Heat Loss From An Insulated Pipe

This Excel spreadsheet models heat loss from an insulated pipe. This is a very common system in the process industries - insulated pipes are everywhere, and engineers need a sound grasp of heat transfer principles to model their effects. Although the model in the spreadsheet is simplified to aid understanding, complexity can be easily added.

Liquid flows through the pipe, with heat exchanged with the insulation. Heat is lost from the insulation to the environment via convection (no radiation losses are considered). The thermal effects of the pipe wall are ignored (although this can be easily implemented).

These equations are used in the spreadsheet to define the heat transfer process.

• q is the heat flowrate through the pipe and insulation (W m^-1)
• T_s is the temperature at the surface of the insulation (K)
• T_a is the ambient air temperature (K)
• T_f is the fluid temperature inside the pipe (K)
• D_O is the pipe diameter (m)
• D_S is the outside diameter of the insulated pipe (i.e. the pipe diameter plus two times the insulation thickness) (m)
• k is the insulation thermal conductivity (W m^-1 K^-1)
• ΔT is the temperature difference between the insulation surface and ambient air T_s-T_a (K)
• h_s is the insulation-to-air heat surface heat transfer coefficient (W m² K^-1)

The equation for the surface heat transfer h_s coefficient is a correlation; any other valid relationship can be substituted.

The equations are implicit - the heat transfer coefficient is a function of the surface temperature T_s, but the surface temperature is a function of the heat transfer coefficient. 

Hence the equations need to be solved iteratively with Goal Seek in Excel. Simply 

• break the loop by estimating a value of T_s, 
• use this to calculate all other properties (including the heat transfer rate)
• use the heat transfer rate to backcalculate T_s
• use Goal Seek to make the two values of T_s equal by varying the estimated value of T_s (or any other parameter

You can easily modify the heat transfer equations to include more complex effects, such as effect of fouling on the pipe surface, multiple layers of different insulation, radiative losses, thick large pipe walls (which act as a heat sink) etc.

Download Excel Spreadsheet to Model Heat Loss from Insulated Pipe

TEMA Type E Heat Exchanger Design

This Excel spreadsheet helps you design a TEMA Type E heat exchanger. The spreadsheet uses the Bell-Delaware method to calculate the overall heat transfer coefficient and the shell-side pressure drop.

TEMA Type E heat exchangers are the basis of many other designs. They offer a single pass, with liquid entry and exist on opposing sides of the shell

The spreadsheet allows you to pick from a triangle, square or rotated square tube placement, and specify the precise geometry of the shell, and then calculates the shell-side pressure drop and heat transfer coefficient accordingly.

The spreadsheet contains several empirical correlations, including those to calculate the Colburn J factor (used in determining the shell-side friction factor) and the pressure drop.

In the Bell-Delaware method, the shell-side heat transfer coefficient is the ideal heat transfer coefficient for cross-flow across a tube bank, multiplied by several correction factors as follows

The correction factors adjust the ideal heat transfer coefficient for leakage effects, bundle bypass, baffle spacing, and baffle cut. The correction factors are all calculated inside the spreadsheet for your convenience. The product of all the correction factors are equal to about 0.6 for an efficiently designed heat exchanger.

The spreadsheet is easy to use. Simply enter the process parameters (i.e. flowrates, temperatures, etc) and the geometrical parameters (number of tube passes, shell dimensions etc) in the pink cells.  You will need to equalize heat transfer across the shell-side and tube-side streams by varying a process parameter (this is indicated inside the spreadsheet).

Download Excel Spreadsheet for TEMA Type E Heat Exchanger Design using Bell-Delaware

Double Pipe Heat Exchanger

This Excel spreadsheet helps you design a double pipe heat exchanger (also known as a concentric tube heat exchanger). Double pipe heat exchangers are often used in the chemical, food processing and oil & gas industries. They have a particular advantage when close temperature approaches are needed or in high pressure applications.

The spreadsheet will give you important design parameters, such as the overall heat transfer area, the length required, pressure drops, fluid velocities and much more.  The spreadsheet uses the

• Gnielinski correlation for the heat transfer coefficient of the shell side and tube side fluids (hh and hc). The Gnielinski correlation is valid for 0.5 ≤ Pr ≤ 2000 and 2300 ≤ Re ≤ 5⁶.It gives the heat transfer coefficient in terms of the friction factor, the Reynolds number and the Prandtl number.
• Filonenko correlation for the friction factor (valid for smooth pipes in turbulent flow with 10⁴ ≤ Re ≤ 10⁷).

The equations for the heat transfer coefficients, the friction factor, the length of the heat exchanger and the overall heat transfer coefficient are given below

Double Pipe Heat Exchanger Equations

• Nu is the Nusselt Number
• Re is the Reynolds Number
• f is the friction factor
• Q is the rate of heat transfer (determined from a heat balance)
• d_ic is the internal diameter of the inner pipe
• d_oc is the external diameter of the inner pipe
• kp is the thermal conductivity of the pipe material
• h_c is the heat transfer coefficient of the cold fluid (in the inner pipe)
• h_h is the heat transfer coefficient of the hot fluid (in the outer pipe)
• ΔT_LMTD is the log mean temperature difference

The Excel spreadsheet uses variable names in the formulas to help you better understand the equations. Generally, the suffixes h and c represents quantities defined for the hot and cold streams respectively (e.g. hh is the heat transfer coefficient for the hot stream, hc is the heat transfer coefficient for the cold stream)

Named variables

INSTRUCTIONS

Step 1. Enter your parameters. The spreadsheet will calculate initial values of the heat transfer coefficients, the rate of heat transfer across both fluids, and the length of the heat exchanger. Provide an initial guess for the parameter (i.e. mass flowrate) you will change in Step 2.

Specify your parameters

Step 2. Equalize heat transfer across both streams. The rate of heat transfer across the shell side and tube side fluids must be the same. You must use Goal Seek to make the difference between the two rates of heat transfer equal to zero by changing a design parameter (e.g. mass flowrates)

Goal Seek

You have now established important design parameters, such as the fluid velocities, the tube-side and shell-side pressure drops, Prandtl numbers, the length of the heat exchanger and so on. 

Intermediate Calculations and Results

This spreadsheet is completely free. If you have any comments, then please let me know. Download it from the link below, and please bookmark or share this website wherever you feel it appropriate.

Download Excel Spreadsheet to Design a Double Pipe Heat Exchanger

Dynamic Model of a Cross-Flow Heat Exchanger

Introduction
This article will develop a dynamic model of a cross-flow heat exchanger from first principles, and then discretize the governing partial differential equation with finite difference approximations.  It will then demonstrate how this equation can be implemented in Excel (or indeed any other math tool)

If you just want the Excel implementation, then click here, but I encourage you to read the rest of the article so you understand how the spreadsheet is implemented.

First Principles Modeling
Consider liquid flowing (at mass flowrate F) through a length Δx of pipe (diameter D), subject to cooling by cross-flow air (at temperature Ta and heat transfer coefficient U)

A heat balance over time Δt gives the following.

 

Dividing by Δx and Δt and simplifying gives

As Δx and Δt tend to zero, we get the following parabolic partial differential equation

Equation 1

Finite Difference Approximation

A forward difference approximation for the first of temperature with respect to time is

Equation 2

A backward difference approximation for the first of temperature with respect to space is

Equation 4

Substituting Equation 2 and 3 into Equation 1, and rearranging gives

Equation 4

We only need to know the temperature of the bar at time t (on the RHS of Equation 4) to calculate the temperature at time t + Δt (on the LHS of Equation 4).

Implementating in Excel

This is how Equation 4 will be implemented in Excel

We will now discuss the individual steps in detail.

Step 1  - Specify your parameters, including your chosen time and space step.  I've named the cells in Column C with the names in Column E.  I'll use named values when entering Equation 4.

Step 2 - Create a column and row containing your space and time steps

Step 3 - Fill in your initial conditions at time t = 0 (this will be the inlet liquid temperature as specified in the parameters).

Step 4 - Insert your boundary conditions at distance x = 0 (this will be the inlet liquid temperature - the same as the initial condition).

Step 5 - Implement Equation 4 into the first empty cell (at t = Δt and x = Δx)

Step 5 - Copy this formula to all other times and positions.  For my implementation, I go up to t = 1 and x = 0.4.

The techniques I've demonstrated above can be applied to many other challenges in science, engineering and math.  If you have any requests, then let me know.

Download the Excel 97 spreadsheet that models a Cross-Flow Heat Exchanger