers? ›**

**Increase the shell-side design pressure up to 10/13 of the tube-side design pressure**. (The logic behind this “10/13” rule is that the hydrotest is done, as per ASME, at 1.3-times the design pressure—it was popularly known as the ⅔ rule based on old code hydrotest pressure before the year 2000).

**What is the 10 13 rule heat exchangers? ›**

10/13 Rule Loss of containment of the low-pressure side of shell and tube heat exchangers to atmosphere is unlikely to result from a tube rupture where the pressure in the low-pressure side during the tube rupture does not exceed the corrected hydrotest pressure.

**What is heat exchanger rules of thumb? ›**

In heat transfer engineering, rules of thumb are **used to estimate the optimum design performance of a heat exchanger**; weighing the capital cost (CAPEX) with the operating cost (OPEX) of its performance. Many times a minimum approach temperature (pinch temperature) is used to approximate the optimum design point.

**How big of a plate exchanger do I need? ›**

Re: Sizing a plate heat exchanger? You will want to get a **5x12" or 5x13" plate**. 20 plate will work fine unless you are very near the limits on boiler water flow. If you are, going with a 30 plate will usually work without needing to get a larger pump.

**What is the equation for the rate of plate motion? ›**

Remember, a rate of movement (velocity) can be calculated if you know the distance traveled and the time it took to make the "trip," according to the following formula: velocity = (distance traveled) / (travel time), or more simply, **v = d / t**.

**What is the sizing of plated heat exchanger? ›**

Plate heat exchangers can vary significantly in size. Available sizes range from: **9.7 x 32 x 51 mm (or 0.97 x 3.2 x 5.1 cm) at the lower end**. **524.4 x 112 x 24.1 mm (or 52.44 x 11.2 x 2.41 cm) at the higher capacity end**.

**How do you calculate plate cooler? ›**

Measure at the discharge point to account for any flow rate restrictions in the pipework downstream of the plate cooler. Calculate the cooling water flow rate; for example, **if it takes 15 seconds to fill a 23L bucket the flow rate is 23/15 = 1.5L/sec**.

**How do I calculate BTU for heat exchanger? ›**

A BTU calculation is performed by **placing temperature elements in both the inlet and outlet piping of the heat exchanger.** **Using the difference of these two temperatures and multiplying by the flow rate**, a BTU calculation is obtained.

**How do you calculate heat transfer area? ›**

**Q=m \times c \times \Delta T**

Here, Q is the heat supplied to the system, m is the mass of the system, c is the specific heat capacity of the system and \Delta T is the change in temperature of the system. The transfer of heat occurs through three different processes which are, Conduction, Convection, and Radiation.

### How much flow is required for heat exchanger? ›

In many process applications, a flow rate of **2.5 to 3 gal/min per cooling ton** is sufficient to achieve turbulent flow through a heat exchanger.