 Designing a More Effective Car Radiator - Maple Help

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Designing a More Effective Car Radiator

 Introduction 1. Original & Proposed Radiator Dimensions 2.  Heat Transfer Performance of Proposed Radiator 3. Adjusting Heat Transfer Performance of Proposed Radiator 4. Export Optimized Radiator Dimensions to SolidWorks  Introduction 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.   There are several different approaches that one can take to reduce the size of automotive radiators while maintaining the current levels of heat transfer performance expected. 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.   By increasing the surface area to coolant ratio, this application shows how one can minimize the design of a radiator and still have have the same heat dissipation as that of a larger system, given a set of operating conditions. Figure 1: Components within an automotive cooling system 1. Original & Proposed Radiator Dimensions



The dimensions of our original radiator design can be extracted from the SolidWorks® drawing file (CurrentRadiatorDrawing.SLDPRT). The drawing is a scaled down version of the full radiator assembly which measures $24''×17''×1''$.  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 data directory of your Maple installation, under the subdirectory SolidWorks. 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.    2. Heat Transfer Performance of Proposed Radiator Assembly



We expect the heat transfer performance of the smaller radiator assembly to be smaller than that of the original radiator 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: $\mathrm{HeatTransferEquation}≔q=\mathrm{ϵ}\cdot \mathrm{Cmin}\cdot \mathrm{ITD}:$ The rate of conductive heat transfer $\mathrm{UniversalHeatTransferEquation}≔\frac{1}{\mathrm{UA}}=\frac{1}{\mathrm{hc}\cdot \mathrm{Ac}}+\frac{1}{\mathrm{nfha}\cdot \mathrm{Aa}}:$ The overall thermal resistance present in the system $\mathrm{ReynoldsEquation}≔\mathrm{ReynoldsNum}=\left(\frac{\mathrm{\rho }\cdot v\cdot \mathrm{D__H}}{\mathrm{\mu }}\right):$ 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 $\mathrm{NtuEquation}≔\mathrm{Ntu}=\frac{\mathrm{UA}}{\mathrm{Cmin}}:$ A dimensionless modulus that defines the number of transferred units $\mathrm{ϵNtuEquation}≔\mathrm{ϵ}=1-{ⅇ}^{-\left(\frac{\mathrm{Cmax}}{\mathrm{Cmin}}\right)\cdot \left(1-{ⅇ}^{-\mathrm{Cratio}\cdot \mathrm{Ntu}}\right)}:$ 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 $\mathrm{UA__new}$ of the smaller radiator before we can determine its heat transfer performance, $\mathrm{q__new}$.  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 $m$     $\mathrm{ft}$   



$\frac{J}{s}$    $\frac{\mathrm{Btu}}{\mathrm{minute}}$



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 $\mathrm{DetermineNumberOfFins}\left(\mathrm{q__cur}\right)$, 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 row needed to achieve threshold heat transfer performance





$\mathrm{simplify}\left(\mathrm{DetermineNumberOfFins}\left(\mathrm{q__cur}\right)\right)$ = ${\mathrm{NumFinsPerRow}}{=}{436.056}$

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         $m$   $\mathrm{ft}$  $m$  $\mathrm{ft}$  $m$   $\mathrm{ft}$   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 $\left(\mathrm{rL__SolidWorks}\right):$ $\mathrm{ft}$  $m$ Distance Between Fins $\left(\mathrm{fD__SolidWorks}\right):$ $\mathrm{ft}$  $m$  * 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