engine radiator calculator

Designing a More Effective Car RadiatorThe 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 Introduction Problem Definition 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 Results www.maplesoft.com/appsbriefs 1 of 25 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 four-cylinder automobiles, depending on their size, have radiator cores that vary from 19''# 11.5''# 0.7'' to 27''# 17''# 0.9''. 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 24''# 17''# 1'', to determine the heat transfer performance under typical operating conditions. We found our Btu J current radiator assembly to be capable of dissipating heat at a rate of 4025 70729 . Next, minute s using the ε-Ntu (effectiveness-Ntu), 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 (18''# 17''# 1''). As expected, the heat transfer performance decreased. However, by increasing the metal-to-air 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. www.maplesoft.com/appsbriefs 2 of 25 For the purpose of our analysis. A cooling system is used to remove this excess heat. That said. Problem Description From the laws of thermodynamics. the dimensions obtained from CAD are scaled up www. heat is transferred through the fins and tube walls to the air by conduction and convection. many radiators must be redesigned to be more compact while still having sufficient cooling power capabilities. the radiator is the most prominent part of the system because it transfers heat. The new design is capable of dissipating the same heat as the original. the engine temperature becomes too high which results in overheating and viscosity breakdown of the lubricating oil. electric cooling fan. This application proposes a new design for a smaller radiator assembly. and thermostat. it accumulates heat. metal weakening of the overheated engine parts. fuel and air produce power within the engine through combustion. 1.com/appsbriefs 3 of 25 . and stress between engine parts resulting in quicker wear.SDPR). we know that heat transfer increases as we increase the surface area of the radiator assembly. As a result. Original & Proposed Radiator Dimensions The dimensions of our original radiator design can be extracted from the SolidWorks® drawing file (CurrentRadiatorDrawing. If this excess heat is not removed. Of these components. Most automotive cooling systems consists of the following components: radiator. water pump. The drawing is a scaled down version of the full radiator assembly which measures 24''# 17''# 1''. As the coolant flows through the tubes of the radiator. the demand for more powerful engines in smaller hood spaces has created a problem of insufficient rates of heat dissipation in automotive radiators. given a set of operating conditions. radiator pressure cap. 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. Figure 1: Componets within an automotive cooling system As coolant travels through the engine's cylinder block.Introduction In an automobile. Once the coolant temperature increases above a certain threshold value. among other things.maplesoft. the vehicle's thermostat triggers a valve which forces the coolant to flow through the radiator. Figure 2: CAD rendering of current Radiator Model Original Radiator Model Dimensions The table below summarizes the current radiator dimensions. save the design file. Current Radiator Dimensions Radiator length rLcur : ft 0. If you have SolidWorks version 8. Note: This application uses a SolidWorks design diagram to extract the dimensions of the original radiator. the values will be pre-populated. This design file can be found in the zip file this document came in. If you do not have SolidWorks installed on your computer.609600 Radiator width m ft m rWcur : 1.com/appsbriefs 4 of 25 .431771 www.maplesoft. and then click the radio button below to tell Maple™ where to find the file.to reflect the radiator's actual dimensions.0 or above.41657 0. coolant flow rate at different airflow speeds.0246063 ft m ft m ft m ft m ft m ft m ft m Tube width tWcur : 0.0807292 0.0246063 Tube height tHcur : 0.0118813 Fin thickness fTcur : 0.0389808 0.00008333 0.0807292 0.00520833 0.com/appsbriefs 5 of 25 .00158750 Number of tubes ntubecur : 33. www.00512667 0.Radiator height rHcur : 0. Testing this radiator design under different coolant flow and air flow conditions yielded the following graph of heat transfer performance vs.maplesoft.00002540 Distance Between Fins fDcur : 0.0807292 0.00156261 Fin width fWcur : 0.0246063 Fin height fHcur : 0. Figure 3: Heat transfer performance vs. coolant flow rate at different airflow speeds Radiator Operating Conditions Coolant Volumetric Flow vfc 30 0. 2349 ft3 mi .com/appsbriefs 6 of 25 .10860 Air Velocity va 10 4.A heat transfer performance of 4025 Btu was minute obtained using a coolant volumetric flow.4704 Heat Transfer Performance qcur 4025 70729. minute h These results are summarized in the table below.maplesoft. air volumetric flow and air velocity of 30 gpm.0018927 gpm m3 s ft3 minute m3 s mi h m s Btu minute J s Air Volumetric Flow vfa 2349 1.3 www. respectively. 10 . 41657 0.0389808 0.maplesoft. radiator width and radiator height) can be adjusted to any dimension.0807292 0.com/appsbriefs 7 of 25 .0246063 Tube height m ft m ft m ft m tHnew : 0.0246063 Tube width tWnew : 0. The dimensions of the radiator core (radiator length.00512667 0.0118813 www.00156261 Fin width fWnew : 0.0246063 Fin height fHnew : 0.Proposed Radiator Model Dimensions Our proposed design has a radiator length that is 30% smaller than that of the original model.50000 0. Proposed Radiator Dimensions Radiator length rLnew : 1.457200 ft m ft m ft m ft Radiator width rWnew : 1.0807292 0. The table below summarizes the radiator dimensions for our proposed design.431771 Radiator height rHnew : 0. Coolant and Air Property Tables The thermal fluid properties for the coolant and air are listed in the following two tables.889 www.57 Dynamic Viscosity µc : 0.415098 Btu h$ft$degF W m$K Btu lb$degF J kg$K lb ft3 kg m3 lb ft$s Pa$s degF K Specific Heat Cc : 0.88 3681.Fin thickness fTnew : 0.00008333 0.000744082 Coolant Temperature Tc : 250 138.com/appsbriefs 8 of 25 .24 0.maplesoft.00158750 Number of tubes ntubenew : 33.92 Density ρc : 63.0005 0. Coolant Properties: 50-50 Glycol-Water Thermal conductivity kc : 0.4 1015.00002540 ft m ft m Distance Between Fins fDnew : 0.00520833 0. 00001285 0.071 1.Air Properties: Thermal conductivity ka : 0.0154 0.13731 Dynamic Viscosity µa : 0.16 Density ρa : 0.3333 www.com/appsbriefs 9 of 25 .0266355 Btu h$ft$degF W m$K Btu lb$degF J kg$K lb ft3 kg 3 m lb ft$s Pa$s degF K Specific Heat Ca : 0.00001912 Coolant Temperature Ta : 150 83.maplesoft.240 1004. 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. Heat Exchange Equations: HeatTransferEquation d q = ε$Cmin$ITD : UniversalHeatTransferEquation d C 1 : nfha$Aa ρ$v$DH µ 1 1 = UA hc$Ac Definitions: The rate of conductive heat transfer The overall thermal resistance present in the system ReynoldsEquation d ReynoldsNum = HydraulicDiameter d DH = 4$Amin : WP 1 3 : 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 DittusBoelterEquation d NusseltNum = 0.023 $ReynoldsNum0. increase the number of fins per row. The question that we answer in this section is "How much smaller is the heat transfer performance?" If the heat transfer performance is only marginally smaller. The more common equations that are typically used in heat exchange design are listed below.2. we can take other approaches to increase the performance.maplesoft. The ε-Ntu (effectiveness-Ntu) method is used to predict the heat transfer performance of our new system. Heat Transfer Performance of Proposed Radiator Assembly We expect the heat transfer performance of our proposed radiator assembly to be smaller than that of the original model because we are reducing the surface area to coolant ratio. the number of heat transfer units NusseltEquation d NusseltNum = UA : Cmin K : NtuEquation d Ntu = εNtuEquation d ε = 1 K e Cmax Cratio$Ntu $ 1 K eK Cmin : www. change the fin material. for example. or change the flow arrangement.com/appsbriefs 10 of 25 .8$PrandtlNum : C$µ : k hc$DH k PrandtlEquation d PrandtlNum = A dimensionless modulus that relates fluid viscosity to the thermal conductivity. com/appsbriefs 11 of 25 . Solve for UAnew The Universal Heat Transfer Equation is defined in (1) UniversalHeatTransferEquation 1 1 1 = C UA hc Ac nfha Aa The next several steps will take us through the process for solving for the unknown values of Ac. hc and nfha (1) Solve for Ac new & Aa new CoolantSurfaceArea d Ac = NumberOfTubes$ 2$ TubeHeight$RadiatorLength C 2 $ TubeWidth$RadiatorLength : AirSurfaceArea d Aa = TotalNumberOfAirPassages$ 2$ FinDistance$FinHeight C 2 $ FinHeight$FinWidth : where TotNumAirPassages d TotalNumberOfAirPassages = NumRowsOfFins RadiatorLength $ : FinDistance www. qnew.maplesoft. Aa.ITDEquation d ITD = CoolantTemperature KAirTemperature : Measure of the initial temperature difference We must first calculate the overall heat transfer coefficient UAnew of the smaller radiator before we can determine it's heat transfer performance. Aa 61. FinHeight = fHnew. AirSurfaceArea . The ReynoldsEquation defined below can be used to determine the flow characteristics of the coolant as it passes through the tubes. Ac. and Aa. FinDistance = fDnew . 70.Figure 4: Expanded view of tubes Figure 5: Expanded view of fins Solving the unknown values leads to the following values for the TotalNumberOfAirPassages.maplesoft. Acnew d simplify solve subs TubeHeight = tHnew. RadiatorLength = rLnew. fluid velocity and fluid geometry. RadiatorLength = rLnew. FinDistance = fDnew. FinWidth = fWnew . Ac 8. TotalNumberOfAirPassages 9216.49968 ft2 Aanew d simplify solve subs TotalNumberOfAirPassages = TotalNumberOfAirPassagesnew. www.2453 ft2 ft2 (2) (3) (4) (5) Solve for hc new The value of hc depends on the physical and thermal fluid properties. CoolantSurfaceArea .com/appsbriefs 12 of 25 . TotNumAirPassages . TotalNumberOfAirPassagesnew d simplify solve subs NumRowsOfFins = ntubenew K 1 . NumberOfTubes = ntubenew. TubeWidth = tWnew.7456 Atotalnew d simplify Acnew C Aanew . 0. µ = µc . DittusBoelterEquation NusseltNum = 0.023 ReynoldsNum0.000413872 WPc d 2$ simplify tWnew C tHnew . DH 0. WP = WPc . ReynoldsNum O 5000 ).171712 ft DHc d simplify solve subs Amin = Aminc.8 PrandtlNum1/3 PrandtlEquation Cµ PrandtlNum = k NusseltEquation hc DH NusseltNum = k www.00964108 ft The velocity of the coolant as it flows through the tubes is: ft 2 (8) (9) (10) vc d simplify vfc ntubenew$Aminc 4. ρ = ρc. we can use the DittusBoelterEquation to relate the ReynoldsNum wwith the NusseltNum.ReynoldsEquation ReynoldsNum = ρ v DH µ The value DH is found from the HydraulicDiameter equation: (6) HydraulicDiameter DH = where 4 Amin WP (7) Aminc d simplify tWnew$tHnew . Solving for the NusseltNum will enable us to determine the value of hc. ReynoldsEquation . The NusseltNum is dependent upon the fluid flow conditions and can generally be correlated with the ReynoldsNum. 0. HydraulicDiameter .maplesoft. (12) 5982.89391 ft s (11) ReynoldsNumc d simplify solve subs ReynoldsNum DH = DHc.76 For fluids that are in turbulent flow (that is. v = vc.com/appsbriefs (13) (14) (15) 13 of 25 . maplesoft.59999 (16) NusseltNumc d solve subs ReynoldsNum = ReynoldsNumc. we will show how the value of hacur is calculated by first obtaining the heat transfer coefficient for the original radiator UAcur . As a result. 6.000203025 WPa d 2$ simplify fDnew C 8$fDnew 0. ρ = ρa.PrandtlNumc d simplify solve subs PrandtlNum C = Cc. v = va. (22) is. NusseltNum 45.3346 Knowing the NusseltNumber we can now solve for hcnew (17) hcnew d simplify solve subs NusseltEquation . µ = µc. ReynoldsEquation .00866240 ft ReynoldsNuma d simplify solve subs ReynoldsNum 701. DH 0.984 The ReynoldsNum for air indicates that the air flow is laminar (that ft2 (19) (20) (21) DH = DHa. NusseltNum = NusseltNumc .com/appsbriefs 14 of 25 . 1128. In the next section.53 Btu h ft2 degF (18) Determine nfhanew We solve for hanew in a similar manner as we did for hcnew (by determining the ReynoldsNum for air) Amina d simplify fHnew$fDnew 0. DH = DHc. www. k = kc . ReynoldsNuma ! 2100 -- LaminarFlow). Another approach to determining the value of hanew is to solve for the value of hacur since the value of hanew = hacur. we cannot use the DittusBoelterEquation to relate the ReynoldsNum to the NusseltNum and hence determine the value for hanew. µ = µa .0937500 ft DHa d simplify solve subs Amin = Amina. HydraulicDiameter . DittusBoelterEquation . PrandtlEquation . hc k = kc. PrandtlNum = PrandtlNumc . WP = WPa . ThermalCapacityRate .748 Since CRa ! CRc : (28) Cmincur d CRa. 40. which relates Number of Transferred Units used to determine the Universal Heat Transfer Coefficient Ntu to Universal Heat Transfer. mfr lb s FluidViscosity = vfc. CR 40. Cmaxcur d CRc. MassFlowRate d mfr = FluidViscosity$ρ. C = Ca .748 and Btu min degF Btu min degF (29) www. ρ = ρc .Solve for nfha cur The equation. ThermalCapacityRate . will be UAcur of the current model.77964 4. mfr 2.0268 223. CR = C mfr mfr = FluidViscosity ρ The Mass Flow Rate for the coolant and air are: (24) mfa d simplify solve subs FluidViscosity = vfa. ThermalCapacityRate d CR = C$mfr. MassFlowRate .com/appsbriefs 15 of 25 . C = Cc . MassFlowRate .0268 Btu min degF mfr = mfc.23765 lb s (26) mfc d simplify solve subs The Thermal Capacity Rates for the coolant and air are: CRa d simplify solve subs mfr = mfa.maplesoft. CR Btu min degF (27) CRc d simplify solve subs 223. ρ = ρa . NtuEquation Ntu = UA Cmin (23) Cmin is obtained by comparing the thermal capacity rate CR for the coolant and air. UA = Btu 49. ε and qcur from the εNtuEquation HeatTransferEquation.178892 (30) Ntu of the original radiator assembly. Ntu NtuEquation Ntu = UA Cmin (35) UAcur d solve subs Ntu = Ntucur. we can use the UniversalHeatTransferEquation to www. HeatTransferEquation q = ε Cmin ITD (33) (34) Ntucur d solve subs = 1. ε = εcur . εNtuEquation . Cmin = Cmincur. ε = 0.Cratiocur d CRa CRc 0. Cmin = Cmincur.com/appsbriefs 16 of 25 . ITD = ITDvalue . Cmin = Cmincur. NtuEquation . respectively. and cur Next. ITDEquation ITD = CoolantTemperature K AirTemperature ITDvalue d simplify evalf Tc K Ta = 150. q = qcur . we need to calculate the Number of Transfer Units ITDEquation.670384 Using the HeatTransferEquation the value of Ntucurcan be found. degF (31) εNtuEquation K ε = 1 Ke εcur d simplify solve subs Cratio Ntu Cmax 1 K eK Cmin (32) q = qcur. HeatTransferEquation . To do this we for ITDcur.5199 min degF Now that we have the value of UAcur. Cratio = Cratiocur.23717 We can finally solve for UAcur by substituting the values of Ntucur and Cmin in to the NtuEquation Cmax = Cmaxcur.maplesoft. Aa = Aacur . Aa 82. nfha 47. Solving for the unknown values of Aacur and Accur yields the following: TotalNumberOfAirPassagescur d simplify solve subs NumRowsOfFins = ntubecur K 1 .maplesoft. FinWidth = fWcur .determine the value for nfhacur. FinDistance = fDcur. TotNumAirPassages . TubeWidth = tWcur. FinDistance = fDcur . FinHeight = fHcur. NumberOfTubes = ntubecur.com/appsbriefs 17 of 25 . CoolantSurfaceArea .3274 ft2 (37) Accur d simplify solve subs TubeHeight = tHcur.0113 Btu h ft2 degF (41) www. TotalNumberOfAirPassages 12288. (36) Aacur d simplify solve subs TotalNumberOfAirPassages = TotalNumberOfAirPassagescur.0113 Btu h ft2 degF (39) (40) Since the value of nf is the same for both the original and proposed radiator models we can determine the value of nfhanew directly from the value of nfhacur nfhanew d nfhacur 47. AirSurfaceArea . UniversalHeatTransferEquation . RadiatorLength = rLcur. which is equal to the value of nfhanew.3329 ft 2 (38) Finally at this point we can solve for the value of nfhacur by substituting the values for Aacur Accur. Ac 11. and UAcur into the UniversalHeatTransferEquation : UniversalHeatTransferEquation 1 1 1 = C UA hc Ac nfha Aa nfhacur d simplify solve subs UA = UAcur. RadiatorLength = rLcur. hc = hcnew. Ac = Accur. NtuEquation . Ntu = Ntunew. www. (45) Ntunew.927873 Cmax = Cmaxcur. εNtuEquation . Cmin = Cmincur. UniversalHeatTransferEquation . and εnew yields the following: UAnew d simplify solve subs hc = hcnew.Solve for q new qnew of the new radiator assembly by using the We can determine the heat transfer performance HeatTransferEquation : HeatTransferEquation q = ε Cmin ITD We can determine the value of (42) εnew from the εNtuEquation. UA Btu = 37. Ntu = 0.com/appsbriefs 18 of 25 .574696 The heat transfer performance qnew of our smaller radiator design can be found by substituting the value of value of εnew and Cmin into the HeatTransferEquation : qnew d simplify solve subs ε = εnew. Cmin = Cmincur . nfha = nfhanew. Cmin = Cmincur. Aa = Aanew. Cratio Ntu Cmax 1 K eK Cmin εNtuEquation K ε = 1 Ke (43) The unknown value for Ntunew : can be determined using the NtuEquation NtuEquation Ntu = UA Cmin (44) Finally the value of UAnew can be determined from the UniversalHeatTransferEquation UniversalHeatTransferEquation 1 1 1 = C UA hc Ac nfha Aa Solving for UAnew. Cratio = Cratiocur . ITD = ITDvalue .maplesoft. Ac = Acnew . = 0.1398 min degF Ntunew d solve subs εnew d solve subs UA = UAnew. HeatTransferEquation .52 Btu min (47) www. q 3450.com/appsbriefs 19 of 25 . qdiff d simplify qcur K qnew 574.48 Btu min (46) As expected the heat transfer performance of our proposed radiator design is smaller than that of the original.maplesoft. www. As mentioned in the previous section.01 Btu min Btu min Btu min Btu min 27414. Heat Transfer Performance Radiator Length 0.50 4025.3. The heat transfer performance values for four different radiator lengths are summarized in the table below. there are several methods available to increase the heat transfer performance of a radiator assembly.5 ft 2.304800 m 0.maplesoft. we can confirm our hypothesis that changing radiator length alone will not be sufficient to generated the desired heat transfer performance.5 ft 1.9 70729.3 J s Btu minute From the table.152400 m 0.609600 m ft 4025 70729.com/appsbriefs 20 of 25 .09 3450.1 60633.457200 m 0. Radiator Length vs.7 46762. we have chosen to increase the metal-to-air surface area by increasing the number of fins per row.09 2661. For our proposed design.609600 m Heat Transfer Performance 1560.5 J s J s J s J s 0.0 ft 0. 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.0 ft 1. com/appsbriefs 21 of 25 . The two different radiator lengths can be defined in the terms of the percent or absolute change of the reference.maplesoft. calculates the number of is.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 Btu J z 70729. we must increase the number of fins per row. Heat Transfer Performance UnitType Heat Transfer Performance Vs. 4025 fins per row needed to achieve the desired heat transfer performance for our assembly. www. Number of Fins 4500 4000 3500 3000 2500 2000 100 437 300 500 700 Number of Fins 1000 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.3 . the number of fins per row must be increased from 384 to 437 to achieve a heat transfer performance of 4025 Btu J z 70729.3 ). The procedure minute s called DetermineNumberOfFins qcur . The graph in Figure 6 shows the effects of changing the minute s number of fins per row on the heat transfer performance for our smaller radiator design.056 Thus. defined within the Code Edit Region. # Calculate number of fins per simplify DetermineNumberOfFins qcur = NumFinsPerRow = 436. 0 % 0.com/appsbriefs 22 of 25 .Maple Application -.Effects of heat transfer performance vs.304800 m 1 ft 1.0 100.maplesoft.21920 4 m ft www. number of fins per row for different radiator lengths Reference Radiator Length Radiator Length 1 Radiator Length 2 -1.609600 m 2 ft 0. Number of Fins 5000 4000 310 385 575 3000 2000 100 500 600 700 800 900 1000 Number of Fins Reference Radiator Length Radiator Length 1 Radiator Length 2 200 300 400 Plot Response www.Heat Transfer Performance UnitType Heat Transfer Performance Vs.maplesoft.com/appsbriefs 23 of 25 . by increasing the number of fins per row. decreasing the radiator length by 30% caused the heat transfer performance to decrease. That said. how the fins are spread out within a row).4. we proposed the design of a new smaller radiator assembly that is capable of the same heat dissipation as the current design.com/appsbriefs 24 of 25 . we increased the heat transfer performance back to its original level of 4025 Btu J 70729.457200 0.001046 Radiator Length rLSolidWorks : m m Distance Between Fins fDSolidWorks : Export Dimensions to SolidWorks Close SolidWorks Connection * Note: For consistency. the heat transfer performance decreased by ~14%. The parameters of our new radiator model are listed in the table below. Maplesoft is not responsible for any errors contained within and is not liable for any damages resulting from the use of this material. Export Radiator Dimensions to SolidWorks Number of Fins Per Row 437 0.3 . we calculated the heat transfer performance of the proposed design. It is important to note that the number of fins per row is actually a measure of the distance between the fins (that is. Export Optimized Radiator Dimensions to SolidWorks We can create a CAD rendering of our smaller radiator assembly.003432 ft 0.457200 ft 0. except it is smaller in length and has more fins per row. Using the effectivness-Ntu method. minute s Legal Notice: The copyright for this application is owned by Maplesoft. from 384 to 437. As expected. www. 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. The design parameters of our new design are the same as the original.maplesoft. www.com/appsbriefs 25 of 25 .maplesoft.