A rapid prediction method for binary inlet channel-precooler flow heat exchange in series layout

Abstract

The application discloses a kind of binary inlet duct-precooler flow heat exchange fast estimation method of series layout. With inlet duct entrance parameter and precooler structure parameter as variable, by giving the Mach number before inlet duct import and the height of incoming flow, and by giving the diameter of heat exchange pipe in precooler, pitch ratio and tube row number, etc., the estimated heat exchange amount is obtained by constantly assuming air outlet temperature through dichotomous method, compared with calculated heat exchange amount, and the air outlet temperature and temperature drop are iteratively calculated. The advantage is that without complex modeling calculation, the heat exchange effect of binary inlet duct and precooler under different import parameters can be quickly calculated, and the matching relationship of precooler with different structure parameters and binary inlet duct is obtained.

Description

Technical Field

[0001] This invention relates to a rapid prediction method for flow heat transfer in a series-connected two-dimensional intake-precooler, belonging to the field of hypersonic combined power technology. Background Technology

[0002] A single propulsion system cannot meet the requirements of hypersonic vehicles, such as a wide range of incoming flow and a wide range of altitude variations. Pre-cooled combined engines have become one of the key research areas due to their excellent performance and great potential development trend.

[0003] Currently, research on matching precoolers for two-dimensional air intakes is still in its early stages. Common computational analysis methods include experiments and modeling simulations. However, experiments are costly and difficult to study the impact of different precooler structural parameters on heat transfer performance. Furthermore, the precooler contains thousands of microtubes with diameters on the order of millimeters, and the geometric modeling, mesh generation, and subsequent computational time required for direct calculations are all prohibitively expensive from an engineering perspective.

[0004] It can be seen that there is currently a lack of analysis on the rapid heat exchange performance of binary intake ducts and precoolers, including the influence of the intake duct inlet Mach number and the heat exchange tube diameter, pitch ratio, and number of tube rows in the precooler on the heat exchange effect. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, the present invention provides a rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler configuration.

[0006] The present invention provides a rapid prediction method for flow heat transfer in a series-connected two-dimensional inlet-precooler configuration, comprising the following steps:

[0007] Step 1, based on the Mach number of the incoming flow from the two-dimensional intake duct... in Incoming airflow height H, and two-dimensional inlet capture area A inlet,in and the area A at the intake and exhaust outlet inlet,out Calculate the intake outlet temperature T. inlet,out and mass flow rate m air ;

[0008] Step 2, estimate the air outlet temperature T in the precooler. air,out According to the air inlet temperature T of the precooler air,in Estimated air heat exchange Q temp ;

[0009] Step 3: Calculate the air-side Nusselt number (Nu) using qualitative temperature. air and air-side thermal conductivity λ air Then calculate the heat transfer coefficient of the air side outside the tube bundle in the precooler;

[0010] The average temperature T of the air at the inlet and outlet of the qualitative temperature pre-cooler avg ;

[0011] Calculate the thermal conductivity λ of the coolant side by the average temperature of the coolant at the inlet and outlet respectively col , the Nusselt number Nu of the coolant side col , and then calculate the heat transfer coefficient of the coolant side inside the tube bundle in the pre-cooler;

[0012] Calculate the total heat transfer coefficient of the heat transfer tube bundle in the pre-cooler according to the heat transfer coefficient of the air side outside the tube bundle and the heat transfer coefficient of the coolant side inside the tube bundle;

[0013] Step 4, calculate the air heat transfer quantity Q flowing through the pre-cooler according to the temperature difference between the inlet and outlet of the pre-cooler air and the total heat transfer coefficient of the heat transfer tube bundle;

[0014] Step 5. Calculate the estimated air heat transfer quantity Q temp The difference from the air heat transfer quantity Q flowing through the pre-cooler;

[0015] When the ratio of the difference to the air heat transfer quantity Q flowing through the pre-cooler is less than the set threshold, the estimated air heat transfer quantity Q temp Is the obtained heat transfer quantity value;

[0016] When the ratio of the difference to the air heat transfer quantity Q flowing through the pre-cooler is greater than or equal to the set threshold, use the dichotomy iteration to re-estimate the air outlet temperature T in the pre-cooler air,out , repeat the above process 2 - 4.

[0017] Furthermore, the calculation steps of the inlet duct outlet temperature T inlet,out and the mass flow rate m air in step 1 are as follows:

[0018] (1) First, obtain the corresponding static temperature T inlet,in and static pressure P inlet,in from the ambient height in front of the inlet duct;

[0019] When the range of the oncoming flow height H is 11 km < H < 25 km

[0020]

[0021] When the oncoming flow height H > 25 km

[0022]

[0023] (2) Obtain the total temperature in and total pressure at the current height from the total static pressure relationship and the inlet Mach number Ma of the inlet duct where k is 1.4.

[0024]

[0025]

[0026] (3) The total pressure recovery coefficient σ and flow coefficient at the intake outlet are obtained using empirical formulas for the two-dimensional intake.

[0027] σ = 0.95(1-0.075(Ma) in -1) 1.35 (5)

[0028]

[0029] (4) Mach number at the intake manifold in Find the inlet flow rate function q(M) in And by using the flow field parameters at the inlet and outlet positions of the inlet, the inlet outlet flow function q(M) is obtained. out );

[0030]

[0031]

[0032] According to the following formula, the intake outlet flow rate function q(M) is known. out Find the Mach number at the intake and exhaust outlet. out ,

[0033]

[0034] (4) Calculate the intake outlet temperature T. inlet,out Intake outlet temperature T inlet,out That is, the inlet temperature T of the precooler. air,in :

[0035]

[0036] The mass flow rate m at the intake outlet can be calculated using the flow rate formula. air for:

[0037]

[0038] Furthermore, in step 2, the initial estimated air outlet temperature T in the precooler... air,out This equals the precooler air inlet temperature minus 1.

[0039] The specific heat capacity Cp is obtained through the following formula.

[0040] Cp=1048.63-0.3838T+9.45576E-4T 2-5.4915E-7T 3 +7.9315E-11T 4 (11)

[0041] Estimated air heat exchange Q temp Represented as:

[0042] Q temp =m air (Cp air,in T air,in -Cp air,out T air,out (12)

[0043] Furthermore, the calculation process for the overall heat transfer coefficient of the heat exchange tube bundle in the precooler in step 3 is as follows:

[0044] Step 3.1, calculate the heat transfer coefficient h on the air side outside the tube bundle in the precooler. air ;

[0045]

[0046] Step 3.2, calculate the heat transfer coefficient h of the coolant side inside the tube bundle in the precooler. col :

[0047]

[0048] Step 3.3: Using the calculated external and internal heat transfer coefficients, the overall heat transfer coefficient is then determined.

[0049]

[0050] Compared with the prior art, the beneficial effects of the present invention are:

[0051] 1) No complex modeling calculations are required; the heat exchange effect of the two-dimensional intake duct-precooler under different inlet parameters can be quickly calculated.

[0052] 2) No complex modeling calculations are required; the heat exchange effect of the two-dimensional inlet-precooler under different precooler structural parameters can be quickly calculated. Attached Figure Description

[0053] Figure 1 This is a flowchart of a method for predicting the flow heat transfer effect of a two-dimensional intake-precooler with a series layout.

[0054] Figure 2 This is a schematic diagram of a two-dimensional intake-precooler model with a series layout;

[0055] Figure 3 This refers to the air outlet temperature drop under different Ma conditions in Specific Implementation Example 1;

[0056] Figure 4 is the temperature drop at the air outlet under different numbers of tube rows in Specific Embodiment 2.

[0057] Among them, 1. intake duct, 2. pre-cooler. Specific Embodiment

[0058] The following further describes the present invention with reference to the accompanying drawings.

[0059] A rapid prediction method for the flow heat transfer of a tandem-layout dual intake duct - pre-cooler of the present invention is applicable to the tandem layout of a dual intake duct 1 and a pre-cooler 2. As Figure 2 shown, the heat transfer effects under different oncoming flow parameters in front of the intake duct and different pre-cooler structure parameters can be obtained. As Figure 1 shown, it is realized through the following steps:

[0060] Step 1: According to the oncoming flow Mach number Ma in in front of the dual intake duct 1, the oncoming flow height H, the capture area A inlet,in at the inlet of the dual intake duct, and the area A inlet,out at the outlet of the intake duct, the flow field parameters at the outlet position of the intake duct are calculated, including the outlet temperature T inlet,out of the intake duct and the mass flow rate m air .

[0061] First, the corresponding static temperature T inlet,in and static pressure P inlet,in are calculated from the environmental height in front of the intake duct;

[0062] When the range of the oncoming flow height H is 11 km < H < 25 km

[0063]

[0064] When the oncoming flow height H > 25 km

[0065]

[0066] The total temperature in and total pressure at the current height are calculated from the total static pressure relationship and the inlet Mach number Ma of the intake duct 1, where k is 1.4.

[0067]

[0068]

[0069] The total pressure recovery coefficient σ and the flow coefficient at the outlet of the intake duct 1 are obtained through the empirical formula of the dual intake duct 1

[0070] σ = 0.95(1 - 0.075(Main -1) 1.35 (5)

[0071]

[0072] Mach number from the intake duct in Find the inlet flow rate function q(M) in And by using the flow field parameters at the inlet and outlet positions of the inlet, the inlet outlet flow function q(M) is obtained. out The flow field parameters at the inlet and outlet positions of the air intake include the total pressure recovery coefficient σ and the flow rate coefficient. and the intake capture area A inlet,in and the area A at the intake and exhaust outlet inlet,out

[0073]

[0074]

[0075] According to the following formula, the intake outlet flow rate function q(M) is known. out Find the Mach number at the intake and exhaust outlet. out ,

[0076]

[0077] The airflow path includes parameters at four cross-sectional locations: the air inlet, air outlet, precooler air inlet, and precooler air outlet. Since air inlet 1 and precooler 2 are connected in series, with the air outlet being the precooler air inlet, the aforementioned air outlet temperature T... inlet,out That is, the inlet temperature T of the precooler. air,in :

[0078] Calculate the intake outlet temperature T. inlet,out .

[0079]

[0080] The mass flow rate m at the intake outlet can be calculated using the flow rate formula. air for:

[0081]

[0082] Step 2, estimate the air outlet temperature T in precooler 2 air,out According to the air inlet temperature T of precooler 2 air,in Estimated air heat exchange Q temp ;

[0083] Given the air inlet temperature T of the precooler air,in However, the air outlet T of the precoolerair,out Given the unknown, we first assume the precooler air outlet temperature is the precooler air temperature minus 1. Using the precooler air inlet temperature and precooler air outlet temperature, we calculate the heat transfer rate Q using the heat transfer equation. temp The specific heat capacity Cp is fitted using a polynomial, where T is the temperature.

[0084] Cp=1048.63-0.3838T+9.45576E-4T 2 -5.4915E-7T 3 +7.9315E-11T 4 (11)

[0085] Q temp =m air (Cp air,in T air,in -Cp air,out T air,out (12)

[0086] Where E represents scientific notation, expressed as the precooler air inlet temperature T. air,in and outlet temperature T air,out Substituting into formula (11) respectively, we can calculate Cp. air,in and Cp air,out .

[0087] Step 3: Calculate the overall heat transfer coefficient of the heat exchange tube bundle in precooler 2.

[0088] The precooler 2 consists of a low-temperature heat exchange tube bundle. Air flows outside the tube bundle, and coolant flows inside. The tube bundle is circular and is used to cool the high-temperature air captured by the intake duct 1. The overall heat transfer coefficient is calculated from the heat transfer coefficients of the air side outside the tube bundle and the coolant side inside the tube bundle, specifically including the following calculation process:

[0089] Step 3.1: Calculate the heat transfer coefficient on the air side outside the tube bundle in precooler 2;

[0090] Calculate relevant parameters of the external air of the tube bundle using qualitative temperature, including the air-side dynamic viscosity μ. air Air-side thermal conductivity λ air Air-side Reynolds number Re air Airside Prandtl number Pr air Nusselt number on the air side air Heat transfer coefficient h on the air side air The air qualitative temperature is determined by the average inlet and outlet temperature T of the air in precooler 2. avg :

[0091]

[0092] (1) Air-side dynamic viscosity μair :

[0093]

[0094] The dynamic viscosity was calculated using the Sutherland formula, where T0 is 273.11 and B is 110.56.

[0095] (2) Thermal conductivity λ on the air side air :

[0096]

[0097] The thermal conductivity was calculated using kinetic-theory, where R is the gas constant and M is the molar mass of air.

[0098] (3) Air-side Reynolds number Re air :

[0099]

[0100] The value in parentheses is the product of the characteristic velocity and density of the tube bundle, and d is the outer diameter of the circular tube in the heat exchange tube bundle.

[0101] (4) Prandtl number on the air side Pr air :

[0102]

[0103] (5) Nusselt number on the air side air :

[0104]

[0105] Where P T and P L These represent the transverse pitch ratio perpendicular to the incoming air and the longitudinal pitch ratio parallel to the incoming air direction of the heat exchange tube bundle in precooler 2, respectively. The Nusselt number adopts the Zukauskas empirical formula, and there are different applicable formulas for different Reynolds numbers. The above formula is applicable when Re>1000.

[0106] (6) Air-side heat transfer coefficient h air :

[0107]

[0108] Step 3.2: Calculate the heat transfer coefficient of the coolant side inside the tube bundle in precooler 2.

[0109] First, the structural parameters of precooler 2 are given, including the number of transverse tube rows m, the number of longitudinal tube rows n, the tube diameter d, the pitch ratio, etc., and the number of transverse tube rows m and the transverse pitch ratio P.T Due to the influence of the width of the intake duct 1, the product of the two cannot be greater than the width of the intake duct 1; in addition, since the tube bundle is arranged in an S-shape, with 5 rows of horizontal tubes as the inlet and 5 rows of horizontal tubes as the outlet, the number of longitudinal tube rows n should be an even multiple of 5, such as 10, 20, 30, etc.

[0110] Next, the type of coolant is selected, including liquid hydrogen or liquid helium, given the coolant inlet temperature T. col,in and flow m col Calculate the coolant inlet area A. col Import speed v col and coolant outlet temperature T col,out .

[0111]

[0112]

[0113] In the formula d i ρ is the inner diameter of the tube bundle. col Cp is the density of the coolant. col It is calculated using formula (22).

[0114] Then, the physical properties of the coolant are calculated based on the average temperatures of the coolant inlet and outlet. Taking liquid hydrogen as an example, the basic physical properties are obtained by polynomial fitting.

[0115] (1) Coolant specific heat capacity Cp col :

[0116] Cp col =9125.03 + 38.02T - 0.09541T 2 +1.01E-4T 3 -3.81E-8T 4 (twenty two)

[0117] In the formula, T is the average temperature of the coolant inlet and outlet;

[0118] (2) Thermal conductivity λ of the coolant side col :

[0119] λ col =0.01283+7.13318E-4T-4.99E-7T 2 +2.367E-10T 3 (twenty three)

[0120] (3) Coolant side dynamic viscosity μ col :

[0121] μ col=1.717E-6+2.786E-8T-1.42E-11T 2 +5.435E-15T 3 (twenty four)

[0122] (4) Reynolds number on the coolant side col :

[0123]

[0124] (5) Prandtl number Pr on the coolant side col :

[0125]

[0126] (6) Coolant-side Nusselt number Nu col :

[0127] Nu col =0.023Re col 0.8 Pr col 0.4 (27)

[0128] (7) Coolant side heat transfer coefficient h col :

[0129]

[0130] Step 3.3: Using the external and internal heat transfer coefficients obtained above, the overall heat transfer coefficient is then calculated.

[0131]

[0132] Because the tube wall is very thin, typically only about 0.1 mm, the wall thermal resistance R w It can be ignored;

[0133] Step 4: Calculation of heat exchange of air flowing through precooler 2

[0134] The heat exchange area A of precooler 2 can be obtained from the structural parameters of precooler 2 as follows:

[0135] A=mnπdL (30)

[0136] In the formula, L is the tube bundle length, which is determined by the intake outlet height and the installation angle.

[0137] The temperature difference between the air inlet and outlet of the precooler was calculated using the logarithmic mean temperature difference, and the PR method was used to correct the temperature difference.

[0138] △T m =φ△T lm (31)

[0139]

[0140]

[0141]

[0142] The heat exchange rate Q of the air flowing through the precooler can be calculated by combining the above formula:

[0143] Q = KA△T m (35)

[0144] The parameters K, A and ΔT are calculated by formulas (29), (30) and (31-34) respectively.

[0145] Step 5, calculate the estimated air heat exchange Q temp The difference between the heat exchanged by the air flowing through precooler 2 and the heat exchanged by the air flowing through precooler 2, Q, is considered to be converged when the ratio of the difference to Q is less than 0.001, and the heat exchange value is obtained. At this time, the air outlet temperature T in precooler 2 is... air,out The corresponding temperature is the air outlet temperature, and the corresponding temperature drop can be obtained. When the ratio of the difference to the heat exchange Q of the air flowing through the precooler 2 is greater than or equal to the set value of 0.001, the binary method is used for iteration, and the outlet temperature is changed to repeat the above process 2-4.

[0146]

[0147]

[0148] The present invention will now be further described based on specific examples:

[0149] Example 1

[0150] The incoming airflow altitude is set at 25km, and the capture area of ​​intake 1 is set at 7500mm. 2 The intake duct outlet area is set at 3750mm. 2 In precooler 2, the tube bundle diameter is set to 2mm, the transverse pitch ratio to 2.5, the longitudinal pitch ratio to 1.5, the number of longitudinal tube rows to 30, liquid hydrogen is used as the coolant, the coolant-to-air flow ratio is set to 0.6, the coolant inlet temperature is set to 125K, and the incoming Mach numbers are set to 2, 3, 4, 5, and 6 respectively. The calculated air temperature drop at different Mach numbers is shown in the attached figure. Figure 3 As shown.

[0151] Example 2

[0152] The incoming Mach number is set to 6, the incoming height is set to 25 km, and the capture area of ​​inlet 1 is set to 7500 mm². 2The intake duct outlet area is set at 3750mm. 2 In precooler 2, the tube bundle diameter is set to 2mm, the transverse pitch ratio to 2.5, the longitudinal pitch ratio to 1.5, liquid hydrogen is used as the coolant, the coolant-to-air flow ratio is set to 0.6, the coolant inlet temperature is set to 125K, and the number of longitudinal tube rows is set to 10, 20, 30, and 40 respectively. The calculated air temperature drop for different numbers of tube rows is shown in the attached figure. Figure 4 As shown.

[0153] Furthermore, this invention can also be designed with other incoming flow parameters and structural parameters. For example, the incoming flow Mach number can be set to 4.5, the incoming flow height to 22, the tube bundle diameter to 1 mm, and the number of tube rows to 25, etc. The above embodiments are only used to explain this invention and should not be considered as limiting it. Therefore, all embodiments with the same design concept as this invention are within the protection scope of this invention.

[0154] The parts of this invention not described in detail are techniques known to those skilled in the art.

Claims

1. A rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler configuration, characterized in that, It includes the following steps: Step 1, based on the Mach number of the incoming flow from the two-dimensional intake duct... in Incoming airflow height H, and the two-dimensional intake duct inlet capture area A inlet,in and the area A at the intake and exhaust outlet inlet,out Calculate the intake outlet temperature T. inlet,out and mass flow rate m air ; Step 2, estimate the air outlet temperature T in the precooler. air,out According to the air inlet temperature T of the precooler air,in Estimated air heat exchange Q temp ; Step 3: Calculate the air-side Nusselt number (Nu) using qualitative temperature. air and air-side thermal conductivity λ air Then calculate the heat transfer coefficient of the air side outside the tube bundle in the precooler; The average air inlet and outlet temperature T in the qualitative temperature precooler avg ; The thermal conductivity λ of the coolant side is calculated based on the average temperatures of the coolant inlet and outlet. col Nusselt number on the coolant side col Then calculate the heat transfer coefficient of the coolant side inside the tube bundle in the precooler; Calculate the total heat transfer coefficient of the heat exchange tubes in the pre-cooler based on the heat transfer coefficient on the air side outside the tube bundle and the heat transfer coefficient on the coolant side inside the tube bundle; Step 4, calculate the heat transfer amount Q of the air flowing through the pre-cooler based on the temperature difference between the inlet and outlet of the air in the pre-cooler and the total heat transfer coefficient of the heat exchange tubes; Step 5: Calculate the estimated air heat exchange Q temp The difference between the heat exchanged with the air flowing through the precooler and Q, When the ratio of the difference to the heat exchange capacity Q of the air flowing through the precooler is less than a set threshold, the estimated heat exchange capacity Q is... temp This means obtaining the heat exchange value; When the ratio of the difference to the heat exchange capacity Q of the air flowing through the precooler is greater than or equal to a set threshold, the bisection method is used iteratively to re-estimate the air outlet temperature T in the precooler. air,out Repeat steps 2-4 above.

2. The rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler according to claim 1, characterized in that, Intake outlet temperature T inlet,out and mass flow rate m air The calculation steps are as follows: (1) First, the corresponding static temperature T is calculated from the ambient height in front of the air intake. inlet,in and static pressure P inlet,in ; When the range of the oncoming flow height H is 11 km < H < 25 km When the oncoming flow height H > 25 km (2) Based on the total static pressure relationship and the inlet Mach number of the intake manifold. in Calculate the total temperature at the current altitude. and total pressure Where k is 1.4; (3) The total pressure recovery coefficient σ and flow coefficient at the intake outlet are obtained using empirical formulas for the two-dimensional intake. σ=0.95(1-0.075(Ma in -1) 1.35 ) (5) (4) Mach number at the intake manifold in Find the inlet flow rate function q(M) in And by using the flow field parameters at the inlet and outlet positions of the inlet, the inlet outlet flow function q(M) is obtained. out ); According to the following formula, the intake outlet flow rate function q(M) is known. out Find the Mach number at the intake and exhaust outlet. out , (5) Calculate the intake outlet temperature T. inlet,out Intake outlet temperature T inlet,out That is, the inlet temperature T of the precooler. air,in : The mass flow rate m at the intake outlet can be calculated using the flow rate formula. air for:

3. The rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler according to claim 1, characterized in that, In step 2, the initial estimated air outlet temperature T in the precooler air,out It equals the precooler air inlet temperature minus 1; The specific heat capacity Cp through the following formula Cp=1048.63-0.3838T+9.45576E-4T 2 -5.4915E-7T 3 +7.9315E-11T 4 (11) Estimated air heat exchange Q temp Represented as: Q temp = m air (Cp air,in T air,in -Cp air,out T air,out ) (12).

4. The rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler according to claim 1, characterized in that, The calculation process of the total heat transfer coefficient of the heat exchange tubes in the pre-cooler in Step 3 is as follows: Step 3.1, calculate the heat transfer coefficient h on the air side outside the tube bundle in the precooler. air ; Step 3.2, calculate the heat transfer coefficient h of the coolant side inside the tube bundle in the precooler. col : Step 3.3, use the calculated external heat transfer coefficient and internal heat transfer coefficient to further obtain the total heat transfer coefficient:

5. The rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler according to claim 4, characterized in that, In step 3, the air-side Nusselt number (Nu) air and air-side thermal conductivity λ air The calculation process is as follows: (1) Air-side dynamic viscosity μ air : The dynamic viscosity is calculated using the Sutherland formula, where T0 is 273.11 and B is 110.56; (2) Thermal conductivity λ on the air side air : Among them, the thermal conductivity is calculated using the kinetic-theory theory, R is the gas constant, and M is the molar mass of air; (3) Air-side Reynolds number Re air : In the formula, the content in the brackets is the product of the characteristic velocity and density of the tube bundle, and d is the outer diameter of the circular tube in the heat exchange tube bundle; (4) Prandtl number on the air side Pr air : (5) Nusselt number on the air side air : Where P T and P L These represent the lateral pitch ratio of the heat exchange tube bundle in the precooler perpendicular to the incoming airflow and the longitudinal pitch ratio parallel to the incoming airflow direction, respectively.

6. The rapid prediction method for flow heat transfer in a series-connected binary inlet-precooler according to claim 1, characterized in that, In step 3, the thermal conductivity λ of the coolant side col and coolant side Nusselt number col The calculation process is as follows: (1) Coolant specific heat capacity Cp col : Cp col =9125.03+38.02T-0.09541T 2 +1.01E-4T 3 -3.81E-8T 4 (22) In the formula, T is the average temperature of the inlet and outlet of the coolant; (2) Thermal conductivity λ of the coolant side col : λ col =0.01283+7.13318E-4T-4.99E-7T 2 +2.367E-10T 3 (23) (3) Coolant side dynamic viscosity μ col : μ col =1.717E-6+2.786E-8T-1.42E-11T 2 +5.435E-15T 3 (24) (4) Reynolds number on the coolant side col : (5) Prandtl number Pr on the coolant side col : (6) Coolant-side Nusselt number Nu col : Now col =0.023Re col 0.8 Per col 0.4 (27).

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