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# Designing a More Effective Car Radiator

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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

 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 pre-populated.

The table below summarizes the current radiator dimensions.

 Current Radiator Dimensions Radiator length Radiator width Radiator height Tube width Tube height Fin width Fin height Fin thickness Distance Between Fins Number of tubes

 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

 Radiator Operating Conditions Coolant Volumetric Flow Air Volumetric Flow Air Velocity Heat Transfer Performance

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.

 Proposed Radiator Dimensions Radiator length Radiator width Radiator height Tube width Tube height Fin width Fin height Fin thickness Distance Between Fins Number of tubes

Coolant and Air Property Tables

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

 Coolant Properties: 50-50 Glycol-Water Thermal conductivity Specific Heat Density Dynamic Viscosity Coolant Temperature

 Air Properties: Thermal conductivity Specific Heat Density Dynamic Viscosity Air Temperature

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 ε-Ntu (effectiveness-Ntu) 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)

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 metal-to-air 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.

 Maple Application -- Effects of heat transfer performance vs. number of fins per row for different radiator lengths Reference Radiator Length Radiator Length 1 Radiator Length 2

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).

 Export Radiator Dimensions to SolidWorks Number of Fins Per Row Radiator Length Distance Between Fins

* 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 effectivness-Ntu 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.