Designing a More Effective Car Radiator
The challenge: To determine the design parameters of a smaller radiator assembly capable of dissipating the same amount of heat as the original assembly.
© Maplesoft, a division of Waterloo Maple Inc., 2008

Executive Summary


The demand for more powerful engines in smaller hood spaces has created a problem of insufficient rates of heat dissipation in automotive radiators. Upwards of 33% of the energy generated by the engine through combustion is lost in heat. Insufficient heat dissipation can result in the overheating of the engine, which leads to the breakdown of lubricating oil, metal weakening of engine parts, and significant wear between engine parts. To minimize the stress on the engine as a result of heat generation, automotive radiators must be redesigned to be more compact while still maintaining high levels of heat transfer performance.
Most fourcylinder automobiles, depending on their size, have radiator cores that vary from to . We believe that we can greatly reduce the size of automotive radiators while maintaining the current levels of heat transfer performance expected. Moreover, this can be done without significant modification to the existing internal radiator structure. There are several different approaches that one can take to optimize the heat transfer performance of a smaller radiator design. These include: 1) changing the fin design, 2) increasing the core depth, 3) changing the tube type, 4) changing the flow arrangement, 5) changing the fin material, and 6) increasing the surface area to coolant ratio. The latter method was chosen for our proposed design.
To prove this hypothesis, we conducted tests on our current radiator assembly, which measures , to determine the heat transfer performance under typical operating conditions. We found our current radiator assembly to be capable of dissipating heat at a rate of . Next, using the εNtu (effectivenessNtu), we calculated the heat transfer performance of our new radiator assembly, which has a radiator length 30% smaller than the length of the current design (). As expected, the heat transfer performance decreased. However, by increasing the metaltoair surface area from 384 fins per row to 437 fins per row, we increased the heat transfer performance of our proposed design to the same level as the current design under the same operating conditions.


Introduction


Figure 1: Componets within an automotive cooling system
In an automobile, fuel and air produce power within the engine through combustion. Only a portion of the total generated power actually supplies the automobile with power  the rest is wasted in the form of exhaust and heat. If this excess heat is not removed, the engine temperature becomes too high which results in overheating and viscosity breakdown of the lubricating oil, metal weakening of the overheated engine parts, and stress between engine parts resulting in quicker wear, among other things.
A cooling system is used to remove this excess heat. Most automotive cooling systems consists of the following components: radiator, water pump, electric cooling fan, radiator pressure cap, and thermostat. Of these components, the radiator is the most prominent part of the system because it transfers heat.
As coolant travels through the engine's cylinder block, it accumulates heat. Once the coolant temperature increases above a certain threshold value, the vehicle's thermostat triggers a valve which forces the coolant to flow through the radiator.
As the coolant flows through the tubes of the radiator, heat is transferred through the fins and tube walls to the air by conduction and convection.


Problem Description


From the laws of thermodynamics, we know that heat transfer increases as we increase the surface area of the radiator assembly. That said, the demand for more powerful engines in smaller hood spaces has created a problem of insufficient rates of heat dissipation in automotive radiators. As a result, many radiators must be redesigned to be more compact while still having sufficient cooling power capabilities.
This application proposes a new design for a smaller radiator assembly. The new design is capable of dissipating the same heat as the original, given a set of operating conditions.


1. Original & Proposed Radiator Dimensions


The dimensions of our original radiator design can be extracted from the SolidWorks® drawing file (CurrentRadiatorDrawing.SDPR). The drawing is a scaled down version of the full radiator assembly which measures . For the purpose of our analysis, the dimensions obtained from CAD are scaled up to reflect the radiator's actual dimensions.
Note: This application uses a SolidWorks design diagram to extract the dimensions of the original radiator. This design file can be found in the zip file this document came in. If you have SolidWorks version 8.0 or above, save the design file, and then click the radio button below to tell Maple™ where to find the file. If you do not have SolidWorks installed on your computer, the values will be prepopulated.
Figure 2: CAD rendering of current Radiator Model

Original Radiator Model Dimensions


The table below summarizes the current radiator dimensions.
Testing this radiator design under different coolant flow and air flow conditions yielded the following graph of heat transfer performance vs. coolant flow rate at different airflow speeds.
A heat transfer performance of was obtained using a coolant volumetric flow, air volumetric flow and air velocity of respectively.
These results are summarized in the table below.

Figure 3: Heat transfer performance vs. coolant flow rate at different airflow speeds



Proposed Radiator Model Dimensions


Our proposed design has a radiator length that is 30% smaller than that of the original model. The dimensions of the radiator core (radiator length, radiator width and radiator height) can be adjusted to any dimension.
The table below summarizes the radiator dimensions for our proposed design.


Coolant and Air Property Tables


The thermal fluid properties for the coolant and air are listed in the following two tables.



2. Heat Transfer Performance of Proposed Radiator Assembly


We expect the heat transfer performance of our proposed radiator assembly to be smaller than that of the original model because we are reducing the surface area to coolant ratio. The question that we answer in this section is "How much smaller is the heat transfer performance?" If the heat transfer performance is only marginally smaller, we can take other approaches to increase the performance, for example, increase the number of fins per row, change the fin material, or change the flow arrangement.
The εNtu (effectivenessNtu) method is used to predict the heat transfer performance of our new system.
The more common equations that are typically used in heat exchange design are listed below.
Heat Exchange Equations:

Definitions:


The rate of conductive heat transfer


The overall thermal resistance present in the system


A dimensionless modulus that represents fluid flow conditions


Parameter used to equate any flow geometry to that of a round pipe


An equation used to calculate the surface coefficient of heat transfer for fluids in turbulent flow


A dimensionless modulus that relates fluid viscosity to the thermal conductivity, a low number indicates high convection


A dimensionless modulus that relates surface convection heat transfer to fluid conduction heat transfer


A dimensionless modulus that defines the number of transferred units


A mathematical expression of heat exchange effectiveness vs. the number of heat transfer units


Measure of the initial temperature difference

We must first calculate the overall heat transfer coefficient of the smaller radiator before we can determine it's heat transfer performance, .

Solve for


The Universal Heat Transfer Equation is defined in (1)
 (1) 
The next several steps will take us through the process for solving for the unknown values of and

Solve for &


where


Figure 4: Expanded view of tubes

Figure 5: Expanded view of fins

Solving the unknown values leads to the following values for the , , and .
 (2) 
 (3) 
 (4) 
 (5) 


Solve for


The value of hc depends on the physical and thermal fluid properties, fluid velocity and fluid geometry.
The ReynoldsEquation defined below can be used to determine the flow characteristics of the coolant as it passes through the tubes.
 (6) 
The value is found from the HydraulicDiameter equation:
 (7) 
where
 (8) 
 (9) 
 (10) 
The velocity of the coolant as it flows through the tubes is:
 (11) 
 (12) 
For fluids that are in turbulent flow (that is, ReynoldsNum ), we can use the DittusBoelterEquation to relate the ReynoldsNum wwith the NusseltNum. The NusseltNum is dependent upon the fluid flow conditions and can generally be correlated with the ReynoldsNum. Solving for the NusseltNum will enable us to determine the value of hc.
 (13) 
 (14) 
 (15) 
 (16) 
 (17) 
Knowing the NusseltNumber we can now solve for
 (18) 


Determine


We solve for in a similar manner as we did for (by determining the ReynoldsNum for air)
 (19) 
 (20) 
 (21) 
 (22) 
The ReynoldsNum for air indicates that the air flow is laminar  LaminarFlow). As a result, we cannot use the DittusBoelterEquation to relate the ReynoldsNum to the NusseltNum and hence determine the value for . Another approach to determining the value of is to solve for the value of since the value of . In the next section, we will show how the value of is calculated by first obtaining the heat transfer coefficient for the original radiator .

Solve for


The equation, which relates Number of Transferred Units to Universal Heat Transfer, will be used to determine the Universal Heat Transfer Coefficient of the current model.
 (23) 
is obtained by comparing the thermal capacity rate for the coolant and air.
 (24) 
The Mass Flow Rate for the coolant and air are:
 (25) 
 (26) 
The Thermal Capacity Rates for the coolant and air are:
 (27) 
 (28) 
Since
 (29) 
and
 (30) 
Next, we need to calculate the Number of Transfer Units of the original radiator assembly. To do this we for , and from the , and, respectively.
 (31) 
=
 (32) 
=
Using the , the value of can be found.
 (33) 
 (34) 
=
We can finally solve for by substituting the values of and in to the
 (35) 
=
Now that we have the value of , we can use the to determine the value for , which is equal to the value of .
Solving for the unknown values of and yields the following:
 (36) 
 (37) 
 (38) 
Finally at this point we can solve for the value of by substituting the values for , and into the
 (39) 
 (40) 

Since the value of is the same for both the original and proposed radiator models we can determine the value of directly from the value of
 (41) 



Solve for


We can determine the heat transfer performance of the new radiator assembly by using the
 (42) 
We can determine the value of from the .
 (43) 
The unknown value for can be determined using the
 (44) 
Finally the value of can be determined from the
 (45) 
Solving for , and yields the following:
=
=
=
The heat transfer performance of our smaller radiator design can be found by substituting the value of value of and into the
 (46) 
As expected the heat transfer performance of our proposed radiator design is smaller than that of the original.
 (47) 



3. Adjusting Heat Transfer Performance of Proposed Radiator Design



Effects of Radiator Length on Heat Transfer Performance


The effects of radiator length on heat transfer performance (while keeping all other parameters the same as in the proposed design) can be examined by changing the adjacent dial.
The heat transfer performance values for four different radiator lengths are summarized in the table below.

Radiator Length vs. Heat Transfer Performance


From the table, we can confirm our hypothesis that changing radiator length alone will not be sufficient to generated the desired heat transfer performance. As mentioned in the previous section, there are several methods available to increase the heat transfer performance of a radiator assembly. For our proposed design, we have chosen to increase the metaltoair surface area by increasing the number of fins per row.


Effects of Surface Area on Heat Transfer Performance


To achieve a heat transfer performance for our proposed design equal to that of the current design ( that is), we must increase the number of fins per row. The procedure called , defined within the Code Edit Region, calculates the number of fins per row needed to achieve the desired heat transfer performance for our assembly.
Calculate number of fins per r
=
Thus, the number of fins per row must be increased from 384 to 437 to achieve a heat transfer performance of . The graph in Figure 6 shows the effects of changing the number of fins per row on the heat transfer performance for our smaller radiator design.
Figure 6: Effects of surface area on heat transfer performance
The application below allows you to compare the effects of changing the number of fins per row on the heat transfer performance for two different radiator lengths based on a given reference radiator length. The two different radiator lengths can be defined in the terms of the percent or absolute change of the reference.



4. Export Optimized Radiator Dimensions to SolidWorks


We can create a CAD rendering of our smaller radiator assembly. The design parameters of our new design are the same as the original, except it is smaller in length and has more fins per row.
The parameters of our new radiator model are listed in the table below. It is important to note that the number of fins per row is actually a measure of the distance between the fins (that is, how the fins are spread out within a row).
* Note: For consistency, we are creating a scaled CAD rendering model of the new optimized radiator assembly similar to that of the original CAD rendering


Results


In this worksheet, we proposed the design of a new smaller radiator assembly that is capable of the same heat dissipation as the current design.
Using the effectivnessNtu method, we calculated the heat transfer performance of the proposed design. As expected, decreasing the radiator length by 30% caused the heat transfer performance to decrease; the heat transfer performance decreased by ~14%. That said, by increasing the number of fins per row, from 384 to 437, we increased the heat transfer performance back to its original level of .

Legal Notice: The copyright for this application is owned by Maplesoft. Maplesoft is not responsible for any errors contained within and is not liable for any damages resulting from the use of this material.
