Conductive transfer. Conductive heat transfer in a flat wall. Uniqueness conditions – boundary conditions

Among the processes of complex heat exchange, a distinction is made between radiation-convective and radiation-conductive heat exchange.

is divided by their sum. Radiation-conduction heat transfer in a flat layer for other initial conditions is considered in [L. 5, 117, 163]; for a cylindrical layer - in [L. 116].

So why, in the region classified as fluidized beds of large particles, do the maximum heat transfer coefficients increase with increasing diameter? It's all about gas-convective heat exchange. In layers of small particles, gas filtration rates are too low for the convective component of heat transfer to “manifest” itself. But with increasing grain diameter it increases. Despite the low conductive heat transfer, in a fluidized bed of large particles, the growth of the convective component compensates for this disadvantage.

Chapter fourteen Radiation-conduction heat transfer

14-2. Radiation-conduction heat transfer in a flat layer of a gray absorbing medium without heat sources

14-3. Radiation-conduction heat exchange in a flat layer of a selective and anisotropically scattering medium with heat sources

Thus, based on the above and some other, more specific works, it becomes obvious that radiation-conduction heat transfer in systems containing volumetric heat sources has clearly not been sufficiently studied. In particular, the influence of the selectivity of the medium and boundary surfaces and the influence of the anisotropy of volume and surface scattering have not been clarified. In connection with this, the author undertook an approximate analytical solution to the problem of radiation-coductive heat transfer in a flat layer.

thermal and convective heat transfer. Special cases of this guide to heat transfer are: radiation heat transfer in a moving medium (in the absence of conductive transfer), radiation-conductive heat transfer in a stationary medium (in the absence of convective (transfer) and purely “convective heat transfer in a moving medium, when there is no radiative transfer. The complete system of equations describing the processes of radiation-convective heat transfer was considered and analyzed in IB Chapter 12.

In equation (15-1), the total heat transfer coefficient from the flow to the channel wall can be found based on (14-14) and (14-15). For this purpose, we will consider, within the framework of the adopted scheme, the process of heat exchange between the flowing medium and the boundary surface as radiation-conduction heat exchange between the flow core and the channel wall through a boundary layer of thickness b. Let us equate the temperature of the flow core with the average calorimetric temperature of the medium in a given section, which can be done taking into account the small thickness of the boundary layer compared to the diameter of the channel. Considering the flow core as one of the boundary surfaces [with the temperature in a given section of the channel T(x) and absorption capacity ag], and as another - the channel wall (with temperature Tw and absorption capacity aw), we consider the process of radiation-conduction heat transfer through the boundary layer. Applying (14-14), we obtain an expression for the local heat transfer coefficient a in a given section: Problems of radiation-convective heat transfer, even for simple cases, are usually more difficult than the problem of radiation-conductive heat transfer. Below is an approximate solution [L. 205] of one common problem of radiation-convective heat transfer. Significant simplifications allow us to complete the solution.

As shown in [L. 88, 350], the tensor approximation under certain conditions is a more accurate method that opens up new opportunities in the study of heat transfer processes by radiation. In (L. 351] the proposed tensor approximation (L. 88, 350] was used to solve the combined problem of radiation-conductive heat transfer and gave good results. Subsequently, the author generalized the tensor approximation “and the case of spectral and total radiation for arbitrary indicatrices volumetric and surface scattering in radiating systems [L. 29, 89].

Using an iterative method for solving problems of complex heat transfer, one should first specify the values ​​of Qpea.i for all zones and determine on an electrical integrator of the described type the resulting temperature field for the accepted distribution Qpea.i (i=l 2,..., n), on the basis of which the temperature field is calculated second approximation of all quantities
Radiation-conduction heat transfer is considered in relation to a flat layer of an attenuating medium. Two problems have been solved. The first is an analytical consideration of radiation-conduction heat transfer in a flat layer of a medium without any restrictions regarding the temperatures of the surfaces of the layer. In this case, the medium and boundary surfaces were assumed to be gray, and there were no internal heat sources in the medium. The second solution relates to the symmetric problem of radiation -conductive heat exchange in a flat layer of a selective and anisotropically dissipating medium with heat sources inside the layer. Results of solving the first problem

As special cases, from the system of complex heat transfer equations follow all the individual equations considered in hydrodynamics and heat transfer theory: the equations of motion and continuity of the medium, the equations of purely conductive, convective and radiation heat transfer, the equations of radiation-conductive heat transfer in a stationary medium and, finally, the equations of radiative heat transfer in a moving but non-heat-conductive medium.

Radiation-conduction heat exchange, which is one of the six types of complex heat exchange, takes place in various fields of science and technology (astro- and geophysics, metallurgical and glass industries, electrovacuum technology, production of new materials, etc.). The need to study the processes of radiation-conduction heat transfer also leads to problems of energy transfer in the boundary layers of flows of liquid and gaseous media and problems of studying the thermal conductivity of various translucent materials.

but to calculate the process of radiation-"conductive heat transfer IB those conditions for which the obtained solutions are valid. Numerical solutions of the problem provide a clear picture of the process under study for (specific cases, without requiring the introduction of many restrictions inherent in approximate analytical studies. Both analytical and Numerical solutions are undoubtedly a well-known (progress in the study of radiative-tonductive heat transfer processes, despite their limited and private nature.

This chapter discusses two analytical solutions performed by the author to the problem of radiation-conduction heat transfer in a flat layer of a medium. The first solution considers the problem in the absence of restrictions regarding temperatures, absorption abilities of boundary surfaces and optical thicknesses of the medium layer [L. 89, 203]. This solution was carried out by the iteration method, and the medium and boundary surfaces are assumed to be gray, and there are no heat sources in the volume of the medium.

Rice. 14-1. Scheme for solving the problem of radiation-conduction heat transfer in a flat layer of an absorbing and heat-conducting medium in the absence of internal heat sources in the medium.

The most detailed analytical study was carried out on the above-considered problem of radiation-conductive heat transfer through a layer of gray, purely absorbing medium when the temperatures of the gray boundary surfaces of the layer are specified and in the absence of heat sources in the medium itself. The problem of radiation-conduction heat exchange between a layer of radiating and heat-conducting medium with boundary surfaces in the presence of heat sources in the volume has been considered in a very limited number of works with the adoption of certain assumptions.

For the first time, an attempt to take into account internal heat sources in the processes of “radiation-conduction heat transfer” was made in [L. 208], where the problem of heat transfer by radiation and thermal conductivity through a layer of gray, non-scattering medium with a uniform distribution of sources throughout the volume was considered. However, a mathematical error made in the work negated the results obtained.

The process of heat transfer by thermal conductivity is explained by the exchange of kinetic energy between the molecules of a substance and the diffusion of electrons. These phenomena occur when the temperature of a substance is different at different points or when two bodies with different degrees of heating come into contact.

The basic law of thermal conductivity (Fourier's law) states that the amount of heat passing through a homogeneous (homogeneous) body per unit time is directly proportional to the cross-sectional area normal to the heat flow and the temperature gradient along the flow

where R T is the power of the heat flow transmitted by thermal conductivity, W;

l - thermal conductivity coefficient, ;

d - wall thickness, m;

t 1, t 2 - temperature of the heated and cold surface, K;

S - surface area, m2.

From this expression we can conclude that when developing the design of RES, the heat-conducting walls should be made thin, thermal contact should be ensured over the entire area in the connections of parts, and materials with a high thermal conductivity coefficient should be selected.

Let us consider the case of heat transfer through a flat wall of thickness d.

Figure 7.2 – Heat transfer through the wall

The amount of heat transferred per unit time through a section of the wall with area S will be determined by the already known formula

This formula is compared to Ohm's law equation for electrical circuits. It is not difficult to see their complete analogy. So the amount of heat per unit time P T corresponds to the current value I, the temperature gradient (t 1 - t 2) corresponds to the potential difference U.

The attitude is called T e r m i c h e s k i m resistance and denoted by R T,

The considered analogy between the flow of heat flow and electric current not only allows us to note the commonality of physical processes, but also facilitates the calculation of thermal conductivity in complex structures.

If in the considered case the element that needs to be cooled is located on a plane having a temperature t CT1, then

t ST1 = P T d/(lS) + t ST2.

Therefore, to reduce t CT1, it is necessary to increase the area of ​​the heat-removing surface, reduce the thickness of the heat-transmitting wall, and select materials with a high thermal conductivity coefficient.

To improve thermal contact, it is necessary to reduce the roughness of the contacting surfaces, cover them with heat-conducting materials and create contact pressure between them.

The quality of thermal contact between structural elements also depends on electrical resistance. The lower the electrical resistance of the contact surface, the lower its thermal resistance, the better the heat dissipation.

The lower the heat removal capacity of the environment, the longer it will take to establish a stationary heat transfer regime.

Typically the cooling part of the design is the chassis, housing or casing. Therefore, when choosing a design layout option, you need to look at whether the cooling part of the structure chosen for mounting has the conditions for good heat exchange with the environment or is heat-resistant.

PREFACE

“Hydraulics and Heat Engineering” is a basic general engineering discipline for students studying in the direction of “Environmental Protection”. It consists of two parts:

Theoretical foundations of technological processes;

Typical processes and devices of industrial technology.

The second part includes three main sections:

Hydrodynamics and hydrodynamic processes;

Thermal processes and apparatus;

Mass transfer processes and apparatus.

For the first part of the discipline, lecture notes by N.Kh. Zinnatullina, A.I. Guryanova, V.K. Ilyina (Hydraulics
and Heat Engineering, 2005); for the first section of the second part of the discipline - textbook N.Kh. Zinnatullina, A.I. Guryanova, V.K. Ilyina, D.A. Eldasheva (Hydrodynamics and hydrodynamic processes, 2010).

This manual outlines the second section of the second part. This section will discuss the most common cases of conductive and convective heat transfer, industrial methods of heat transfer, evaporation, as well as the operating principle and design of heat exchange equipment.

The textbook consists of three chapters, each of which ends with questions that students can use for self-control.

The main objective of the presented textbook is to teach students to carry out engineering calculations of thermal processes and select the necessary equipment for their implementation.

PART. 1. HEAT TRANSFER

Industrial technological processes proceed in a given direction only at certain temperatures, which are created by supplying or removing thermal energy (heat). Processes, the rate of which depends on the rate of heat supply or removal, are called thermal. The driving force of thermal processes is the temperature difference between the phases. The devices in which thermal processes are carried out are called heat exchangers; heat is transferred into them by coolants.

The calculation of heat transfer processes usually comes down to determining the interphase heat transfer surface. This surface is
from the heat transfer equation in integral form. The heat transfer coefficient, as is known, depends on the heat transfer coefficients of the phases,
as well as from the thermal resistance of the wall. Below we will consider methods for determining them, finding the temperature field and heat flows. Where possible, the required quantities are found from solving the equations of conservation laws, and in other cases simplified mathematical models or the method of physical modeling are used.

Convective heat transfer

During convection, heat transfer occurs by macrovolume particles of the coolant flow. Convection is always accompanied by thermal conductivity. As is known, thermal conductivity is a molecular phenomenon, convection is a macroscopic phenomenon, in which
Whole layers of coolant with different temperatures are involved in heat transfer. Heat is transferred much faster by convection than by conduction. Convection near the surface of the apparatus wall decays.

Convective heat transfer is described by the Fourier-Kirchhoff equation. The patterns of medium flow are described by the Navier-Stokes (laminar regime) and Reynolds (turbulent regime) equations, as well as the continuity equation. The study of the patterns of convective heat transfer can be carried out in isothermal and non-isothermal formulations.

In the isothermal formulation, the Navier-Stokes and continuity equations are first solved, then the obtained velocity values ​​are used to solve the Fourier-Kirchhoff equation. The values ​​of heat transfer coefficients obtained in this way are subsequently refined and corrected.

In the non-isothermal formulation, the Navier-Stokes, continuity and Fourier-Kirchhoff equations are solved jointly, taking into account the dependence of the thermophysical properties of the medium on temperature.
As experimental data show, the dependences with p(T), l( T)
and r( T) are weak, and m( T) - very strong. Therefore, usually only the dependence m( T). It, this dependence, can be presented in the form of an Arrhenius dependence or, more simply, in the form of an algebraic equation. Thus, so-called coupled problems arise.

Recently, methods have been developed for solving many problems of heat transfer in laminar fluid flows, taking into account the dependence of the fluid viscosity on temperature. For turbulent flows everything is more complicated. However, it is possible to use approximate numerical solutions using computer technology.

To solve these equations, it is necessary to set uniqueness conditions, which include initial and boundary conditions.

Heat transfer boundary conditions can be specified in various ways:

Boundary conditions of the first kind are specified by the wall temperature distribution:

; (19)

the simplest case is when T c t = const;

Boundary conditions of the second kind - the heat flow distribution on the wall is specified

; (20)

Boundary conditions of the third kind - the temperature distribution of the medium surrounding the channel and the heat transfer coefficient are specified
from the environment to the wall or vice versa

. (21)

The choice of the type of boundary condition depends on the operating conditions of the heat exchange equipment.

On a flat plate

Let us consider a flow with constant thermophysical characteristics (r, m, l, c p= const), performing forced movement along a flat semi-infinite thin plate and exchanging heat with it. Let us assume that an unlimited flow with a speed
and temperature T° runs into a semi-infinite plate coinciding
with plane X – z and having a temperature T st = const.

Let us distinguish the hydrodynamic and thermal boundary layers
with thickness d g and d t respectively (area 99% change in speed w x
and temperature T). In the thread core and T° are constant.

Let us analyze the continuity and Navier-Stokes equations. The problem is two-dimensional because w z, . According to experimental data, it is known that in the hydrodynamic boundary layer . In the thread core const, therefore, according to the Bernoulli equation , in the boundary layer the same

.

As is known " X» d g, therefore .

Therefore, we have

; (22)

. (23)

Write similar equations for the axis at doesn't make sense because w y can be found from the continuity equation (22). Using similar procedures, you can simplify the Fourier-Kirchhoff equation

. (24)

The system of differential equations (22)–(24) constitutes an isothermal mathematical model of a flat stationary thermal laminar boundary layer. Let us formulate the boundary conditions
at the boundary with the plate, i.e. at at= 0: for any X speed w x= 0 (no-slip condition). On the boundary and outside the hydrodynamic boundary layer,
those. at at≥ d g ( X), as well as X= 0 for any at: w x= . For the temperature field there are similar arguments.

So, the boundary conditions:

w x ( x, 0) = 0, x > 0; w x (x, ∞) = ; w x(0, y) = ; (25)

T (x, 0) = T st, x > 0; T (x, ∞) = T ° ; T (0, y) = T°. (26)

An exact solution to this problem in the form of infinite series was obtained by Blasius. There are simpler approximate solutions: the method of integral relations (Yudaev) and the momentum theorem (Schlichting). A.I. Razinov solved the problem using the method of conjugate physical
and mathematical modeling. Velocity profiles were obtained
w x (x, y), w y ( x,y) and temperatures T, as well as the thickness of the boundary layers
d g ( x) and d t ( X)

; (27)

, Pr ≥ 1; (28)

Pr= ν/a.

Coefficient A in formula (27) for Razinov – 5.83; Yudaeva – 4.64; Blausius – 4; Sizing – 5.0. An approximate form of the found dependencies is shown in Fig. 1.3.

As is known, for gases Pr≈ 1, drip liquids Pr > 1.

The results obtained make it possible to determine the coefficients of momentum and heat transfer. Local values ​​γ( x) And Nu G, x

, . (29)

y

w x

T st

(T–T st)

d g ( x)

d t ( x)

x

Rice. 1.3. Hydrodynamic and thermal laminar boundary layers

on a flat plate

Average values ​​and along a section length l

,
, . (30)

Similarly for heat transfer

,
; (31)

, . (32)

In this case, the analogy of heat and impulse transfer is preserved (the initial equations are the same, the boundary conditions are similar). The criterion characterizing the hydrodynamic analogy of the heat transfer process has the form

P t-g, x = Nu T, x/Nu G, x = Pr 1/3 . (33)

If Pr= 1, then P t-g, x= 1, therefore a complete analogy of the processes of pulse and heat transfer.

From the resulting equations it follows

γ ~ , m; a ~ , l. (34)

As a rule, such a qualitative dependence holds
not only for a flat boundary layer, but also for more complex cases.

The problem is considered in an isothermal formulation, thermal boundary conditions of the first kind T st = const.

As you move away from the edge of the plate (increasing coordinates X) there is an increase in d g ( X). In this case, the inhomogeneity of the velocity field w x spreads to areas increasingly distant from the phase boundary,
which is a prerequisite for the occurrence of turbulence. Finally, when Rex, kp the transition from laminar to turbulent regime begins. The transition zone corresponds to the values X, calculated according to Rex from 3.5 × 10 5 ÷ 5 × 10 5.
At distances Rex> 5 × 10 5 the entire boundary layer is turbulized,
with the exception of a viscous or laminar sublayer with a thickness of d 1g. In the core of the flow, the speed does not change. If Pr> 1, then inside the viscous sublayer we can distinguish a thermal sublayer of thickness d 1m, in which molecular heat transfer prevails over turbulent heat transfer.

The thickness of the entire turbulent thermal boundary layer is usually determined from the condition ν t = a t, therefore d g = d t.

First, consider a turbulent hydrodynamic boundary layer (Fig. 1.4). Let us leave in force all the approximations made for the laminar layer. The only difference is the presence of ν t ( at), That's why

. (35)

Let us also preserve the boundary conditions. By solving the system of equations (35)
and (22) with boundary conditions (25), using the semi-empirical Prandtl wall turbulence model, the characteristics of the turbulent boundary layer can be obtained. In the viscous sublayer, where the linear law of velocity distribution is implemented, turbulent momentum transfer can be neglected, and outside it, molecular transfer. In the near-wall region
(minus the viscous sublayer), a logarithmic velocity profile is usually adopted, and in the outer region, a power law with an exponent of 1/7 (Fig. 1.4).

Rice. 1.4. Hydrodynamic and thermal turbulent boundary layers

on a flat plate

As in the case of a laminar boundary layer, it is possible to use length-averaged l impulse return coefficients

. (36)

Let us consider a thermal turbulent boundary layer. The energy equation is

. (37)

If Pr> 1, then inside the viscous sublayer we can distinguish a thermal sublayer, where molecular heat transfer

. (38)

For the local heat transfer coefficient, the solution of the mathematical model has the form

Average value over the plate length defined like this

Below are the formation of a turbulent boundary layer (a) and the distribution of the local heat transfer coefficient (b) during longitudinal flow around a flat semi-infinite plate (Fig. 1.5).

Rice. 1.5. Boundary layers d g and d t and local heat transfer coefficient a

on a flat plate

In the laminar layer ( X ≤ l kr) heat flow only due to thermal conductivity; for a qualitative assessment, the relation a ~ can be used.

In the transition zone, the total thickness of the boundary layer increases. However, the value of a increases in this case, because the thickness of the laminar sublayer decreases, and in the resulting turbulent layer, heat is transferred not only by thermal conductivity, but also by convection together
with a moving mass of liquid, i.e. more intense. As a result, the total thermal resistance of heat transfer decreases. In the zone of developed turbulent regime, the heat transfer coefficient again begins to decrease due to an increase in the total thickness of the boundary layer a ~ .

So, the hydrodynamic and thermal boundary layers on a flat plate are considered. The qualitative nature of the obtained dependencies is also valid for boundary layers formed during flow around more complex surfaces.

Heat transfer in a round pipe

Let us consider stationary heat exchange between the walls of a horizontal straight pipe of circular cross-section and a flow that has constant thermophysical characteristics and moves due to forced convection inside it. Let us accept thermal boundary conditions of the first kind, i.e. T st = const.

I.Areas of hydrodynamic and thermal stabilization.

When liquid enters the pipe, due to braking caused by the walls, a hydrodynamic boundary layer is formed on them.
As you move away from the entrance, the thickness of the boundary layer increases,
while the boundary layers adjacent to the opposite walls
won't close. This section is called the initial or hydrodynamic stabilization section - l ng.

Just as the velocity profile changes along the length of the pipe, the
and temperature profile.

II.Let's consider laminar fluid motion.

Earlier, in the section of the discipline “Hydrodynamics and hydrodynamic processes”, we considered the hydrodynamic initial section. To determine the length of the initial section, the following relationship was proposed

.

For liquid Pr> 1, therefore, the thermal boundary layer will be located inside the hydrodynamic boundary layer.
This circumstance allows us to assume that the thermal boundary layer develops in a stabilized hydrodynamic section and the velocity profile is known - parabolic.

The temperature of the liquid in the inlet section of the heat exchange section is constant over the cross section and is equal to T° and in the thread core it does not change. Under these conditions, the thermal boundary layer equation has the form

. (41)

Solving this equation under the above conditions gives:

for the length of the thermal initial section

; (42)

for local heat transfer coefficient

; (43)

for average heat transfer coefficient length

; (44)

· for local Nusselt number

; (45)

· for the average Nusselt number

. (46)

Let's consider equation (42). If , That .
For liquids Pr> 1, so in most cases, especially
for liquids with large Pr, heat exchange during laminar movement occurs mainly in the thermal stabilization section. As can be seen from relation (43), a for a pipe in the thermal stabilization section decreases with distance from the inlet (the thickness of the thermal boundary layer dt increases) (Fig. 1.6).

Rice. 1.6. Temperature profile at the initial and stabilized sections

with laminar flow of liquid in a cylindrical pipe

With a turbulent flow in a pipe, as on a flat plate, firstly, the thicknesses of the hydrodynamic and thermal boundary layers coincide; and secondly, they grow much faster than for laminar ones. This leads to a decrease in the length of thermal sections
and hydrodynamic stabilization, which allows in most cases to neglect them when calculating heat transfer

. (47)

III.Stabilized heat transfer with laminar movement of the medium.

Let us consider stationary heat transfer in a round pipe, when the thermophysical properties of the liquid are constant (isothermal case), the velocity profile does not change along the length, the temperature of the pipe wall is constant and equal to T st, there are no internal heat sources in the flow,
and the amount of heat released due to energy dissipation is negligible. Under these conditions, the heat transfer equation has the same form as for the boundary layer. Therefore, the initial equation for studying heat transfer is equation (41).

Border conditions:

(48)

The solution to this problem was first obtained by Graetz, then by Nusselt, in the form of a sum of an infinite series. A slightly different solution was obtained by Shumilov and Yablonsky. The resulting solution is correct
and for the thermal stabilization section, subject to preliminary hydrodynamic stabilization of the flow.

For the region of stabilized heat transfer, the local heat transfer coefficient is equal to the limiting one

or (49)

As can be seen from the figure (Fig. 1.7), with increasing number Nu decreases, asymptotically approaching in the second section of the curve
to a constant value Nu= 3.66. This occurs because for stabilized heat transfer the temperature profile along the length of the pipe
does not change. In the first section, a temperature profile is formed. The first section corresponds to the thermal initial section.

10 –5 10 –4 10 –3 10 –2 10 –1 10 0

1

3,66

Nu

Nu

Rice. 1.7. Change local and average Nu along the length of a round pipe at T st = const

IV.Stabilized heat transfer during turbulent movement of the medium.

Original equation

. (50)

Border conditions:

(51)

When solving the problem, the problem of choosing a speed profile arises w x. Some for w x use the logarithmic law (A.I. Razinov), others use the 1/7 law (V.B. Kogan). The conservatism of turbulent flows is noted, which consists in the weak influence of boundary conditions and the velocity field w x on heat transfer coefficients.

The following formula is proposed for the Nusselt number

. (52)

As for laminar movement in the region of stabilized heat exchange with turbulent flow of the medium Nu does not depend on the coordinate X.

We considered above special cases of heat transfer, namely: with an isothermal formulation of the problem and thermal boundary conditions of the first kind, heat transfer in smooth cylindrical pipes and flat horizontal plates.

In the literature there are solutions to thermal problems for other cases. Note that the surface roughness of the pipe and plate leads to
to increase the heat transfer coefficient.

Heat supply

To solve this problem, various coolants are used.
TN are classified by:

1. By purpose:

Heating HP;

Cooling HP, coolant;

Intermediate TN;

Drying agent.

2. According to the state of aggregation:

· Single-phase:

Low temperature plasma;

Non-condensing vapors;

Liquids that do not boil and do not evaporate at a given pressure;

Solutions;

Grainy materials.

· Multi-, two-phase:

Boiling, evaporating and gaseous liquids;

Condensing vapors;

Melting, solidifying materials;

Foams, gas suspensions;

Aerosols;

Emulsions, suspensions, etc.

3. By temperature and pressure range:

High-temperature HP (smoke, flue gases, molten salts, liquid metals);

Medium temperature heat pumps (water vapor, water, air);

Low temperature HP (at atmospheric pressure T kip ≤ 0 °C);

cryogenic (liquefied gases - oxygen, hydrogen, nitrogen, air, etc.).

As pressure increases, the boiling point of liquids also increases.

Industrial enterprises use flue gases and electricity as direct sources of thermal energy. Substances that transfer heat from these sources are called intermediate heating elements. The most common intermediate TN:

Water vapor is saturated;

Hot water;

Overheated water;

Organic liquids and their vapors;

Mineral oils, liquid metals.

Requirements for TN:

Big r, with p;

High heat of vaporization;

Low viscosity;

Non-flammable, non-toxic, heat resistant;

Cheapness.

Heat removal

Many industrial technology processes take place under conditions where there is a need to remove heat, for example, when cooling gases, liquids or during condensation of vapors.

Let's look at some cooling methods.

Cooling with water and low-temperature liquid refrigerants.

Water cooling is used to cool the medium to 10–30 °C. River, pond and lake water, depending on the time of year, has a temperature of 4–25 °C, artesian water – 8–12 °C, and circulating water (in summer) – about 30 °C.

Cooling water flow determined from the heat balance equation

. (83)

Here is the flow rate of the coolant; N n and N k – initial
and the final enthalpy of the coolant being cooled; N nv and N kv – initial
and final enthalpy of cooling water; – losses to the environment.

Achieving lower cooling temperatures can be achieved
using low temperature liquid refrigerants.

Air cooling. Air is most widely used as a cooling agent in mixing heat exchangers - cooling towers, which are the main element of the water circulation cycle equipment (Fig. 2.5).

Rice. 2.5. Cooling towers with natural (a) and forced (b) draft

The hot water in the cooling tower is cooled both by contact with cold air and by so-called evaporative cooling,
in the process of evaporation of part of the water flow.

Mixing heat exchangers

In mixing heat exchangers (MHE), heat transfer from one coolant to another occurs when they are in direct contact or mixing, therefore, there is no thermal resistance of the wall (separating the coolant). Most often, SRT is used for condensing vapors, heating and cooling water and vapors. Based on the design principle, service stations are divided into bubbling, shelf, packed and hollow (with liquid splashing) (Fig. 2.18).

steam

water

V

air

water

water

water

steam

G

steam

heated liquid

A

air

water

steam

water + condensate

b

liquid

Rice. 2.18. Service station diagrams: a) bubbling mixing heat exchanger for heating water;

b) packed heat exchanger-condenser; c) shelf barometric capacitor; d) hollow

PART 3. EVAPORATION

Evaporation is the process of concentrating solutions of non-volatile solids by removing the volatile solvent in the form of vapor. Evaporation is usually carried out at boiling. Typically, only part of the solvent is removed from a solution, since the substance must remain
in a fluid state.

There are three evaporation methods:

Surface evaporation is carried out by heating the solution on the heat exchange surface due to the supply of heat to the solution through the wall from the heating steam;

Adiabatic evaporation, which occurs by flashing a solution in a chamber where the pressure is lower than the saturated vapor pressure;

Evaporation by contact evaporation - heating of a solution is carried out by direct contact between a moving solution
and hot coolant (gas or liquid).

In industrial technology, the first evaporation method is mainly used. Next about the first method. To carry out the evaporation process, it is necessary to transfer heat from the coolant to the boiling solution, which is only possible if there is a temperature difference between them. The temperature difference between the coolant and the boiling solution is called the useful temperature difference.

Saturated water vapor (heating or primary) is used as a coolant in evaporators. Evaporation is a typical heat exchange process - the transfer of heat due to the condensation of saturated water vapor to a boiling solution.

Unlike conventional heat exchangers, evaporators consist of two main units: a heating chamber or boiler and a separator. The separator is designed to catch drops of solution from steam that forms during boiling. This steam is called secondary or juice. The temperature of the secondary steam is always less than the boiling point of the solution. To maintain a constant vacuum in the condenser, it is necessary to suck out the vapor-gas mixture with a vacuum pump.

Depending on the pressure of the secondary steam, evaporation is distinguished at R atm, R hut, R vac. In case of evaporation at R vac the boiling point of the solution decreases, with p hut - secondary steam is used for technological purposes. The boiling point of a solution is always higher than the boiling point of a pure solvent. For example, for a saturated aqueous solution
NaCl (26%) T kip = 110 °C, for water T kip = 100 °C. Secondary steam taken from the evaporation plant for other needs is called extra ferry.

Temperature losses

Usually in single-shell evaporation plants the pressures of the heating and secondary vapors are known, i.e. their temperatures. The difference between the temperatures of the heating and secondary vapors is called the total temperature difference of the evaporators

. (96)

Total temperature difference is related to the useful temperature difference by the relation

Here D¢ is the concentration temperature depression; D¢¢ - hydrostatic temperature depression; D¢ is determined as the difference in boiling point of the solution T kip. p and pure solvent T kip. chr at p = = const

D¢ = T kip. R - T kip. chr, T kip. chr, D¢ = T kip. R - T vp. (98)

The temperature of the secondary vapors formed during boiling of the solution is lower than the boiling point of the solution itself, i.e. some temperatures are lost uselessly; D¢¢ characterizes the increase in the boiling point of a solution with increasing hydrostatic pressure. Usually, the average pressure is determined by the height of the boiling pipes, and for this pressure the average boiling point of the solvent is determined T Wed

Here p a is the pressure in the apparatus; r pz - density of the vapor-liquid mixture
in boiling pipes ; H- height of boiling pipes.

D² = T Wed - T ch, (99)

Where T cp is the boiling point of the solvent at p = p Wed; T VP - temperature of secondary steam at pressure p A.

Multi-effect evaporation

In a multi-effect evaporator installation, secondary steam (Fig. 3.2, 3.3) from the previous body is used as heating steam
in the subsequent building. This organization of evaporation leads
to significant savings in heating steam. If we accept for all buildings, then the total consumption of heating steam for the process decreases in proportion to the number of buildings. In practice, in real conditions this ratio is not maintained; it is usually higher. Next, we will consider the equations of material and heat balances for a multi-vessel evaporation plant (see Fig. 3.2), which are a system of equations written for each vessel separately.

Thermal processes

And devices

HEAT EXCHANGE

Chemical technological processes proceed in a given direction only at certain temperatures, which are created by supplying or removing thermal energy (heat). Processes, the rate of which depends on the rate of heat supply or removal, are called thermal. The driving force of thermal processes is the temperature difference between the phases. The devices in which thermal processes are carried out are called heat exchangers; heat is transferred into them by coolants.

Calculation of heat transfer processes and devices usually comes down to determining the interphase heat transfer surface. This surface is from heat transfer equations in an integral form. Heat transfer coefficient, as is known, depends on the heat transfer coefficients of the phases, as well as on the thermal resistance of the wall. Below we will consider methods for determining them, finding the temperature field and heat flows. Where possible, the required quantities are found from solving the equations of conservation laws, and in other cases simplified mathematical models or the method of physical modeling are used.

Conductive heat transfer in a flat wall

Let us consider heat transfer in a stationary flat wall
from a homogeneous material whose thermophysical properties are constant
(with p, l, r = const) (Fig. 1.1).

Rice. 1.1. Temperature distribution in a flat wall

The general equation of non-stationary Fourier thermal conductivity has the form

(1)

The heat transfer process is stationary, then . We believe
that the height and length are much greater than the wall thickness d, therefore, there is no heat transfer in these directions, then the temperature changes only along one coordinate X, from here we have

Because the , we have

(2)

The obvious solution to this equation is

,

(3)

Border conditions:

at ;

at

We find And , , Then

. (4)

Distribution T by thickness d

. (5)

From the resulting equation (5) it is clear that in a flat wall the distribution T is straightforward.

Heat flow due to thermal conductivity is determined by Fourier's law

; (6)

. (7)

Here characterizes the thermal conductivity of the wall, and is the thermal resistance of the wall.

For a multilayer wall, the thermal resistance of the individual walls must be summed

. (8)

Let us determine the amount of heat transferred over time t across the square F

Conductive heat transfer (lat. conduce, conductum to reduce, connect) T. by conducting heat to (or from) the surface of any solid body in contact with the surface of the body.

Large medical dictionary. 2000 .

See what “conductive heat transfer” is in other dictionaries:

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Books

• Heat transfer and thermal testing of materials and structures of aerospace technology during radiation heating, Viktor Eliseev. The monograph is devoted to the problems of heat transfer and thermal testing of materials and structures of aerospace technology using high-intensity radiation sources. The results are given...