Performing calculations to compare thermal fluid efficiency improves operations. Use this method to check your system.
There are many reasons to choose a particular heat transfer fluid: operating temperature, fluid life, budget constraints, process compatibility, a need for liquid- or vapor-phase operation, availability, and so on. With so much to consider, the ability of the fluid to move energy through the system in an efficient manner - the actual purpose of a heat transfer fluid - is overlooked surprisingly often.
One useful method is to compare the relative heat transfer coefficient in a stated condition. A fluid’s relative heat transfer coefficient is calculated from the density, viscosity, thermal conductivity and specific heat at a determined flow velocity and pipe diameter. These variables typically are known and the calculation is a simple and reliable comparison between heat transfer fluids. This is important because, at a given temperature, the relative heat transfer coefficients of different fluids vary as much as 30 percent, considerably impacting system performance.
Depending on the system design and thermal resistance factors of system components, a fluid with a substantial relative heat transfer coefficient advantage may allow a reduction in sizing of system equipment. Replacing existing heat transfer fluids with a more efficient fluid may significantly increase production output or reduce energy costs.
Setting Up the Calculations
When there is a motion of fluid with respect to a surface, the transport of heat is commonly referred to as convection. This energy transfer between a solid surface at one temperature and an adjacent moving liquid at another temperature is the basis of the calculation. When an external force, such as a pump, generates motion of flow, this is called forced convection. If it is driven by gravity forces due to temperature gradients, this is referred to as natural or free convection.
The heat transfer coefficient is generally defined by the equation:
h is the heat transfer coefficient.
ΔQ is the total heat transfer.
A is the heat transfer surface area.
ΔT is the difference in temperature between the solid surface and surrounding fluid area.
Because heat transfer systems are not as simple as one uniform surface area, a more comprehensive calculation is required to account for a typical forced convection heat transfer system.
Dittus–Boelter Correlation. The Dittus–Boelter heat transfer correlation is appropriate for fluids in turbulent flow inside pipes. This correlation is only effective if the following conditions are met:
Forced convection is the only mode of heat transfer.
The Reynolds number is between 10,000 and 120,000 for a liquid flowing in a straight circular pipe.
The Prandtl number is between 0.7 and 120.
The location of calculation is far from the pipe entrance or other flow disturbances.
The pipe surface is hydraulically smooth.
The heat transfer coefficient between the bulk of the fluid and the pipe surface can be expressed as:
kw is the thermal conductivity of the liquid.
DH is the pipe inner diameter.
Nu is the Nusselt number.
As an example, the relative heat transfer coefficient for dibenzyltoluene (DBT), a common synthetic heat transfer fluid, is calculated at 160°F (71°C). The only value to be solved is the Nusselt number. The other variables are given by the application design and fluid specifications. However, to calculate the Nusselt number, we need to determine the Prandtl and Reynolds numbers first. (Note that for this example calculation, the standard velocity is given as 8 ft/sec and the standard pipe inner diameter is 0.17225'.)
The Prandtl Number
The Prandtl number is a dimensionless number, estimating the ratio of momentum diffusivity and thermal diffusivity. It is defined as:
Cp is the specific heat.
µ is dynamic viscosity (centipoise).
k is thermal conductivity.
For dibenzyltoluene at 160°F (71°C), the following engineering specifications are found in the published data:
Also, note the conversion:
Thus, plugging these values into the Prandtl number equation gives
Because the Prandtl number is dimensionless, units need to be converted so they cancel out.
The Reynolds Number
For flow in a pipe or tube, the Reynolds number determines if flow is laminar, transient or turbulent. A value less than 2,300 signifies laminar flow while a value above 4,000 is turbulent flow. Values in between are transient flow. It is defined as
ρ is the fluid density.
V is the fluid velocity.
DH is the pipe inner diameter.
µ is the dynamic viscosity.
The values for dibenzyltoluene at 160°F (71°C) are as follows:
Note these conversions:
1 gal = 0.134 ft3
1 hr = 3,600 sec
Using these values in the Reynolds number equation yields:
The conversion factors given above cancel all units of measure.
The Nusselt Number
The Nusselt number is defined as the ratio of convection heat transfer to fluid conduction heat transfer under the same conditions. A Nusselt number of order unity would indicate a slower, sluggish motion, e.g. laminar flow in a long pipe. The larger the number, the more efficient convection becomes. For example, turbulent pipe flow yields Nu of order 100 to 1,000. For this specific correlation, the Nusselt number is calculated as:
Pr is the Prandtl number.
Re is the Reynolds number.
n is the heating exponent. It is 0.4 for heating (wall hotter than the bulk fluid) and 0.33 for cooling (wall cooler than the bulk fluid).
With values previously calculated for the Reynolds and Prandtl number, we can solve for the Nusselt number using this equation:
Calculating the Heat Transfer Coefficient
Now we can use the Nusselt number to calculate the heat transfer coefficient.
Heat transfer fluids come in various chemical compositions, and naturally offer many distinct physical properties. Comparing the other physical properties is the next step in choosing the fluid that is best for the system design. Starting with efficiency makes the final choice clearer.
Incropera, Frank P., and David P. DeWitt. Introduction to Heat Transfer. New York: Wiley, 2002.