CN104615872A - Method for calculating film condensation heat transfer outside vertical spiral coil - Google Patents

Abstract

The invention discloses a method for calculating film condensation heat transfer outside a vertical spiral coil. According to the method, a Cartesian coordinate system is translated into a dynamic rectangular coordinate system, an equilibrium relationship between a force and energy on a liquid film is analyzed, an expression of a normal vector of a tangent plane of the liquid film is found out, an expression of a liquid film velocity direction is calculated out, equilibrium of forces and conservation of energy exist on the tangent plane of the liquid film flow velocity direction, according to an equilibrium relation expression between the force and the energy on the liquid film, liquid film thickness is 0 at an initial stage, boundary conditions for calculating the liquid film thickness are listed, and finally the liquid film thickness are calculated out; for coils other than the first layer, effects of liquid film accumulation are taken into consideration, and a comprehensive mean heat transfer coefficient of coils ranging from the first layer to the n layer is calculated by means of continuous iteration. The method for calculating the film condensation heat transfer outside the vertical spiral coil has the advantages that a calculation model applicable to vertical spiral coil type heat exchanger shell pass side heat transfer is presented, and the calculation result is accurate.

Description

The computing method of the outer film condensation heat transfer of a kind of Vertical spiral coil

Technical field

The invention belongs to technical field of heat exchangers, relate to the computing method of the outer film condensation heat transfer of a kind of Vertical spiral coil.

Background technology

Condenser is as heat transmission equipment, be widely used in the every profession and trades such as Heating,Ventilating and Air Conditioning (HVAC), energy source and power, petrochemical complex, in view of present situation and the heat interchanger vital role in the industrial production of China's high energy consumption, the lifting of its enhanced heat exchange and efficiency is the target that relevant industries and academia make great efforts always.Vertical spiral coil formula condenser is a kind of energy-efficient, the heat interchanger of compact conformation, is paid close attention to widely and application at present.The complex heat transfer coefficient of Vertical spiral coil heat interchanger should comprise: the convection heat transfer of water in pipe, the heat conduction between tube wall, the thermal resistance that the film condensation heat transfer of shell side side cold-producing medium and incrustation scale oil film etc. produce.

Due to the special construction of Vertical spiral coil, shell side side form shape condensation heat transfer coefficient theoretical foundation is weak, there is no generally acknowledged dependable algorithm.Film condensation heat transfer model conventional at present has: perpendicular wall film condensation computation model is (see Nusselt W.Die desWasserdampfes.Z.Vereines Deutsch.Ing.1916, 60:541-546, 569-575), Horizontal single-pipe film condensation heat transfer model is (see Yilbas B S, Altuntop N.CondensationHeat Transfer ofFreon-21on Plain Horizontal Tubes [J] .Indian Journal ofTechnology, 1990, 28:100-106.), horizontal tube bundle computation model etc. (see Ma Zhixian. horizontal tube bundle film condensation heat transfer test and theoretical research [D]. Harbin: Harbin Institute of Technology, 2012) and flat spin coil pipe film condensation heat transfer model (see Xiao Min, Zhang Yanmou. the theoretical research [J] of flat spin coil heat exchange. power machineny engineering physics. publishing house of Xi'an Communications University .) etc.According to Vertical spiral coil design feature and heat transfer mechanism analysis, with its heat exchange models relatively be flat spin coil pipe and horizontal tube bundle two kinds.

The Xiao Min of Xi'an Communications University, Zhang Yanmou expand theoretical research for the outer membranaceous heat of condensation of flat spin coil pipe and verify by experiment.The method of theoretical research mainly sets up performance graph coordinate system according to spiral coil structure, finds liquid film equilibrium of forces and energy conservation relation formula, provide the expression formula of thickness of liquid film in curvilinear coordinates.The thickness of liquid film is measured by conductance method experiment.Empirical tests theoretical model and experimental error are within 20%.The people such as the Ma Zhixian of Harbin Institute of Technology, on the basis studied, determine the film condensation heat transfer model of horizontal tube bundle at home and abroad by the theoretical method combined with experiment.Specify that the concept of body lime set, migration lime set, effect lime set and the computation model of heat exchanging impact.Above-mentioned two kinds of methods are all rational for respective Structure Calculation, but have problems for Vertical spiral coil structure.Though flat spin coil arrangement considers spiral form, do not consider the impact of the liquid film accumulation heat exchanging of vertical direction, and liquid film is along with the increase of the coil pipe degree of depth, Accumulation Phenomenon is inevitable, and the impact of heat exchanging is very large, and directly application will inevitably cause error.For horizontal tube bundle model, propose the concept of migration lime set, consider the impact of liquid film accumulation, but horizontal tube certainly exists difference compared with spiral coil, direct calculating can produce error equally.

The specific question that Vertical spiral coil structure liquid film is accumulated all do not considered by existing film condensation heat transfer model, and result of calculation and actual result all can produce very big error.For improving the accuracy that the Vertical spiral coil condenser coefficient of heat transfer calculates, meeting the needs that this kind of condenser is applied, the present invention proposes a kind of computation model being applicable to the side heat exchange of Vertical spiral coil formula heat exchanger shell pass.With the singularity of vertical spin structure, find out the computing method of first floor lime set thickness.Again according to liquid film cumulative effect, calculate overall complex heat transfer coefficient mean value.

Summary of the invention

The object of the present invention is to provide the computing method of the outer film condensation heat transfer of a kind of Vertical spiral coil, solve existing film condensation heat transfer model and all do not consider the specific question that Vertical spiral coil structure liquid film is accumulated, result of calculation and actual result all can produce the problem of very big error.

The technical solution adopted in the present invention is carried out according to following steps:

Step 1: cartesian coordinate system is converted into dynamic rectangular coordinate system: dynamically rectangular coordinate system constantly changes along with the point on coil pipe, but dynamically the foundation of rectangular coordinate system all along the central axis of spiral coil, wherein X ₁axle along spiral pipe center position, X ₂x ₃axle is positioned on spiral pipe cross section, X ₃cross summit, cross section, wherein P ₀point is the center of circle in this cross section, i.e. P ₀point is coordinate system X ₁x ₂x ₃initial point, P point is any point on spiral pipe surface;

Step 2: the equilibrium relation of analytic liquid membrane forces and energy, find out the expression formula of liquid film speed Surface by Tangent Plane Method vector, calculate the expression formula of liquid film velocity reversal:

φ is liquid film speed direction and tube section (X ₂x ₃face) angle.Speed direction should be

Step 3: the conservation that there is equilibrium of forces and energy on the section of thin film drainage velocity reversal, the balanced relationship of power and energy on liquid film:

Equilibrium of forces relational expression is:

$({\mathrm{\ρ}}_f-{\mathrm{\ρ}}_g)\·g\·\mathrm{dv}\·\sin \mathrm{\θ}=\mathrm{\μ}\·\frac{\∂V}{\∂y^{\′}}\·\mathrm{dx}\·\mathrm{ds}$

Energy balance relations formula is: Q _lead=Q _dive

Heat conduction amount is produced by thickness of liquid film, can try to achieve according to Heat Conduction Differential Equations; Latent heat amount is because the vaporescence of liquid refrigerant produces, relevant with the physical parameter of cold-producing medium.

Step 4: according to the balanced relationship of power on liquid film and energy, at initial period, thickness of liquid film is 0, lists the boundary condition that thickness of liquid film solves:

δ| _γ＝0＝0

In conjunction with the balanced relationship of equilibrium of forces and heat, finally solve the thickness of liquid film;

Step 5: for non-first floor coil pipe, considers the effect of liquid film accumulation, by the method for continuous iteration, calculates the comprehensive mean heat transfer coefficient from the 1st layer of coil pipe to n-th layer coil pipe.

Further, in described step 2, the expression formula solution procedure of liquid film velocity reversal is as follows:

First, by spiral coil kernel of section line and X ₁axial projection on surface level XOY face, its projection polar coordinates angle be γ, then in cartesian coordinate system with parametric equation by X ₁axle describes out, then calculates tangent vector according to parametric equation, and vector equation is:

In formula: β angle is lead angle;

Secondly, X is solved ₁the angle α of axle tangent line and surface level, in Vertical spiral coil coordinate system, α should be equal in lead angle, i.e. α=β;

Then: calculate section in the angle theta of surface level.Can calculate with the angle of the normal vector of two planes.

The normal vector of surface level:

The normal vector in section:

Wherein: for the polar coordinates angle of pipeline section.

e ₃be respectively along X ₁x ₂x ₃the unit vector in three directions

Then according to dot product formula:

The expression formula finally obtaining θ is:

Further, in described step 5, the step that the comprehensive mean heat transfer coefficient from the 1st layer of coil pipe to n-th layer coil pipe calculates is:

1) calculate the standard flow pattern of sheet migration lime set, accounting equation is:

Re _film＝1.448Ar _l ^0.236

In formula: Re _film-be sheet migration lime set Reynolds number;

Ar _l-be the Archimedes number of liquid phase working fluid;

2) for non-first comb and n-th layer (n >=2), the calculation relational expression of migration lime set impact is provided:

${\mathrm{Re}}_{\mathrm{fall}}=\underset{i=1}{\overset{n-1}{\mathrm{\Σ}}}{\mathrm{Re}}_{\mathrm{con},i}$

In formula: Re _film-be Reynolds number corresponding to migration lime set;

Re _{con, i}the Reynolds number that-the i-th layer of body lime set is corresponding; For first floor lime set, after thickness of liquid film and refrigerant flow rates are determined, Reynolds number is determined, is then determined by continuous iteration for non-first floor lime set;

3) calculate the angle χ corresponding when boundary layer reaches thickness of liquid film, its calculation relational expression is:

${\∫}_0^{\mathrm{\χ}}{\left(\sin \mathrm{\χ}\right)}^{1/3}\mathrm{d\χ}=0.606\mathrm{Pr}{{\mathrm{Re}}^{4/3}}_{\mathrm{fall},n}{\mathrm{Ga}}^{-1/3}$

In formula: Pr-be Prandtl number, refrigeration working medium is determined, this value can be looked into and get;

Ga-be Galileo number.

4) equivalent sheet migration length ratio P is calculated _film, its computing formula is:

P _film＝Re _fall,n/Re _film

5) according to P _filmand χ judges the computation model selected; Discriminant approach is as follows

Work as P _film>=1,

$\stackrel{\‾}{\mathrm{Nu}}=1.016{\mathrm{Pr}}^{1/3}{\mathrm{Re}}_{\mathrm{fall},n}^{1/9}{\mathrm{Ga}}^{-1/9}$

Work as P _film>=1, time,

Work as P _film<1, time,

${\stackrel{\&OverBar;}{\mathrm{Nu}}}^{*}=P_{\mathrm{film}}{\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{film}}+(1-P_{\mathrm{film}}){\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{con},n}^{*}$

Work as P _film<1, time,

The invention has the beneficial effects as follows and propose a kind of computation model being applicable to the side heat exchange of Vertical spiral coil formula heat exchanger shell pass, result of calculation is accurate.

Accompanying drawing explanation

Fig. 1 is performance graph coordinate system X ₁x ₂x ₃schematic diagram;

Fig. 2 is that the direction of liquid film speed is along direction, P point section schematic diagram;

Fig. 3 is heat interchanger side structure schematic diagram;

Fig. 4 is heat exchanger coils schematic diagram;

Fig. 5 is heat interchanger vertical view.

Embodiment

Below in conjunction with embodiment, the present invention is described in detail.

The computing method of the outer film condensation heat transfer of Vertical spiral coil:

The first step: the structure due to spiral coil makes liquid film all carry out along the direction of helix in the process formed and move, the description of cartesian coordinate system to problem of application static state is unclear, in order to the convenience studied, first cartesian coordinate system is converted into dynamic rectangular coordinate system

Performance graph coordinate system X ₁x ₂x ₃schematic diagram as shown in Figure 1.X in Fig. 1 ₁axle is along spiral pipe center position.X ₂x ₃axle is positioned on spiral pipe cross section.X ₃cross summit, cross section.Wherein P ₀point is the center of circle in this cross section, i.e. P ₀point is coordinate system X ₁x ₂x ₃initial point.P point is any point on spiral pipe surface.Coordinate system constantly changes along with the point on coil pipe, but the foundation of coordinate system is all along the central axis of spiral coil.

Second step: be the equilibrium relation of analytic liquid membrane forces and energy, find out the expression formula of liquid film speed Surface by Tangent Plane Method vector.Solving of expression formula will by determining the analysis of coil geometry.Solution procedure is as follows:

First, by spiral coil kernel of section line and X ₁axial projection on surface level XOY face, its projection polar coordinates angle be γ, then in cartesian coordinate system with parametric equation by X ₁axle describes out, then calculates tangent vector according to parametric equation: vector equation is:

In formula: β angle is lead angle;

Secondly, X is solved ₁the angle α of axle tangent line and surface level, in Vertical spiral coil coordinate system, α should be equal in lead angle, i.e. α=β;

Then: calculate section in the angle theta of surface level.Can calculate with the angle of the normal vector of two planes.

The normal vector of surface level:

The normal vector in section:

Wherein: for the polar coordinates angle of pipeline section.

e ₃be respectively along X ₁x ₂x ₃the unit vector in three directions

Then according to dot product formula:

The expression formula finally obtaining θ is:

Finally, the expression formula of liquid film speed is calculated.For the outer film condensation heat transfer of spiral pipe, the direction of liquid film speed should move down along direction, P point section, cuts the intersection perpendicular to section and surface level.Its schematic diagram as shown in Figure 2.

φ is liquid film speed direction and tube section (X ₂x ₃face) angle.Speed direction should be can arrange and obtain:

3rd step: the conservation that there is equilibrium of forces and energy on the section of thin film drainage velocity reversal, sets up physical model;

Using P point as research object on section, utilize the geometric relationship given by previous step, the equilibrium of forces suffered by analysis P point and the balance of energy.Thickness of liquid film gets micro unit, equilibrium of forces is carried out to micro unit and energy equilibrium lists equilibrium of forces relational expression:

$({\mathrm{\&rho;}}_f-{\mathrm{\&rho;}}_g)\&CenterDot;g\&CenterDot;\mathrm{dv}\&CenterDot;\sin \mathrm{\&theta;}=\mathrm{\&mu;}\&CenterDot;\frac{\&PartialD;V}{\&PartialD;y^{\&prime;}}\&CenterDot;\mathrm{dx}\&CenterDot;\mathrm{ds}$

Namely in micro unit, the heat conduction amount of liquid film is equal with the latent heat of vaporization amount that steam condensation produces.Equilibrium of forces relational expression is:

$({\mathrm{\&rho;}}_f-{\mathrm{\&rho;}}_g)\&CenterDot;g\&CenterDot;\mathrm{dv}\&CenterDot;\sin \mathrm{\&theta;}=\mathrm{\&mu;}\&CenterDot;\frac{\&PartialD;V}{\&PartialD;y^{\&prime;}}\&CenterDot;\mathrm{dx}\&CenterDot;\mathrm{ds}$

Energy balance relations formula is: Q _lead=Q _dive

Heat conduction amount is produced by thickness of liquid film, can try to achieve according to Heat Conduction Differential Equations; Latent heat amount is because the vaporescence of liquid refrigerant produces, relevant with the physical parameter of cold-producing medium.So far, the balanced relationship of power and energy on liquid film is listed.

4th step: according to above-mentioned equilibrium of forces and energy balance relations formula, can find out, thickness of liquid film is and pipeline section center (X ₁axle) to the polar coordinates angle γ of XOY face projection and the polar coordinates angle of pipeline section relevant physical quantity.At initial period, thickness of liquid film is 0.Accordingly, the boundary condition that thickness of liquid film solves is listed:

δ| _γ＝0＝0

In conjunction with the balanced relationship of equilibrium of forces and heat, finally solve the thickness of liquid film.Because equation is partial differential equation of second order form, direct solution is more difficult, needs to utilize Mathematical software such as MATLAB to solve.

5th step: for non-first floor coil pipe, considers the effect that liquid film is accumulative.By the method for continuous iteration, calculate the comprehensive mean heat transfer coefficient from the 1st layer of coil pipe to n-th layer coil pipe.The step calculated is:

1) calculate the standard flow pattern of sheet migration lime set, accounting equation is:

Re _film＝1.448Ar _l ^0.236

In formula: Re _film-be sheet migration lime set Reynolds number;

Ar _l-be the Archimedes number of liquid phase working fluid.

2) for non-first comb and n-th layer (n >=2), the calculation relational expression of migration lime set impact is provided:

${\mathrm{Re}}_{\mathrm{fall}}=\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{\mathrm{Re}}_{\mathrm{con},i}$

In formula: Re _film-be Reynolds number corresponding to migration lime set;

Re _{con, i}the Reynolds number that-the i-th layer of body lime set is corresponding; For first floor lime set, after thickness of liquid film and refrigerant flow rates are determined, Reynolds number is determined.Non-first floor lime set is then determined by continuous iteration.

3) calculate the angle χ corresponding when boundary layer reaches thickness of liquid film, its calculation relational expression is:

${\&Integral;}_0^{\mathrm{\&chi;}}{\left(\sin \mathrm{\&chi;}\right)}^{1/3}\mathrm{d\&chi;}=0.606\mathrm{Pr}{{\mathrm{Re}}^{4/3}}_{\mathrm{fall},n}{\mathrm{Ga}}^{-1/3}$

In formula: Pr-be Prandtl number, refrigeration working medium is determined, this value can be looked into and get;

Ga-be Galileo number.

4) calculate equivalent sheet migration length ratio Pfilm, its computing formula is:

P _film＝Re _fall,n/Re _film

5) according to P _filmand χ judges the computation model selected.Discriminant approach is as follows

Work as P _film>=1,

$\stackrel{\&OverBar;}{\mathrm{Nu}}=1.016{\mathrm{Pr}}^{1/3}{\mathrm{Re}}_{\mathrm{fall},n}^{1/9}{\mathrm{Ga}}^{-1/9}$

Work as P _film>=1, time,

Work as P _film<1, time,

${\stackrel{\&OverBar;}{\mathrm{Nu}}}^{*}=P_{\mathrm{film}}{\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{film}}+(1-P_{\mathrm{film}}){\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{con},n}^{*}$

Work as P _film<1, time,

By the calculating of above-mentioned five steps, finally obtain the computation model of Vertical spiral coil film condensation heat transfer.

For verifying the correctness of computation model of the present invention, herein by building experiment table, shell side side form shape condensation heat transfer coefficient is measured.This Vertical spiral coil formula condenser of the heat interchanger selected is the two waterway structure of cross-helicity, and the object done like this is to reduce water effluent dynamic resistance, increases heat interchanging area, reaches the object of enhanced heat exchange.As shown in Figures 3 to 5, Fig. 3 is side schematic view to the version of heat interchanger, and Fig. 4 is coil pipe schematic diagram, and Fig. 5 is vertical view, and wherein 1 is refrigerant inlet, and cold-producing medium flows out from 2 after spraying spiral coil from top to bottom comprehensively.Water enters from 4 entrances, moves from bottom to top in coil pipe, flows out from 3 outlets.This structure ensure that the counter-current flow of water and cold-producing medium, makes heat exchange more abundant.

Experimentation is as follows:

1) experimentally object, determines experimental system schematic diagram, as shown in Figure 5;

2) according to the applicable situation of condenser, experiment table parameter is preset;

3) experimentally parameter, carries out type selecting to experimental facilities, builds experiment table according to experimental principle figure;

4) utilize LabVIEW software to carry out acquisition and processing to experiment parameter, experiment parameter is stablized in the reasonable scope;

5) process experimental data, it is α=2279W/ (m that the method utilizing estimation to be separated calculates shell side side heat transfer coefficient ²k);

6) according to the operating mode measured, utilize computation model provided by the invention to calculate shell side side heat transfer coefficient, the heat transfer coefficient of calculating is α _j=2058W/ (m ²k);

Both errors are 9.7%.Prove that computation model is accurately reasonable.

The present invention has taken into full account Vertical spiral coil design feature, is applied in the computation process of film condensation heat transfer by liquid film cumulative effect simultaneously, and method is novel.Simultaneously by building experiment table checking, utilize the result of calculation of model compared with experimental result, error is within 10%.Proof model holds water.

The above is only to better embodiment of the present invention, not any pro forma restriction is done to the present invention, every any simple modification done above embodiment according to technical spirit of the present invention, equivalent variations and modification, all belong in the scope of technical solution of the present invention.

Claims (3)

1. computing method for the outer film condensation heat transfer of Vertical spiral coil, is characterized in that carrying out according to following steps:

Step 1: cartesian coordinate system is converted into dynamic rectangular coordinate system: dynamically rectangular coordinate system constantly changes along with the point on coil pipe, but dynamically the foundation of rectangular coordinate system all along the central axis of spiral coil, wherein X ₁axle along spiral pipe center position, X ₂x ₃axle is positioned on spiral pipe cross section, X ₃cross summit, cross section, wherein P ₀point is the center of circle in this cross section, i.e. P ₀point is coordinate system X ₁x ₂x ₃initial point, P point is any point on spiral pipe surface;

Step 2: the equilibrium relation of analytic liquid membrane forces and energy, find out the expression formula of liquid film velocity reversal Surface by Tangent Plane Method vector, calculate the expression formula of liquid film velocity reversal:

φ is liquid film speed direction and tube section (X ₂x ₃face) angle, speed direction should be

Step 3: the conservation that there is equilibrium of forces and energy on the section of thin film drainage velocity reversal, the balanced relationship of power and energy on liquid film:

Step 4: according to the balanced relationship of power on liquid film and energy, at initial period, thickness of liquid film is 0, lists the boundary condition that thickness of liquid film solves:

δ| _γ＝0＝0

In conjunction with the balanced relationship of equilibrium of forces and heat, finally solve the thickness of liquid film;

Step 5: for non-first floor coil pipe, considers the effect that liquid film is accumulative by the method for continuous iteration, to calculate the comprehensive mean heat transfer coefficient from the 1st layer of coil pipe to n-th layer coil pipe.

2., according to the computing method of the outer film condensation heat transfer of Vertical spiral coil a kind of described in claim 1, it is characterized in that: in described step 2, the expression formula solution procedure of liquid film velocity reversal is as follows:

First, by spiral coil kernel of section line and X ₁axial projection on surface level XOY face, its projection polar coordinates angle be γ, then in cartesian coordinate system with parametric equation by X ₁axle describes out, then calculates tangent vector according to parametric equation: vector equation is:

In formula: β angle is lead angle, t is pitch, and R is spirally-wound tubes radius;

Secondly, X is solved ₁the angle α of axle tangent line and surface level, in Vertical spiral coil coordinate system, α should be equal in lead angle, i.e. α=β;

Then: calculate section in the angle theta of surface level, calculate with the angle of the normal vector of two planes,

The normal vector of surface level:

The normal vector in section:

Wherein: for the polar coordinates angle of pipeline section,

e ₃be respectively along X ₁x ₂x ₃the unit vector in three directions

Then according to dot product formula:

The expression formula finally obtaining θ is:

3. according to the computing method of the outer film condensation heat transfer of Vertical spiral coil a kind of described in claim 1, it is characterized in that: in described step 5, the step that the comprehensive mean heat transfer coefficient from the 1st layer of coil pipe to n-th layer coil pipe calculates is:

1) calculate the standard flow pattern of sheet migration lime set, accounting equation is:

Re _film＝1.448Ar _l ^0.236

In formula: Re _film-be sheet migration lime set Reynolds number;

Ar _l-be the Archimedes number of liquid phase working fluid, its computing formula is wherein σ is the surface tension of liquid, and unit is Nm ^-1;

2) for non-first comb and n-th layer (n >=2), the calculation relational expression of migration lime set impact is provided:

${\mathrm{Re}}_{\mathrm{fall}}=\underset{i=1}{\overset{n-1}{\mathrm{\&Sigma;}}}{\mathrm{Re}}_{\mathrm{con},i}$

In formula: Re _film-be Reynolds number corresponding to migration lime set;

Re _{con, i}the Reynolds number that-the i-th layer of body lime set is corresponding; For first floor lime set, after thickness of liquid film and refrigerant flow rates are determined, Reynolds number is determined, is then determined by continuous iteration for non-first floor lime set;

3) calculate the angle χ corresponding when boundary layer reaches thickness of liquid film, its calculation relational expression is:

${\&Integral;}_0^{\mathrm{\&chi;}}{\left(\sin \mathrm{\&chi;}\right)}^{1/3}\mathrm{d\&chi;}=0.606\mathrm{Pr}{{\mathrm{Re}}^{4/3}}_{\mathrm{fall},n}{\mathrm{Ga}}^{-1/3}$

In formula: Pr-be Prandtl number, refrigeration working medium is determined, this value can be looked into and get;

Ga-be Galileo number, computing formula is:

4) equivalent sheet migration length ratio P is calculated _film, its computing formula is:

P _film＝Re _fall,n/Re _film；

5) according to P _filmand χ judges the computation model selected; Discriminant approach is as follows

Work as P _film>=1,

$\stackrel{\&OverBar;}{\mathrm{Nu}}=1.016{\mathrm{Pr}}^{1/3}{\mathrm{Re}}_{\mathrm{fall},n}^{1/9}{\mathrm{Ga}}^{-1/9}$

Work as P _film>=1, time,

Work as P _film<1, time,

${\stackrel{\&OverBar;}{\mathrm{Nu}}}^{*}=P_{\mathrm{film}}{\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{film}}+(1-P_{\mathrm{film}}){\stackrel{\&OverBar;}{\mathrm{Nu}}}_{\mathrm{con},n}^{*}$

Work as P _film<1, time,