Blog

1. Reynolds number (Re) Reynolds number, which relates inertial forces to viscous forces and thereby characterizes the type of flow regime
2. Prandtl number (Pr), which relates the thermal properties of the fluid to the conductivity of the pipe.
3. Nusselt number (Nu) , a dimensionless group defining the relative significance of the film heat transfer coefficient to the conductivity of the pipe wall

where:

Dh is the hydraulic diameter of the pipe; its characteristic travelled length, , (m).

Q is the volumetric flow rate (m3/s).

A is the pipe cross-sectional area (m²).

v is the mean velocity of the object relative to the fluid (SI units: m/s).

mu is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s)).

nue is the kinematic viscosity ( (m²/s).

rho is the density of the fluid (kg/m³).

Calculation of Prandtle number :

Where

Based on these parameter, we can now calculated Heat transfer co-efficient on either side.

Where kw is thermal conductivity of the bulk fluid.

With this you are now equipped to calculate over all heat transfer.
 

To Calculate LMTD, we need to understand the flow and type of process (Isothermal or not)

Generally we have complication, when either of fluid is showing isothermal characteristics. see the following variation.

Two fluids are separated by a heat transfer surface (wall), these fluids ideally do not mix, and there are no moving parts.In this blog the thermal design theory of recuperates is presented. In a heat exchanger, when hot and cold fluids are maintained at constant temperatures of Th and Tc as shown in above Fig(a)..The driving force for overall heat transfer in the exchanger, referred to as mean temperature difference (MTD), is simply Th-Tc.

Such idealized constant temperatures on both sides may occur in idealized single-component condensation on one fluid side and idealized single-component evaporation on the other fluid side of the exchanger. However, a number of heat transfer applications have condensation or evaporation of
single-component fluid on one side and single-phase fluid on the other side. In such cases, the idealized temperature distribution is shown in Fig(b) and (c)

The First major step in Thermal design, is to understand the assumptions that are considered while we disign the heat exchanger, but we forgot to understand them, they are:-

1. The heat exchanger operates under steady-state conditions [i.e., constant flowrates and fluid temperatures (at the inlet and within the exchanger) independent of time].

2. Heat losses to or from the surroundings are negligible (i.e. the heat exchanger outside walls are adiabatic).

3. There are no thermal energy sources or sinks in the exchanger walls or fluids, suchas electric heating, chemical reaction, or nuclear processes.

4. The temperature of each fluid is uniform over every cross section in counter flow and parallel flow exchangers (i.e., perfect transverse mixing and no temperature gradient normal to the flow direction). Each fluid is considered mixed or unmixed from the temperature distribution viewpoint at every cross section in single-pass cross flow exchangers, depending on the specifications. For a multi pass exchanger, the foregoing statements apply to each pass depending on the basic flow arrangement of the passes; the fluid is considered mixed or unmixed between passes as specified.

5. Wall thermal resistance is distributed uniformly in the entire exchanger.

6. Either there are no phase changes (condensation or vaporization) in the fluidstreams flowing through the exchanger or the phase change occurs under thefollowing condition. The phase change occurs at a constant temperature as for a single-component fluid at constant pressure.

7. Longitudinal heat conduction in the fluids and in the wall is negligible.

8. The individual and overall heat transfer coefficients are constant (independent of temperature, time, and position) throughout the exchanger, including the case of phase-changing fluids in assumption 6.

9. The specific heat of each fluid is constant throughout the exchanger, so that the heat capacity rate on each side is treated as constant. Note that the other fluid properties are not involved directly in the energy balance and rate equations, but are involved implicitly in NTU and are treated as constant.

10. For an extended surface exchanger, the overall extended surface efficiency is considered uniform and constant.

11. The heat transfer surface area A is distributed uniformly on each fluid side in a single-pass or multi pass exchanger. In a multi pass unit, the heat transfer surface area is distributed uniformly in each pass, although different passes can have different surface areas.

12. For a plate-baffled (1–n) shell-and-tube exchanger, the temperature rise (or drop) per baffle pass (or compartment) is small compared to the total temperature rise (or drop) of the shell fluid in the exchanger, so that the shell fluid can be treated as mixed at any cross section. This implies that the number of baffles is large in the exchanger.

13. The velocity and temperature at the entrance of the heat exchanger on each fluidside are uniform over the flow cross section. There is no gross flow maldistribution at the inlet.

14. The fluid flow rate is uniformly distributed through the exchanger on each fluid side in each pass i.e., no passage-to-passage or viscosity-induced maldistribution occurs in the exchanger core. Also, no flow stratification, flow bypassing, or flow leakages occur in any stream. The flow condition is characterized by the bulk (or mean) velocity at any cross section.

Question??? So many assumption… still we are ‘designing’ a heat exchanger with Guarantee on performance!! sure we are Engineers 😉

Following Table will show the impact of various parameters on design of heat exchanger.
(NTU stands for number of transfer unit, and alternate to LMTD method)

1st Position : 23 : Defines, ID of Vessel
2nd Position : 192 : Defines, Tube length
3rd Position : BEM : it further splited in three parts as per fing N-1.2
e.g B-E-M,
the 1st section, defines the Type of Front head (B for Bonnet Integral cover)
the 2nd section, defines the shell type (E – One pass shell)
the 3rd section, defines the type of rear head (M – Fixed tube sheet, stationary head)

Above figure shows typical flow arrangement inside a heat exchanger.

Typically for a heat exchanger, their are two type Tube Bundle exist. see the picture below.

Generally we can get reference from various resources listed below, either expected heat flux (W/m2) or range of heat transfer co-efficient. based on this information, we can estimate the heat transfer area required.

But if the case is, you are doing for first time, and have no earlier experience in that type of heat exchanger, then better is make your self ready with all information e.g fluid properties which includes

1. Dynamic viscosity (for the temperature ranges)
2. Conductivity (for the temperature ranges)
3. Density (for the temperature ranges)
4. Boiling temperature
5. Specific heat

The grate equation (you can see in my earlier post) for heat duty is:
Q = U A LMTD & Q = m. cp. DT

where
Q = heat duty (kcal/hr)
U = over all heat transfer co-efficient (Kcal/hr.m2.oC)
A = heat transfer area (m2)
LMTD = Log mean temperature (degC)
cp = Specific heat of the fluid to be heated / or to be cooled (kcal/kg)
DT = temperature difference of any one of the fluid (degC)
m = mass flow rate of the fluid (kg/hr)

LMTD is calculated based on the temperature on both the side for both the fluid
it’s simple if you understand the following figure

& LMTD = (dt_o – dt_i) / ln(dt_o / dt_i)

Just Plot your temperature, take difference on each side, and do the arithmatics…

Some good refrences (Free google search results 🙂

http://www.chemsof.com/lmtd/lmtd.htm
http://en.wikipedia.org/wiki/Log_mean_temperature_difference
http://www.wlv.com/products/databook/databook.pdf