CN103150439B - Plate-fin heat exchanger oriented forecasting method for flow and heat exchange performances of fin - Google Patents

Abstract

The invention relates to a plate-fin heat exchanger oriented forecasting method for flow and heat exchange performances of a fin. The method comprises the steps of selecting basic structure parameters of a sawtoothed fin, calculating corresponding dimensionless parameters alpha, beta and gamma, checking whether the dimensionless parameters are within a correlation forecasting structure range, calculating the fin section equivalent diameter Dh and the fin passage equivalent diameter De according to the structure parameters of the sawtoothed fin, querying and obtaining air density rho and air viscosity mu at qualitative temperature and qualitative pressure, calculating Re according to a determined mean flow rate u passing through a passage of the sawtoothed fin, checking whether the Re is within the correlation forecasting range, determining a compound dimensionless parameter phi f of the sawtoothed fin, and calculating factors j and f. The method has a wider forecasting range for the flow and heat exchange performances of the sawtoothed fin for the plate-fin heat exchanger, the normal-pressure sawtoothed fin and the high-pressure sawtoothed fin are included, and forecasting is relatively accurate.

Description

Towards fin flowing and the heat exchange property Forecasting Methodology of plate type finned heat exchanger design

Technical field

The invention belongs to plate type finned heat exchanger design ap-plication technical field, be specifically related to the fin flowing towards plate type finned heat exchanger design and heat exchange property Forecasting Methodology.

Technical background

Plate type finned heat exchanger is a kind of enhanced heat exchange equipment efficiently, is widely used in Aero-Space, petrochemical complex and the industry such as gas separaion and liquefaction.Serrated fin is one of high-efficiency fin be applied in plate type finned heat exchanger, and it has higher ratio heat interchanging area, effectively can improve the heat exchange situation of weak side (as air side) in heat interchanger.

When layout board fin heat exchanger, the important performance parameter j Summing Factor f factor of fin not only can instruct the selection of plate type finned heat exchanger fin configuration used, and determines there is important impact with the size design of whole heat interchanger to the structural parameters of selected fin.The j Summing Factor f factor generally need in the design process according to design conditions and deviser select correlation parameter prediction obtain.And the prediction of the j Summing Factor f factor is mainly determined by j Summing Factor f factor correlation.

Early stage j Summing Factor f factor correlation obtains mainly through matching experimental data.The serrated fin experiment of the comparatively system can found according to documents and materials is what to be undertaken by the research group headed by Kays W.Y. and London A.L., take air as the flow media of experimental side, and employing wind tunnel experiment platform is tested.The data of gained are quoted by numerous scholar, thus have occurred the j Summing Factor f factor correlation of various serrated fin.The domestic Air separation industry serrated fin j Summing Factor f factor used predicts the fin performance curve mainly drawn from day Benshen steel " ALEX ".Along with the fast development of computer technology and Fluid Mechanics Computation (CFD), make to adopt method for numerical simulation to solve fin channels interior flow field and temperature field becomes possibility, by carrying out analyzing and processing to field data, just can obtain the performance factor of fin, as long as and numerical model foundation is reasonable, the fin performance data of gained and experimental data have good consistance.Therefore, the combination of experiment and CFD method is also more and more applied in the middle of the design of plate type finned heat exchanger.

Because the serrated fin model of experiment is less, traditional serrated fin j Summing Factor f factor correlation is examined comprehensive not on the structural factor affecting fluid interchange performance in serrated fin passage, effective estimation range is less, and often there is larger error in j and the f factor calculated, is unfavorable for the engineering design of plate type finned heat exchanger.Thus, propose a kind of can in relative broad range the flowing of Accurate Prediction serrated fin most important with the Forecasting Methodology of heat exchange property, have important practical significance.

Summary of the invention

In order to overcome the shortcoming of above-mentioned prior art, the object of the present invention is to provide the fin flowing towards plate type finned heat exchanger design and heat exchange property Forecasting Methodology, this Forecasting Methodology is first to serrated fin j, the f factor is predicted more accurately, secondly effectively estimation range is comparatively large, covers normal pressure serrated fin (fin thickness is relatively little) and high pressure serrated fin (fin thickness is relatively large).

In order to achieve the above object, the technical scheme that the present invention takes is:

Towards fin flowing and the heat exchange property Forecasting Methodology of plate type finned heat exchanger design, comprise the following steps:

Step 1, the thermal load of plate type finned heat exchanger that will design according to deviser and the elementary structure parameter of flow operating mode selection serrated fin, the elementary structure parameter of serrated fin has: fin height h _f, fin width s _f, fin thickness δ _f, fin unit length l _f, fin height h _frefer to the distance from the most feather edge of serrated fin to most high rim, fin width s _ffor the distance between adjacent two serrated fins;

Step 2, calculate corresponding basic dimensionless group α, β, γ according to the elementary structure parameter of selected serrated fin, each basic dimensionless group is calculated as follows:

$\mathrm{\α}=\frac{{\mathrm{\δ}}_f}{h_f},$ $\mathrm{\β}=\frac{{\mathrm{\δ}}_f}{s_f},$ $\mathrm{\γ}=\frac{{\mathrm{\δ}}_f}{l_f}$

And verify α, β, γ whether in scope of design, α, β, γ scope of design is: 0 < α < 0.5,0 < β < 0.5, γ >0.01;

Step 3, the elementary structure parameter according to serrated fin calculates fin cross section equivalent diameter D _hwith fin channels equivalent diameter D _e,

D _hcomputing method as follows:

$D_h=\frac{2h_f{s}_f}{h_f+s_f}$

D _eobtained by two kinds of modes, the first is directly calculated by the elementary structure parameter of serrated fin:

$D_e=\frac{2l_f(h_f-{\mathrm{\&delta;}}_f)(s_f-{\mathrm{\&delta;}}_f)}{l_f(h_f+s_f-2{\mathrm{\&delta;}}_f)+{\mathrm{\&delta;}}_f(h_f-{\mathrm{\&delta;}}_f)+\frac{2{\mathrm{\&delta;}}_f(s_f-2{\mathrm{\&delta;}}_f)}{4}}$

The second is the basic dimensionless group that drawn by the step 1 height h in conjunction with serrated fin _fwith fin width s _fcalculate:

$D_e=\frac{2(1-\mathrm{\&alpha;})(1-\mathrm{\&beta;})}{\frac{1}{s_f}(1-\mathrm{\&alpha;})(1+\mathrm{\&beta;})+\frac{1}{h_f}(1+\frac{1}{2}\mathrm{\&gamma;}-\mathrm{\&beta;}(1+\mathrm{\&gamma;}))}$

Step 4, inquiry air physical property table or air physical property query software obtain the density p of air under qualitative temperature and qualitative pressure and kinetic viscosity μ, and the flow velocity u designed by deviser calculates Re number, $\mathrm{Re}=\frac{\mathrm{\&rho;u}{D}_e}{\mathrm{\&mu;}}$

If deviser adopts the MAF m by unit fin passage _fdesign, then Re also can be obtained by such as under type:

$\mathrm{Re}=\frac{m_f}{A_{\mathrm{front}}}\frac{D_e}{\mathrm{\&mu;}}$

In formula: A _front=(h _f-δ _f) (s _f-δ _f)

Then verify Re number whether in the scope of design of the serrated fin j Summing Factor f factor, Re number scope of design is: 200≤Re≤10000;

Step 5, determines the compound dimensionless group Φ of serrated fin _f, formula is as follows:

${\mathrm{\&Phi;}}_f={(\frac{1}{\mathrm{\&alpha;}}+\frac{1}{2\mathrm{\&beta;}}-2)}^{\mathrm{\&alpha;}(1-2\mathrm{\&beta;})+2\mathrm{\&beta;}(1-\mathrm{\&alpha;})}+\frac{4(1-\mathrm{\&alpha;})\mathrm{\&beta;}+\mathrm{\&alpha;}(1-2\mathrm{\&beta;})}{4(\mathrm{\&alpha;}+\mathrm{\&beta;}-2\mathrm{\&alpha;\&beta;})}$

Step 6, according to the parameter obtained by step 1-4, calculate the j Summing Factor f factor of serrated fin used, computing formula is as follows:

$j=2.34812{\left(\frac{l_f}{D_h}\right)}^{0.19411}{{\mathrm{\&Phi;}}_f}^{0.00656}{\mathrm{\&alpha;}}^{-0.35987}{\mathrm{\&beta;}}^{0.10391}{\mathrm{\&gamma;}}^{0.45337}R{e}^{-1.01546+0.05633\ln \left(\mathrm{Re}\right)-0.00064{\left(\frac{h_f}{D_h}\right)}^{0.49317}{\mathrm{\&beta;}}^{-0.16019}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}$

$f=2300.24{\left(\frac{l_f}{D_h}\right)}^{-1.42491}{{\mathrm{\&Phi;}}_f}^{0.26188}{\left(\frac{1}{1-2\mathrm{\&alpha;}}\right)}^{2.04570}{\left(\frac{1}{1-2\mathrm{\&beta;}}\right)}^{2.16338}{\mathrm{\&gamma;}}^{-0.93414}$

$\&times;R{e}^{-4.52412+0.49785\ln \left(\mathrm{Re}\right)-0.01580{\left(\frac{h_f}{D_h}\right)}^{0.00222}{\mathrm{\&beta;}}^{-0.08664}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}$

Step 7, the total length of serrated fin used is determined according to the j factor of the serrated fin calculated and the thermal load of plate type finned heat exchanger that will design, and then under the condition meeting design heating load, determine total heat interchanging area and the volume of selected serrated fin, the pressure drop of selected serrated fin and pump merit under calculating the flow operating mode of the plate type finned heat exchanger that will design deviser by the f factor of serrated fin that calculates and the total length of serrated fin, then according to the maximum pump merit that pressure condition or the reality of the import and export of actual plate fin heat exchanger can provide for plate type finned heat exchanger import, verify selected serrated fin and whether meet design flow operating mode condition, if do not meet design flow operating mode condition, deviser needs the elementary structure parameter reselecting serrated fin, and repeat step 2-step 7, until selected serrated fin not only meets the design heating load of plate type finned heat exchanger but also meets the flow operating mode of fin heat exchanger, after the design heating load meeting plate type finned heat exchanger when selected serrated fin and flow operating mode, then be optimized type selecting to serrated fin, the heat exchange core of plate type finned heat exchanger is determined.

Advantage of the present invention be mainly can within the scope of wider fin structure the j Summing Factor f factor of Accurate Prediction serrated fin, because the serrated fin compound dimensionless group summed up according to simulated data in the j Summing Factor f factor fully can reflect the architectural characteristic of serrated fin, the j factor and f factor correlation all adopt the simulated performance data of index-a large amount of different model serrated fin of polynomial form matching simultaneously, and by the inspection of relevant experimental data, the Accurate Prediction of the j Summing Factor f factor to serrated fin thus can be realized.The j Summing Factor f factor of Accurate Prediction serrated fin, the fluid interchange performance of the plate type finned heat exchanger gone out designed by can making in actual moving process more close to design performance, thus can reduce the material consumption because j, f factor predicated error causes, reduce the material cost of producing plate type finned heat exchanger; In addition, the Accurate Prediction of the serrated fin j Summing Factor f factor makes the fluid interchange performance of the serrated fin after optimizing in actual motion best, therefore can reduce the fluid interchange irreversible loss of plate type finned heat exchanger, thus improve the heat exchange efficiency of plate type finned heat exchanger.

Accompanying drawing explanation

Accompanying drawing 1 is the serrated fin structural parameters schematic diagram used in the present invention.

Embodiment

Below in conjunction with accompanying drawing and example, the present invention is described in detail.

Towards fin flowing and the heat exchange property Forecasting Methodology of plate type finned heat exchanger design, comprise the following steps:

Step 1, with reference to accompanying drawing 1, the thermal load of plate type finned heat exchanger that will design according to deviser and the elementary structure parameter of flow operating mode selection serrated fin, the model choosing serrated fin to be 95JC1402 fin unit length the be serrated fin of 5mm is as calculating object, and to be the elementary structure parameter of the serrated fin of 95JC1402 be model: fin height h _f=9.5mm, fin width s _f=1.4mm, fin thickness δ _f=0.2mm, fin unit length l _f=5.0mm;

Step 2, calculates corresponding basic dimensionless group α, β, γ according to the elementary structure parameter of selected serrated fin,

Basic dimensionless group result of calculation is:

$\mathrm{\&alpha;}=\frac{{\mathrm{\&delta;}}_f}{h_f}=\frac{0.2\mathrm{mm}}{9.5\mathrm{mm}}=0.0211$

$\mathrm{\&beta;}=\frac{{\mathrm{\&delta;}}_f}{s_f}=\frac{0.2\mathrm{mm}}{1.4\mathrm{mm}}=0.1429$

$\mathrm{\&gamma;}=\frac{{\mathrm{\&delta;}}_f}{l_f}=\frac{0.2\mathrm{mm}}{5.0\mathrm{mm}}=0.0400$

And verify α, β, γ whether in scope of design, α, β, γ scope of design is: 0 < α < 0.5,0 < β < 0.5, γ >0.01, through comparison, α, β, γ value is all within the scope of given structural design;

Step 3, the elementary structure parameter according to serrated fin calculates fin cross section equivalent diameter D _hwith fin channels equivalent diameter D _e,

$D_h=\frac{2h_f{s}_f}{h_f+s_f}=\frac{2\&times;9.5\mathrm{mm}\&times;1.4\mathrm{mm}}{9.5\mathrm{mm}+1.4\mathrm{mm}}=2.4404\mathrm{mm}$

$D_e=\frac{2l_f(h_f-{\mathrm{\&delta;}}_f)(s_f-{\mathrm{\&delta;}}_f)}{l_f(h_f+s_f-2{\mathrm{\&delta;}}_f)+{\mathrm{\&delta;}}_f(h_f-{\mathrm{\&delta;}}_f)+\frac{2{\mathrm{\&delta;}}_f(s_f-2{\mathrm{\&delta;}}_f)}{4}}$

$=\frac{2\&times;5.0\mathrm{mm}\&times;(9.5\mathrm{mm}-0.2\mathrm{mm})\&times;(1.4\mathrm{mm}-0.2\mathrm{mm})}{5.0\mathrm{mm}\&times;(9.5\mathrm{mm}+1.4\mathrm{mm}-2\&times;0.2\mathrm{mm})+0.2\mathrm{mm}\&times;(9.5\mathrm{mm}-0.2\mathrm{mm})+\frac{2\&times;0.2\mathrm{mm}\&times;(1.4\mathrm{mm}-2\&times;0.2\mathrm{mm})}{4}}$

$=2.0492\mathrm{mm}$

D _ealso by calculating as follows:

$D_e=\frac{2(1-\mathrm{\&alpha;})(1-\mathrm{\&beta;})}{\frac{1}{s_f}(1-\mathrm{\&alpha;})(1+\mathrm{\&beta;})+\frac{1}{h_f}(1+\frac{1}{2}\mathrm{\&gamma;}-\mathrm{\&beta;}(1+\mathrm{\&gamma;}))}$

$=\frac{2\&times;(1-0.0211)\&times;(1-0.1429)}{\frac{1}{1.4\mathrm{mm}}(1-0.0211)\&times;(1+0.1429)+\frac{1}{9.5\mathrm{mm}}(1+\frac{0.0400}{2}-0.1429\&times;(1+0.0400))}$

$=2.0492\mathrm{mm}$

Step 4, inquiry air physical property table or air physical property query software obtain the density p of air under qualitative temperature and qualitative pressure and kinetic viscosity μ, calculate Re number according to deviser according to the determined mean flow rate u by serrated fin passage of flow operating mode,

Such as adopting NIST-REFPROP to inquire about qualitative temperature is 334K, and qualitative pressure is the physical property of air under 100000Pa:

Density p=the 1.0428kg/m of air ³, kinetic viscosity μ=20.189 × 10 of air ^-6pa/s,

Suppose that by the flow velocity of serrated fin passage be u=18m/s, then:

$\mathrm{Re}=\frac{\mathrm{\&rho;u}{D}_e}{\mathrm{\&mu;}}=\frac{1.0428\mathrm{kg}/m^3\&times;18m/s\&times;2.0492\&times;{10}^{-3}m}{20.189\&times;{10}^{-6}\mathrm{Pa}/s}=1905.2$

Then verify Re number whether in the scope of design of the serrated fin j Summing Factor f factor, Re number scope of design is: 200≤Re≤10000; Through comparison, the Re number calculated is in scope of design;

Step 5, determines the compound dimensionless group Φ of serrated fin _f,

According to the basic dimensionless group that step 1 provides, compound dimensionless group Φ can be obtained _f:

${\mathrm{\&Phi;}}_f={(\frac{1}{\mathrm{\&alpha;}}+\frac{1}{2\mathrm{\&beta;}}-2)}^{\mathrm{\&alpha;}(1-2\mathrm{\&beta;})+2\mathrm{\&beta;}(1-\mathrm{\&alpha;})}+\frac{4(1-\mathrm{\&alpha;})\mathrm{\&beta;}+\mathrm{\&alpha;}(1-2\mathrm{\&beta;})}{4(\mathrm{\&alpha;}+\mathrm{\&beta;}-2\mathrm{\&alpha;\&beta;})}$

$={(\frac{1}{0.0211}+\frac{1}{2\&times;0.1429}-2)}^{0.0211\&times;(1-2\&times;0.1429)+2\&times;0.1429\&times;(1-0.0211)}$

$+\frac{4\&times;(1-0.0211)\&times;0.1429+0.0211\&times;(1-2\&times;0.1429)}{4(0.0211+0.1429-2\&times;0.0211\&times;0.1429)}$

$=4.05845$

Step 6, calculates the j Summing Factor f factor according to the parameter obtained by step 1-4,

Bring in the correlation provided by step 1-4 gained correlation parameter, calculating can obtain the j Summing Factor f factor and be respectively:

$j=2.34812{\left(\frac{l_f}{D_h}\right)}^{0.19411}{{\mathrm{\&Phi;}}_f}^{0.00656}{\mathrm{\&alpha;}}^{-0.35987}{\mathrm{\&beta;}}^{0.10391}{\mathrm{\&gamma;}}^{0.45337}R{e}^{-1.01546+0.05633\ln \left(\mathrm{Re}\right)-0.00064{\left(\frac{h_f}{D_h}\right)}^{0.49317}{\mathrm{\&beta;}}^{-0.16019}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}$

$=2.34812\&times;{\left(\frac{5\mathrm{mm}}{2.4404\mathrm{mm}}\right)}^{0.19411}\&times;{4.05845}^{0.00656}\&times;{0.0211}^{-0.35987}\&times;{0.1429}^{0.10391}\&times;{0.0400}^{0.45337}$

$\&times;{1905.2}^{-1.01546+0.05633\&times;\ln \left(1905.2\right)-0.00064\&times;{\left(\frac{9.5\mathrm{mm}}{2.4404\mathrm{mm}}\right)}^{0.49317}\&times;{0.1429}^{-0.16019}\&times;{\left(\ln \left(1905.2\right)\right)}^2}$

$=0.01012$

$f=2300.24{\left(\frac{l_f}{D_h}\right)}^{-1.42491}{{\mathrm{\&Phi;}}_f}^{0.26188}{\left(\frac{1}{1-2\mathrm{\&alpha;}}\right)}^{2.04570}{\left(\frac{1}{1-2\mathrm{\&beta;}}\right)}^{2.16338}{\mathrm{\&gamma;}}^{-0.93414}$

$\&times;R{e}^{-4.52412+0.49785\ln \left(\mathrm{Re}\right)-0.01580{\left(\frac{h_f}{D_h}\right)}^{0.00222}{\mathrm{\&beta;}}^{-0.08664}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}$

$=2300.24\&times;{\left(\frac{5\mathrm{mm}}{2.4404\mathrm{mm}}\right)}^{-1.42491}\&times;{4.05845}^{0.26188}\&times;{\left(\frac{1}{1-2\&times;0.0211}\right)}^{2.04570}\&times;{\left(\frac{1}{1-2\&times;0.1429}\right)}^{2.16338}$

$\&times;{0.0400}^{-0.93414}\&times;{1095.2}^{-4.52412+0.49785\&times;\ln \left(1905.2\right)-0.01580\&times;{\left(\frac{9.5\mathrm{mm}}{2.4404\mathrm{mm}}\right)}^{0.00222}\&times;{0.1429}^{-0.08664}\&times;{\left(\ln \left(1905.2\right)\right)}^2}$

$=0.05268$

Step 7, the total length of serrated fin used is determined according to the j factor of the serrated fin calculated and the thermal load of plate type finned heat exchanger that will design, and then under the condition meeting design heating load again, determine total heat interchanging area and the volume of selected serrated fin, the pressure drop of selected serrated fin and pump merit under calculating the flow operating mode of the plate type finned heat exchanger that will design deviser by the f factor of serrated fin that calculates and the total length of serrated fin, then according to the maximum pump merit that pressure condition or the reality of the import and export of actual plate fin heat exchanger can provide for plate type finned heat exchanger import, selected serrated fin is checked whether to meet design flow operating mode condition, if do not meet design flow operating mode condition, deviser needs the elementary structure parameter reselecting serrated fin, and repeat step 2-step 7, until selected serrated fin not only meets the design heating load of plate type finned heat exchanger but also meets the flow operating mode of fin heat exchanger, after the design heating load meeting plate type finned heat exchanger when selected serrated fin and flow operating mode, then be optimized type selecting to serrated fin, the concrete structure of plate type finned heat exchanger heat exchange core is determined.

Advantage of the present invention is mainly can the j Summing Factor f factor of Accurate Prediction serrated fin, following table gives the some experimental data based on Kays and London, and the some experimental data of domestic Nanjing University of Technology, adopt the root-mean-square error (RMS) of design load under flow operating mode tested entirely by this fin of fin performance and experiment value to contrast the accuracy of method for designing of the present invention and traditional Manglik method for designing.

As can be seen from the table, compared with experimental data, the root-mean-square error of the method for designing gained j factor of the present invention is generally little than traditional Manlik method for designing, for the f factor, root-mean-square error is all less than 10%, obviously be better than Manglik method for designing, illustrate that Forecasting Methodology of the present invention can predict the fluid interchange performance of serrated fin more accurately in plate type finned heat exchanger design; In addition, effective estimation range of Forecasting Methodology of the present invention is larger, from dimensionless group, 0 < α < 0.5,0 < β < 0.5, γ >0.01, almost covers institute's likely structure of serrated fin, can make corresponding prediction to the high pressure serrated fin with larger fin thickness.

Claims (1)

1., towards fin flowing and the heat exchange property Forecasting Methodology of plate type finned heat exchanger design, it is characterized in that, comprise the following steps:

Step 1, the thermal load of plate type finned heat exchanger that will design according to deviser and the elementary structure parameter of flow operating mode selection serrated fin, the elementary structure parameter of serrated fin has: fin height h _f, fin width s _f, fin thickness δ _f, fin unit length l _f, fin height h _frefer to the distance from the most feather edge of serrated fin to most high rim, fin width s _ffor the distance between adjacent two serrated fins;

Step 2, calculate corresponding basic dimensionless group α, β, γ according to the elementary structure parameter of selected serrated fin, each basic dimensionless group is calculated as follows:

$\mathrm{\&alpha;}=\frac{{\mathrm{\&delta;}}_f}{h_f},$ $\mathrm{\&beta;}=\frac{{\mathrm{\&delta;}}_f}{s_f},$ $\mathrm{\&gamma;}=\frac{{\mathrm{\&delta;}}_f}{l_f}$

And verify α, β, γ whether in scope of design, α, β, γ scope of design is: 0 < α < 0.5,0 < β < 0.5, γ >0.01;

Step 3, the elementary structure parameter according to serrated fin calculates fin cross section equivalent diameter D _hwith fin channels equivalent diameter D _e,

D _hcomputing method as follows:

$D_h=\frac{{2h}_f{s}_f}{h_f+s_f}$

D _eobtained by two kinds of modes, the first is directly calculated by the elementary structure parameter of serrated fin:

$D_e=\frac{{2l}_f(h_f-{\mathrm{\&delta;}}_f)(s_f-{\mathrm{\&delta;}}_f)}{l_f(h_f+s_f-{2\mathrm{\&delta;}}_f)+{\mathrm{\&delta;}}_f(h_f-{\mathrm{\&delta;}}_f)+\frac{{2\mathrm{\&delta;}}_f(s_f-{2\mathrm{\&delta;}}_f)}{4}}$

The second is the basic dimensionless group that drawn by the step 1 height h in conjunction with serrated fin _fwith fin width s _fcalculate:

$D_e=\frac{2(1-\mathrm{\&alpha;})(1-\mathrm{\&beta;})}{\frac{1}{s_f}(1-\mathrm{\&alpha;})(1+\mathrm{\&beta;})+\frac{1}{h_f}(1+\frac{1}{2}\mathrm{\&gamma;}-\mathrm{\&beta;}(1+\mathrm{\&gamma;}))}$

Step 4, inquiry air physical property table or air physical property query software obtain the density p of air under qualitative temperature and qualitative pressure and kinetic viscosity μ, and the mean flow rate u by serrated fin passage designed by deviser calculates Re number,

If deviser adopts the MAF m by unit fin passage _fdesign, then Re also can be obtained by such as under type:

$\mathrm{Re}=\frac{m_f}{A_{\mathrm{front}}}\frac{D_e}{\mathrm{\&mu;}}$

In formula: A _front=(h _f-δ _f) (s _f-δ _f)

Then verify Re number whether in the scope of design of the serrated fin j Summing Factor f factor, Re number scope of design is: 200≤Re≤10000;

Step 5, determines the compound dimensionless group Φ of serrated fin _f, formula is as follows:

${\mathrm{\&Phi;}}_f={(\frac{1}{\mathrm{\&alpha;}}+\frac{1}{2\mathrm{\&beta;}}-2)}^{\mathrm{\&alpha;}(1-2\mathrm{\&beta;})+2\mathrm{\&beta;}(1-\mathrm{\&alpha;})}+\frac{4(1-\mathrm{\&alpha;})\mathrm{\&beta;}+\mathrm{\&alpha;}(1-2\mathrm{\&beta;})}{4(\mathrm{\&alpha;}+\mathrm{\&beta;}-2\mathrm{\&alpha;\&beta;})}$

Step 6, according to the parameter obtained by step 1-4, calculate the j Summing Factor f factor of serrated fin used, computing formula is as follows:

$j=2.34812{\left(\frac{l_f}{D_h}\right)}^{0.19411}{{\mathrm{\&Phi;}}_f}^{0.00656}{\mathrm{\&alpha;}}^{-0.35987}{\mathrm{\&beta;}}^{0.10391}{\mathrm{\&gamma;}}^{0.45337}{\mathrm{Re}}^{-1.01546+0.05633\ln \left(\mathrm{Re}\right)-0.00064{\left(\frac{h_f}{D_h}\right)}^{0.49317}{\mathrm{\&beta;}}^{-0.16019}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}$

$\begin{array}{c}f=2300.24{\left(\frac{l_f}{D_h}\right)}^{-1.42491}{{\mathrm{\&Phi;}}_f}^{0.26188}{\left(\frac{1}{1-2\mathrm{\&alpha;}}\right)}^{2.04570}{\left(\frac{1}{1-2\mathrm{\&beta;}}\right)}^{2.16338}{\mathrm{\&gamma;}}^{-0.93414}\\ \&times;{\mathrm{Re}}^{-4.52412+0.49785\ln \left(\mathrm{Re}\right)-0.01580{\left(\frac{h_f}{D_h}\right)}^{0.00222}{\mathrm{\&beta;}}^{-0.08664}{\left(\ln \left(\mathrm{Re}\right)\right)}^2}\end{array}$

Step 7, the total length of serrated fin used is determined according to the j factor of the serrated fin calculated and the thermal load of plate type finned heat exchanger that will design, and then under the condition meeting design heating load, determine total heat interchanging area and the volume of selected serrated fin, the pressure drop of selected serrated fin and pump merit under calculating the flow operating mode of the plate type finned heat exchanger that will design deviser by the f factor of serrated fin that calculates and the total length of serrated fin, then according to the maximum pump merit that pressure condition or the reality of the import and export of actual plate fin heat exchanger can provide for plate type finned heat exchanger import, verify selected serrated fin and whether meet design flow operating mode condition, if do not meet design flow operating mode condition, deviser needs the elementary structure parameter reselecting serrated fin, and repeat step 2-step 7, until selected serrated fin not only meets the design heating load of plate type finned heat exchanger but also meets the flow operating mode of fin heat exchanger, after the design heating load meeting plate type finned heat exchanger when selected serrated fin and flow operating mode, then be optimized type selecting to serrated fin, the heat exchange core of plate type finned heat exchanger is determined.