Shell & tube heat exchanger equations and calculations - EnggCyclopedia (2024)

In this article, we will take a details look at equations required for shell and tube heat exchanger sizing calculations and design.

Shell and tube heat exchangers are widely used and very popular in the process industry, due to their versatility. Different types of shell and tube exchangers can be easily configured by changing the shell and tube arrangement.


  1. Heat exchanger equations

Shell & tube heat exchanger design procedure

Shell and tube heat exchanger design is an iterative process, which goes through the following steps.

  1. Define process requirements for the new exchanger
  2. Select a suitable type of shell and tube exchanger
  3. Define design parameters such as - number of tube passes, tube size, shell ID etc.
  4. Heat exchanger calculations and modeling to get the output - outlet hot/cold fluid temperature, heat transfer rate, pressure drop on shell/tube sides etc.
  5. Check of the output is in accordance with the process requirements
    • If the output is as per process requirements and cost is within budget then finalize the process design and prepare a heat exchanger specification sheet
    • If the design does not match with either the process requirement or if it is over budget then go back to step 3, change the design parameters and repeat this process again.

There are a few equations that are very important for the calculations that we need to perform during heat exchanger design process.

Shell and tube heat exchanger equations

Here is a list of all the important shell and tube heat exchanger equations.

Overall heat transfer equation

Overall heat transfer in any exchanger is governed by the following equation -


where, Q = overall heat transfer rate
U = Overall heat transfer coefficient
AOverall = Overall heat transfer surface ares
LMTD = Logarithmic Mean Temperature Difference

LMTD equation

The logarithmic mean temperature difference is an average quantification of the temperature difference between the shell and tube sides. It is calculated with the following equation.


ΔT1→ the temperature difference between hot and cold fluids at one end of the heat exchanger
ΔT2→ the temperature difference between hot and cold fluids at the other end of the heat exchanger.

LMTD with the Correction factor

However the LMTD is valid only for heat exchanger with one shell pass and one tube pass. For multiple number of shell and tube passes the flow pattern in a heat exchanger is neither purely co-current nor purely counter-current. Hence to account for geometric irregularity, Logarithmic Mean Temperature Difference (LMTD) has to be multiplied by aMean Temperature Difference (MTD) correction factor (FT)to obtain the Corrected Mean Temperature Difference (Corrected MTD).


This correction factor calculator will help you to quickly calculate the LMTD correction factor for a shell and tube exchanger with multiple shell or tube side passes.

Number of tubes based on the heat transfer area required

The number of tubes needed in shell & tube exchanger (NT) can be calculated using the following equation, based on overall heat transfer area requirement.


Where, we get the AOverall (overall heat transfer area required) from the heat transfer rate equation (Equation-1).
OD is the outside diameter of selected tube size
L is the total tube length

This equation is quite straight forward based on the geometry of the selected shell and tube heat exchanger.

Tube side fluid velocity

Tube side velocity is important for estimation of Reynolds number on the tubeside and then for getting the heat transfer coefficient for the tube side fluid. We can use the following equation for tube side velocity.


Where, m = mass flow rate on the tube side
NP = Number of tube passes
NT = Number of tubes
ρ = Tube side fluid density
ID = Tube internal diameter

Further, the Reynold's number for the tube side fluid is calculated as,


Here, μ is the viscosity for tube side fluid

Overall heat transfer coefficient equation

When we have a handle on the heat transfer area (AOverall) and temperature difference (LMTD), the only remaining unknown in the heat transfer equation (Equation-1) is the overall heat transfer coefficient (U). We can use the following equation to get the overall heat transfer coefficient for a shell & tube exchanger.


Where, ho = Shell side heat transfer coefficient
hi = Tube side heat transfer coefficient
Rdo = shell side dirt factor
Rdi = tube side dirt factor
OD and ID are respectively the outer and internal diameters for the selected tube size
Ao and Ai are outer and inner surface area values for the tubes
kw is the resistance value for the tube wall

Note, this overall heat transfer coefficient is calculated based on the outer tube surface area (Ao). So it must be multiplied by the Ao value for using in the overall heat transfer equation.

Shell & tube heat exchanger calculations

We already saw that the design of a shell and tube heat exchanger is an iterative process. Often, engineers prefer to use a heat exchanger design software to create a heat exchanger model. You can then use this model to simulate the heat exchanger performance and to verify if it will meet your process requirements.

However, if you decide to manually perform the heat exchanger sizing calculations, here are some calculators and tutorials that can help you.

Heat exchanger calculators

Note all of the following calculators are for demo. To access the actual working calculators, you will need tocreate a login on EnggCyclopedia.

  1. Here's ato help you calculate the required heat transfer area based on inlet/outlet temperature values on shell and tube sides.This calculator is for sizing the tubeside flow based on a fixed shell side flow. Other required inputs are - flow rate, density, viscosity, specific heat values for fluids on shell and tube sides.
  2. This othercalculator for shell side flowwill help you calculate the required surface area as well as the shell side flow,when you have fixed conditions on the tube side. Other required inputs are - flow rate, density, viscosity, specific heat values for fluids on shell and tube sides.
  3. Thisquick LMTD calculatorhelps to quickly getLMTD valuefor an exchanger.
  4. Then there is anothercalculator for LMTD correction factor.
  5. Apart from these, you will also need to calculate the pressure drop on the shell and tube sides for your process datasheet.This calculator is for shell side pressure drop calculation.
  6. You can use thiscalculator to determine tubeside pressure drop.

Apart from these calculators, you can always use aheat exchanger design softwareto build a model of your heat exchanger design and then to simulate its performance.

Tutorials for shell & tube exchanger calculations

Here are some step by step guided tutorials about how to use those calculators for shell & tube heat exchanger calculations. In these tutorials, we will make use of the shell & tube heat exchanger equations discussed above.

  1. Calculation of overall heat transfer coefficient
  2. Calculation of insulation thickness for furnace wall
  3. LMTD calculation tutorial
  4. Calculating LMTD when the formula fails
  5. Tutorial - Heat Exchanger shellside pressure drop calculation
  6. Tutorial - Heat Exchanger tubeside pressure drop calculation

Recommended steps

Here are some recommended steps to use the heat exchanger design equations -

  1. Fix the inlet/outlet temperature values
  2. Calculate LMTD
  3. Select a shell and tube heat exchanger (TEMA) tube
  4. Decide on shell and tube geometry
  5. Calculate heat transfer area based on selected geometry (AOverall)
  6. Get the overall heat transfer coefficient (U), using a suitable empirical correlation for given fluid - for example, Sieder-Tate equation
  7. Calculate the overall heat transfer rate (Q), using Equation-1
  8. Check of Q matches with the heat lost/gained via temperature change on the hot and cold side. This is the basic energy balance on shell / tube side fluids.
  9. Check the pressure drop on shell and tube sides. Does is match with the allowable pressure drop as per process requirements?
  10. If the design is adequate as per process requirements, check the tentative material costs. Are they within budget?
  11. If either of the design or budget checks fail, go back to step 4 and repeat the process till you get a satisfactory shell & tube heat exchanger design.

Tips and pointers for heat exchanger calculations

  • The shell side baffles are used to promote crossflow and enhance the heat transfer between the two fluids. The spacing between shell side baffles has an important impact on the degree of heat transfer. You can use theseguidelines to select the optimal shell side baffle spacing. It is generally recommended to consider baffle spacing between 0.3 to 0.6 times of shell ID, as per the TEMA standards.
  • Heat exchanger approach temperatureis an important factor influencing the design of an exchanger. It is advisable to carefully consider the selected utility and corresponding approach temperature, before actually proceeding with the sizing calculations.
Shell & tube heat exchanger equations and calculations - EnggCyclopedia (2024)


How do you calculate the shell of a heat exchanger? ›

And is a function of the inlet. And outlet temperatures of each stream for co-current flow delta. T

How do you calculate lmtd for shell and tube heat exchanger? ›

To calculate LMTD: Find the difference between the inlet temperature of hot fluid and outlet temperature of cold fluid, ΔT1. Obtain the difference between outlet temperature of hot fluid and inlet temperature of cold fluid, ΔT2. Subtract the temperature difference, ΔT2 from ΔT1.

How do you calculate shell diameter of a shell and tube heat exchanger? ›

The equivalent diameter is calculated along (instead of across) the long axes of the shell and therefore is taken as four times the net flow area as layout on the tube sheet (for any pitch layout) divided by the wetted perimeter.

What is the formula of heat transfer? ›

Q = c × m × ΔT

The specific heat capacity (c) is defined as the quantity of heat (in Joules) absorbed per unit mass (kg) of the material when its temperature increases by 1 K (or 1 °C). Its units are J/kg/K or J/kg/°C.

What is 2/4 shell and tube heat exchanger? ›

Most shell-and-tube heat exchangers are either 1, 2, or 4 pass designs on the tube side. This refers to the number of times the fluid in the tubes passes through the fluid in the shell. In a single pass heat exchanger, the fluid goes in one end of each tube and out the other.

How do you calculate shells? ›

Electron shells Elements 1-18 - YouTube

What is Q MCP ∆ T? ›

The amount of heat gained or lost by a sample (q) can be calculated using the equation q = mcΔT, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change.

What is the formula for calculating electrons in Shell? ›

The formula to find the maximum number of electrons that can be accommodated in a shell = 2n2 where 'n' is the number of the given shell from the nucleus. The maximum number of electrons that can be filled in the second shell (L - Shell) = 2(2)2 = 8 electrons.

Why do we calculate LMTD? ›

The log mean temperature difference (LMTD) is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger.

How do you calculate log mean? ›

Divide the difference of x and y by the difference of ln x and ln y. Make sure that x and y are in the same order in the quotient and denominator of the fraction. In the example problem, 90/0.38 = 236.84. The logarithmic mean is 236.84.

Why LMTD is used in shell and tube heat exchanger? ›

The LMTD allows to represent the driving force of heat exchange along the exchanger and accounts for the fact that the difference in between the cold side and the hot side is changing all along the equipment. The use of the LMTD is valid for co-axial heat exchangers.

How do you calculate volume of a shell? ›

The volume of the cylindrical shell is then V = 2πrh∆r. Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness. 2π¯xif(¯xi)∆x.

How do you calculate Shell Development length? ›

D' = 2R' = 2 (r' + sL)

How do you calculate bundle diameter? ›

To determine the approximate diameter of a wire bundle when the wires are all the same size, find the factor for the number of wires in the bundle and multiply the wire diameter by that factor.

What are the 3 formulas for heat? ›

The Heat formula is:
  • C = \frac{Q}{m\Delta T} Where, ...
  • Specific heat of iron, C = 0.45 Jg^-1°C. Also, temperature difference,
  • \Delta T = 700° C – 250° C.
  • \Delta T = 450° C. Now applying the heat formula,
  • c = \frac{Q}{m\Delta T} rearranging the formula.
  • Q = mc\Delta T.
  • Q = 1 \times 0.45 \times 10^3 \times 450. = 20.25 J.
  • Q.

What are the 4 types of heat transfer? ›

Various heat transfer mechanisms exist, including convection, conduction, thermal radiation, and evaporative cooling.

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.

What is a 3 pass heat exchanger? ›

Each particle in the tube-side fluid travels three times through the entire length of the heat exchanger. Hence, by convention this can be regarded as a three-pass counterflow heat exchanger.

What do you mean by 2n2 formula? ›

The formula to find the maximum number of electrons that can be accommodated in a shell = 2n2 where 'n' is the number of the given shell from the nucleus. For example, the maximum number of electrons that can be filled in the: First shell (K - Shell) = 2(1)2 = 2 electrons.

What is the formula for energy of a shell? ›

E ( n ) = − 1 n 2 × 13.6 e V

where 13.6 eV is the lowest possible energy of a hydrogen electron E(1).

What is the maximum capacity of L shell? ›

L shell is the second shell and it can hold up to 2(2)2 = 8 electrons.

What is the formula for Delta T? ›

The equation of delta t is: ΔT = T2 - T1

The entrance temperature in the heat exchanger at B would be T1. And the outlet from the heat exchanger coming out at D is T2. The cooling water entering the heat exchanger will get warmer on its way through the exchanger.

How is Q system calculated? ›

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.

How do you calculate delta T? ›

Calculating Delta T is simple: just subtract the return air temperature from the supply air temperature. The difference, or delta, between the two is Delta T.

How many electrons are in each L shell? ›

The first shell (closest to the nucleus) can hold two electrons. The second shell can hold 8 electrons. The third shell can hold 32 electrons. Within the shells, electrons are further grouped into subshells of four different types, identified as s, p, d, and f in order of increasing energy.

How do you find the number of electrons in the first shell? ›

How to find the number of electrons in each electron shell or energy level

How do you calculate the overall heat transfer coefficient in shell and tube? ›

The convective heat transfer coefficient of the shell and tube heat exchanger is calculated based on the following correlation:(4) U = Q A × L M T D where, A is total heat transfer area, m2, Q is heat transfer from hot stream into cold stream, W, LMTD is logarithmic mean temperature difference, K.

How many tubes are in a tube and shell heat exchanger? ›

The number of tube-side passes is usually one, two, four, or six, but may be as high as 16. Multiple passes on the shell side are achieved by partitioning the shell with a longitudinal baffle (type F-shell) or by connecting two or more single-pass shells together.

How do you calculate volume of a shell? ›

The volume of the cylindrical shell is then V = 2πrh∆r. Here the factor 2πr is the average circumference of the cylindrical shell, the factor h is its height, and the factor ∆r is its the thickness. 2π¯xif(¯xi)∆x.

How do you calculate shell? ›

How do you calculate the volume of a shell? The volume of a cylindrical shell is 2pi*rh where r is the radius of the cylinder, and h is the height of the cylinder. This volume can be integrated to find the volume of a cylindrical solid.

How do you calculate total heat content? ›

To calculate heat capacity, use the formula: heat capacity = E / T, where E is the amount of heat energy supplied and T is the change in temperature. For example, if it takes 2,000 Joules of energy to heat up a block 5 degrees Celsius, the formula would look like: heat capacity = 2,000 Joules / 5 C.

How is heat value calculated? ›

Subtract the final and initial temperature to get the change in temperature (ΔT). Multiply the change in temperature with the mass of the sample. Divide the heat supplied/energy with the product. The formula is C = Q / (ΔT ⨉ m) .

How do you calculate transfer coefficient? ›

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

What is a 4 pass heat exchanger? ›

The Shell and Tube Heat Exchanger (4 pass) is an optional heat exchanger in the Pressure, Flow, Level, and Temperature Process Training Systems. The Shell and Tube Heat Exchanger (4 pass) is made of a series of tubes around which a watertight shell is built.

What is the maximum number of tubes in a heat exchanger? ›

waste heat boiler in power plant gas turbine are shell & tube type heat exchanger are also larger size and having 5000-12000 number of tubes.

How do you calculate tube pitch? ›

TEMA standards recommends a minimum tube pitch of 1.25 * Tube outer diameter for triangular pitch. For example, if we have a tube outer diameter of 12.7 mm (0.5 inch) then the recommended tube pitch for triangular pitch arrangement is: 1.25 * 12.7 mm = 16 mm (0.6 inch).

What are 3 ways to calculate volume? ›

Depending on your object shape, you can use different formulas to calculate volume:
  1. Cube volume = side. ...
  2. Cuboid (rectangular box) volume = length × width × height.
  3. Sphere volume = (4/3) × π × radius. ...
  4. Cylinder volume = π × radius2 × height.
  5. Cone volume = (1/3) × π × radius2 × height.
  6. Pyramid volume = (1/3) × base area × height.
20 Jun 2022

What are the 3 methods used to calculate volume? ›

To illustrate the effects of precision on data, volumes will be determined by three different methods: geometrically (measuring lengths); water displacement; and pycnometry. The composition of a mixed brass-aluminum cylinder and the volume of empty space within a hollow cylinder will also be found.

What are the formulas to calculate volume? ›

Volume Formulas of Various Geometric Figures
ShapesVolume FormulaVariables
Rectangular Solid or CuboidV = l × w × hl = Length w = Width h = Height
CubeV = a3a = Length of edge or side
CylinderV = πr2hr = Radius of the circular base h = Height
PrismV = B × hB = Area of base, (B = side2 or length.breadth) h = Height
6 more rows
12 Oct 2020

What is the K shell? ›

Definition of K-shell

: the innermost shell of electrons surrounding an atomic nucleus and constituting the lowest available energy level for the electrons — compare l-shell , m-shell.

How is shell thickness calculated? ›

The Shell Thickness calculation page is to calculate the wall thickness of a cylinder, cone and sphere under pressure without holes. The calculation does not take into account the extra stress around holes for nozzles and is therefore a basic strength calculation.

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