The main factors determining convective heat transfer are temperature difference and heat transfer coefficient. Temperature difference - averaged over the heating surface area, the temperature difference between the heating and heated media, depends on the mutual direction of their movement. The movement of the heating and heated media parallel to each other is called counter-current, and in one direction - direct-flow. The perpendicular direction of movement of one of the flows of media with respect to the direction of movement of another medium is called cross current. Elements of heating surfaces are also used with combined direct-flow and counter-flow, as well as with parallel and cross-flow media.
The schemes for washing the heating surfaces are shown in fig. 9 5. The greatest possible convective heat transfer is achieved with counterflow, the smallest - with forward flow, with all other schemes for switching on heating surfaces, the temperature difference has intermediate values. With a constant mass flow rate of heat carriers and a heat transfer coefficient for a given heating surface, the average temperature difference for the direct-flow and counter-flow schemes of media movement, °С, is determined by the formula
where Δt b is the temperature difference between the media at the end of the surface where the temperature difference is greater, °C; Δt m - temperature difference at the other end of the surface, °C.
At Δt b /Δt m ≤ Δt is determined with sufficient accuracy as the arithmetic mean temperature difference
For a mixed switching circuit, if the condition Δt Direct > 0.92 Δt prot is met, the temperature difference is determined by the formula
According to schemes with parallel and cross currents, the temperature difference is determined by the formula
where ty is the conversion factor. The ψ values increase from about 0.7 with a single cross current to 0.9 with a quadruple cross current.
In the case of significant changes in the heat capacity of one of the media (for example, steam at high pressure), as well as changes state of aggregation environment within a given element of the heating surface, the temperature difference is determined for individual sections, in which the heat capacity is assumed to be constant, and the average temperature difference for the entire element is determined by the formula
where Q 1 , Q 2 ... - heat absorption areas per 1 kg of each of the media, kJ / kg; Δt 1 , Δt 2 temperature differences in the respective areas, °C.
The heat transfer coefficient k, W / (m 2 * K), from heating gases to the working medium in smooth pipes of evaporating, superheating, economizer and air heating surfaces with a small thickness of the pipe wall in relation to its diameter is determined, as for a flat multilayer wall, according to formula
where ai and a 2 - heat transfer coefficients from the heating medium to the wall and from the wall to the heated medium, W / (m 2 * K); δ m and λ m - thickness and thermal conductivity of the metal pipe wall, M and W/(m*K); δc and λc are the thickness and thermal conductivity of the contaminant layer on outer surface pipes, m and W / (m * K); δ n and λ n - thickness and thermal conductivity of the scale layer inner surface pipes, m and W / (m * K).
During normal operation, scale deposits on the pipes of the economizer, the evaporative heating surface and the superheater should not reach a thickness that causes a significant increase in thermal resistance and an increase in the temperature of the pipe wall, and therefore, in the thermal calculation, the fraction δc / λc can be taken zero. The thermal resistance of the steel wall of the pipe with its small thickness (δ m = 0.002 - 0.004 m) and high thermal conductivity of steel at 300 ° C [λ m = 44.4 W / (m * K)] is much less than the thermal resistance on gas and air sides of the pipe, and therefore can be ignored.
Convective heat transfer of external pollution of the heating surface δ n / λ n significantly reduces the value of the heat transfer coefficient. The influence of pollution of convective heating surfaces on heat transfer is quantified by the pollution coefficient ε = δn / λn. In some cases, there is not enough data to determine e and the impact of pollution is estimated by the thermal efficiency coefficient, which is the ratio of the heat transfer coefficients of contaminated and clean pipes: ψ =k n / k. With incomplete washing of the heating surface, an uneven field of velocities and temperatures, as well as the presence dead zones the total decrease in the heat transfer coefficient by all these factors, as well as with pollution, is estimated by the utilization factor D. When burning solid fuels, e in transversely washed beams noticeably decreases with an increase in the washing rate and increases with an increase in the diameter of the pipes. Other same conditions the pollution coefficient in staggered beams turns out to be approximately 2 times lower than in the corridor ones. A decrease in the longitudinal relative pitch of pipes in staggered bundles significantly reduces the value of the pollution factor. In in-line bundles, the size of the longitudinal relative pitch has little effect on the value of e. The influence of the size of the transverse relative pitch of the pipes is also insignificant in their staggered and in-line arrangement. The direction of movement of the gas flow in the beam and the concentration of ash in the gases have almost no effect on it. The pollution of finned tubes is much greater than that of smooth tubes.
The main directions for creating low-polluted heating surfaces are to increase the velocity of gases in them and reduce the diameter of pipes. An increase in the gas flow rate is limited by an increase in the aerodynamic resistance of the bundle, as well as by the conditions for preventing wear of pipes by ash particles. Based on these conditions, the flow velocity for transversely washed tube bundles when operating solid fuel boilers is recommended to be 8-10 m/s, and for air heaters 10-14 m/s.
Pollution, thermal efficiency and use factors in various surfaces heating are given in . The pollution coefficient e, (m 2 * K) / W, in staggered tube bundles is determined from the expression
where ε 0 is the initial pollution factor; With d , With fr - amendments to the diameter of the pipes and the fractional composition of the ash; Δε - correction depending on the type of fuel and the location of the heating surface.
Heat transfer from combustion products to the wall occurs due to convection and radiation, and the heat transfer coefficient for convective beams, W / (m 2 * K), is determined by the formula
where ξ is the utilization factor of the heating surface. For transversely washed tube bundles of modern boilers ξ=1. For screens and difficultly washed tube bundles ξ = 0.85 / 0.9; and k - heat transfer coefficient by convection, W / (m 2 * K); a l - coefficient of heat transfer by radiation, W / (m 2 * K). The value of a k depends on the speed of the gases, the diameter of the pipes and the design of the bundle, as well as on the characteristics of the heating gases. The value of al depends on the temperature of the gases and their composition, as well as on the design of the tube bundle. The heat transfer coefficient from the wall to the working fluid depends on the flow rate and its physical characteristics. Thermal resistance with inside economizer pipes and evaporative heating surfaces, as well as superheaters of ultrahigh pressure boilers 1/a 2 is much less than 1/a 1 and can be neglected. In air heaters, the thermal resistance 1/a 2 is significant and must be taken into account.
Convective heat transfer for the screen heating surface is determined taking into account the heat received by the surface of the screens from the furnace:
where the factor (1+Q l /Q) takes into account the heat received from the firebox by the surface of the screens.
Heat transfer coefficient in staggered tube bundles of superheaters when burning solid fuels
Convective heat transfer for economizers, transition zones of once-through boilers and evaporator surfaces, and superheaters at supercritical pressure
Heat transfer coefficient for smooth-tube staggered and in-line bundles when burning gas and fuel oil, as well as in-line bundles when burning solid fuels:
for superheaters
for economizers, transition zones of once-through boilers, supercritical steam superheaters, as well as bundles and festoons of low-power boilers when operating on solid fuels
where ψ is the coefficient of thermal efficiency of the heating surface.
In case of mixed transverse-longitudinal washing of smooth-tube bundles, the heat transfer coefficients are determined separately for the transversely and longitudinally washed sections according to the average gas velocities for each of them and are averaged according to the formula
Heat transfer coefficient k, W / (m 2 * K), in tubular and plate air heaters
where ξ is the utilization factor, taking into account the combined effect of pollution, incomplete washing of the surface with gases and air, and air overflows in tube sheets.
The heat transfer coefficient of the plate packing of a rotating regenerative air heater, referred to the total double-sided surface of the plates,
where x 1 \u003d H r / H \u003d F in / F is the ratio of the area of \u200b\u200bthe heating surface washed by gases or the corresponding free section to full area surface or full section of the air heater; x 2 - the proportion of the heating surface area washed by air; a 1 and a 2 - heat transfer coefficients from gases to the wall and from the wall to air, W / (m 2 * k); n - coefficient taking into account the non-stationarity of heat transfer, at an air heater rotor speed n > 1.5 rpm ¶=1.
Heat transfer coefficient for cast-iron ribbed and ribbed-toothed, as well as plate air heaters
where ξ - utilization factor; a 1priv and a 2priv - reduced heat transfer coefficients from the gas and air sides, taking into account the heat transfer resistance of the surface and fins, W / (m 2 * K); N / N Vp - area ratio full surfaces from the gas and air sides.
Convective heat transfer by convection. Convective heat transfer by convection in the heating surfaces of the boiler varies over a wide range depending on the speed and temperature of the flow, which determines the linear size and location of the pipes in the bundle, the type of surface (smooth or ribbed) and the nature of its washing (longitudinal, transverse), physical properties washing medium, and in some cases - on the temperature of the wall. Stationary process convective heat transfer at constant physical parameters heat exchange media is described by the system differential equations conservation of energy, conservation of momentum, and conservation of mass flow. Under specific conditions, uniqueness conditions are attached to these equations: the values physical constants, velocity and temperature fields, design parameters, etc. The solution of these equations is difficult, and therefore, in engineering calculations, criterion dependences obtained on the basis of similarity theory and experimental data are used. The results of the study were processed in the form power dependencies Nu = / (Re Рг), where Nu, Re and Рг are the Nusselt, Reynolds and Prandtl numbers, respectively. When determining a to, the flow rate of combustion products, m / s, is determined by the formula
where F is the open area of the flue, m 2 ; В р - estimated fuel consumption, kg/h; W is the volume of combustion products per 1 kg of fuel, m 3 /kg, at a pressure of 100 kPa and 0 ° C, determined by the average coefficient of excess air in the flue.
Air velocity in the air heater, m/s,
where V 0 2 - the theoretical amount of air required for fuel combustion at a pressure of 100 kPa and 0°C; ß vp - coefficient taking into account air losses in the air heater and recirculation of gases into the furnace.
Velocity of water vapor or water in pipes, m/s,
where O is the consumption of steam, water, kg / h; v Ср - average specific volume of steam, water, m 3 /kg; f - area of the free section for the passage of steam, water, m 3 .
Clear area, m 2, for the passage of gases or air in gas ducts filled with pipes:
for transversely washed smooth tube bundles
where a and b are the dimensions of the flue in a given section, m 2; Z 1 - the number of pipes in a row; d and I - diameter and length of pipes, m.
With longitudinal washing of pipes and the flow of the medium inside the pipes
where z is the number of pipes connected in parallel;
when the medium flows between the pipes
Averaging of living sections for different areas on separate sections the gas duct is carried out from the condition of averaging the velocities. The temperature of the gas flow in the flue is taken equal to the sum the average temperature of the heated medium and the temperature difference. When gases are cooled by no more than 300 ° C, their average temperature can be determined as the arithmetic mean between the temperatures at the inlet and outlet of the gas duct. The heat transfer coefficient by convection a k, W / (m 2 * K), with transverse washing of in-line beams and screens, referred to the total area of the outer surface of the pipes, is determined by the formula
where C s - correction for the number of rows of pipes along the gas flow at z ≥ 10, C s = 1; C s - correction for the arrangement of the beam, determined depending on the ratio of the longitudinal and transverse pitch to the diameter . λ - thermal conductivity at an average flow temperature, W / (m 2 * K); v is the kinematic viscosity of the combustion products at the average flow temperature, m 2 /s; d - pipe diameter, m; w is the velocity of combustion products, m/s.
Heat transfer coefficient by convection during transverse washing of chess beams, W / (m 2 * K),
where C s is a coefficient determined depending on the relative transverse pitch σ 1 and the value of φ σ1 = (σ 1 - 1) / (σ "2 - 2), σ" 2= √0.025σ "1 + 2, σ" 2 - relative longitudinal pitch of pipes at 0.1< φ σ <1,7, С a = 0,34φ 0 σ ; С z - поправка на число рядов труб по ходу газов: при числе рядов труб z 2 < 10 и σ 1 <3,0 С z = 3,12 z 0’05 2 - 2,5.
For bundles in which the pipes are located partly in a checkerboard pattern, and partly in a corridor order, the heat transfer coefficient is determined separately for each part. Heat transfer coefficient a k, W / (m 2 * K), with a longitudinal flow around the heating surface by a single-phase turbulent flow at pressures and temperatures far from critical,
where d e - equivalent diameter, m; C t , C d , C l - corrections for flow temperature, pipe diameter and pipe length.
When flowing in a round pipe, the equivalent diameter is equal to the inner diameter. When flowing in a non-circular pipe or in an annular channel, rf 3 \u003d 4F / U, m, where F is the area of \u200b\u200bthe open section of the channel, m 2; U-washed perimeter, m. For a rectangular section filled with tubes of screens or convective bundles,
where a and b are the clear transverse dimensions of the flue, m; g - the number of pipes in the flue; d - outer diameter of pipes, m.
The correction Ct depends on the temperature of the flow and the wall. For combustion products and air, the Ct correction is introduced only when they are heated. With the flow of steam and water in the boiler Ct ≈ 1. Correction for the relative length of the pipe 1.4 at l / d=20.
Heat transfer coefficient from gas to screens, W / (m 2 * K),
where a k is the heat transfer coefficient by convection, referred to the total surface area of the screens, W / (m 2 * K); e - pollution factor, m 2 *K / W; x is the angular coefficient of the screens; S 2 - step between the screens, m. Heat transfer coefficient ak, W / (m 2 * K), for regenerative rotary air heaters (RVV)
The values of the coefficients Ct and C/ are determined in the same way as in the case of a longitudinal flow around the heating surface; when stuffing RVV from corrugated spacer sheets (see Ch. 20) A \u003d 0.027, from smooth spacer sheets A \u003d 0.021. With intensified packing, the equivalent diameter of the packing is d e = 9.6 mm, with non-intensified packing d e = 7.8 mm, for a cold stage consisting of smooth sheets, d e = 9.8 mm.
For cast-iron ribbed and ribbed-toothed air heaters manufactured by domestic factories, the reduced heat transfer coefficient from the gas side for clean pipes a Pr, W / (m 2 * K), referred to the total outer surface, is determined by the formula
where s rb is the step of the ribs, m.
The values of the remaining quantities are indicated above. The reduced convective heat transfer from the air side, referred to the total inner surface of the pipes with longitudinal ribs inside them, is determined by the formulas
where l Pr is the length of the finned part of the pipes, m.
Heat transfer coefficient by radiation. The amount of heat transferred to 1 m 2 of the heating surface by radiation of a gas flow, Q L, W / m 2 is determined using the heat transfer coefficient of radiation W / (m 2 * K),
where q l is the amount of heat transferred to 1 m 2 of the heating surface by radiation kJ / (m 2 * h); θ and t c - temperatures of gases and contaminated walls, 0ºС.
In the products of fuel combustion when using solid fuel, in addition to triatomic gases, there are ash particles suspended in the flow. Heat transfer coefficient of radiation of combustion products a, W / (m 2 * K):
for dusty flow
here a 3 is the integral coefficient of thermal radiation of the contaminated wall (for heating surfaces of the boiler a 3 = 0.8); a - the same gas flow at temperature T, which is determined by the formula a = 1 - e kps , here kps - the total optical thickness of the layer of fuel combustion products; p for naturally aspirated boilers is assumed to be 0.1 MPa; T is the temperature of the products, K; T 3 - temperature of the contaminated outer surface, K.
The optical thickness of the dusty flow kps = (k r r n + k el μ el)ps. The values of k r and k el depending on the partial pressure of triatomic gases, the thickness of the radiating layer and the concentration of ash are given in. For example, when the boiler is operating on solid fuel dust and the distance between the pipes is about 0.17 m, the value of fe 2 ≤ 2.8 and k el ≤ 8.2. For a non-dusty flow (combustion products of gaseous and liquid fuels), the second term is equal to zero.
The attenuation coefficient of rays by triatomic gases and particles is found from (9.19) and is determined from . Effective thickness of the radiating layer in the case of radiation of a gas volume limited on all sides, m,
where V is the volume of the radiating layer, m3; F og - the area of \u200b\u200benclosing surfaces, m 2.
For smooth tube bundles, m,
For bundles of finned tubes, the value of s obtained from (9.65) should be multiplied by 0.4.
The effective thickness of the radiant layer for the upper stage of the air heater is assumed to be 0.9 d for tubular air heaters, where d is the diameter of the pipes, m. pollution, °C.
where Q is the heat absorption of a given heating surface, kJ/kg, determined from the balance equation according to the previously accepted final temperature of one of the media; Q n - heat perceived by the surface by radiation from the furnace or from the volume in front of it, kJ / kg; t is the average temperature of the medium, °С; H - heating surface area, m 2; e - pollution factor, m 2 *K / W; and 2 - heat transfer coefficient from the wall to the steam, W / (m 2 * K).
The value 8 for staggered superheaters and screens is taken according to the data. For in-line and staggered superheaters and wall pipes when burning liquid fuels e» 0.003, and when burning solid fuels 8 ≈ 0.005 m 2 * K / W. In other cases, the wall temperature t 3 = t + Δt, °C.
For scallops Δt = 80 °С. For single-stage economizers at θ = 400°С, second-stage economizers and evaporative bundles of low-power boilers when burning solid and liquid fuels Δt = 60°С. For the first stages of economizers and single-stage air heaters, for staggered and in-line bundles when burning solid and liquid fuels at θ< 400°С Δt = 25ºС. При сжигании газа для всех поверхностей нагрева Δt = 25°С.
The heat transferred by radiation to the wall heating surface by a bundle of pipes to a row of pipes, kJ / kg, is determined by the formula
where a l is the coefficient of heat transfer by radiation, W / (m 2 * K); t a - temperature of the contaminated wall, °C; H l - area of the radiation-receiving heating surface, m 2 .
Section content
The concept of convective heat transfer covers the process of heat transfer during the movement of a liquid or gas. In this case, heat transfer is carried out simultaneously by convection and thermal conductivity. Convection is possible only in a fluid medium, here the transfer of heat is inextricably linked with the transfer of the medium itself. In this case, thermal conductivity is understood as the process of heat transfer with direct contact of individual particles of the medium having different temperatures.
Convective heat transfer between the flow of a liquid or gas and the surface of a solid body is called convective heat transfer. In engineering calculations, heat transfer is determined, while convective heat transfer inside the medium is of indirect interest, since the transfer of heat inside the medium is quantitatively protected on heat transfer.
In practical calculations, the Newton-Richmann law is used. According to the law, the heat flow - Q from the medium to the wall or from the wall to the medium is proportional to the heat transfer coefficient by convection - á k, the heat exchange surface - F and the temperature difference - ∆t = t c -t w, i.e.
Q \u003d á k (t c -t w) ⋅ F, W (kcal / hour),
where: t s – body surface temperature; t w is the temperature of the liquid or gaseous medium surrounding the body.
The heat flow - Q from the heating medium to the heated medium through the surface (wall) separating them is proportional to the heat transfer coefficient - k, the heat exchange surface - F and the temperature difference ∆t, i.e.
Q = ê⋅∆t⋅F, W (kcal/h).
The temperature difference ∆t in this case is the average temperature difference over the entire heating surface of the media involved in heat exchange. In the steady state mode of heat transfer for direct-flow and counter-flow schemes of movement of media, ∆t is determined by the average logarithmic difference between the temperatures of the heating and heated media according to the formula:
∆t = ∆t b - ∆t m, K (°C),
2.31g (∆ t b / ∆t m)
where: ∆ t b- temperature difference of the media at the end of the heat transfer surface, where it is the largest, K (°С); ∆ t m– temperature difference of the media at the other end of the heat transfer surface, where it is the smallest, K (°С); k - coefficient of proportionality, called the heat transfer coefficient, W / (m 2 ⋅K) or kcal / m 2 ⋅h⋅g.
It expresses the amount of heat in watts or kilocalories transferred from the heating medium to the interface heated through 1 m 2 for an hour at a temperature difference of 1 degree.
For a flat surface and for pipes with a ratio of outer diameter to inner diameter as d n≤ 2 heat transfer coefficient is determined by the formula:
ê \u003d 1, W / (m 2 K) or kcal / m 2 ⋅h⋅deg,
1 + Scm + 1
á gr á á naked
where: a gr- thermal resistance of heat transfer from the heating medium to the interface in m 2 ⋅K/W or m 2 ⋅h⋅deg/kcal (á is the coefficient of convective heat transfer of the heating medium);
ë is the thermal resistance of the wall; Scm is the wall thickness in m; ë – thermal conductivity of the wall material in W/(m⋅K) or kcal/m⋅h⋅deg;
á naked- thermal resistance to heat transfer from the wall to the heated medium in m 2 K / W or m 2 ⋅h⋅deg / kcal (á naked is the coefficient of convective heat transfer to the heated medium).
In thermal units (boilers) during heating and cooling of gases (air), the heat transfer coefficient á to varies within 17–58 W/m 2 K (15–50 kcal/m 2 ⋅h⋅deg). When heating and cooling water - within 233–11630 W / m 2 K (200–10000 kcal / m 2 ⋅h⋅deg).
Heat transfer coefficient á to depends on:
The nature of the flow of the medium, determined by the Reynolds criterion
Re = Wd = ñ ⋅ W ⋅d ;
The ratio of internal thermal resistances to external thermal resistances é, called the Nusselt criterion ë
Nu = a to d;
Physical properties of the medium (liquid, gases) characterized by the Prandtl criterion
Pr = í c ñ = í .
Heat transfer in turbulent flow regime
In the turbulent flow of various gases and liquids through long pipes and channels to determine á to the criterion equation of M.A. is most often used. Mikheev:
(with Re ≥ 10000 and é ≥ 50) : Nu = 0.021Re 0.8 Pr avg 0.43 (Pr avg) 0.25 ,
where Pr cf are the values of the Prandtl criterion at an average temperature of gases and liquids equal to half the sum of the flow temperatures at the inlet and outlet of the pipe; Pr st are the values of the Prandtl criterion at the temperature of gases and liquids equal to the average wall temperature.
Heat transfer coefficient á to in short pipes or channels (d< 50) имеет большие значения по сравнению с длинными трубами или каналами. Уравнение М.А. Михеева для течения по коротким трубам или каналам:
Nu = 0.021Re 0.8 Pr av 0.43 (Pr av) 0.25 ⋅ ϕ
The values of ϕ are given in Table. 7.20.
Table 7.20. Correction factor ϕ| Re | é Attitude d | |||||
| 2 | 5 | 10 | 20 | 40 | 50 | |
| 1⋅10 4 2⋅10 4 5⋅10 4 1⋅10 5 1⋅10 6 | 1,50 1,40 1,27 1,22 1,11 | 1,34 2,27 1,18 1,15 1,08 | 1,23 1,18 1,13 1,10 1,05 | 1,13 1,10 1,08 1,06 1,05 | 1,03 1,02 1,02 1,02 1,01 | 1,00 1,00 1,00 1,00 1,00 |
For example, for combustion products, the criterion Pr cf is 0.72, the equation of M.A. Mikheev takes the form:
á to dWd
For long pipes Nu ≅ 0.018Re 0.8 or = 0.018 () 0.8;
á to dWd
For short pipes Nu ≅ 0.018Re 0.8 ⋅ ϕ or = 0.018() 0.8 ⋅ ϕ .
From these equations, the heat transfer coefficients are determined:
For long pipes and channels
á to\u003d 0.018 ⋅ ⋅, W / m 2 K, (kcal / m 2 hour deg).
For short pipes and channels
á to\u003d 0.018 ⋅ ⋅ ⋅ ϕ, W / m 2 K, (kcal / m 2 hour deg).
Coefficient á to when heated is not equal to á to when cooling gases. When cooling á to more ∼ 1.3 times than when heated. Therefore, the heat transfer coefficient by convection during cooling of flue gases in a turbulent flow regime and at Pr av = 0.72 should be determined by the formula:
For long pipes á to\u003d 0.0235 ⋅ ⋅, W / m 2 K, (kcal / m 2 hour deg).
For short pipes:
á to\u003d 0.0235 ⋅ ⋅ ⋅ ϕ, W / m 2 K (kcal / m 2 hour deg).
The physical characteristics of air are given in section 6.1. The physical characteristics of flue gases are given in table. 7.21. The values of the Prandtl criterion for water at the saturation line are given in Section 6.2.
Table 7.21. Physical characteristics of flue gases of medium composition| Temperature | Coefficient thermal conductivityë SR, kcal/m hour °C | Kinematic viscosity coefficientí SR ⋅10 6, m 2 / sec | Prandtl criterion Pr СР |
| 1 | 2 | 3 | 4 |
| 0 | 0,0196 | 12,2 | 0,72 |
| 100 | 0,0269 | 21,5 | 0,69 |
| 200 | 0,0345 | 32,8 | 0,67 |
| 300 | 0,0416 | 45,8 | 0.65 |
| 400 | 0,0490 | 60,4 | 0,64 |
| 500 | 0,0564 | 76,3 | 0,63 |
| 1 | 2 | 3 | 4 |
| 600 | 0,0638 | 93,6 | 0,62 |
| 700 | 0,0711 | 112 | 0,61 |
| 800 | 0,0787 | 132 | 0,60 |
| 900 | 0,0861 | 152 | 0,59 |
| 1000 | 0,0937 | 174 | 0,58 |
| 1100 | 0,101 | 197 | 0,57 |
| 1200 | 0,108 | 221 | 0,56 |
| 1300 | 0,116 | 245 | 0,55 |
| 1400 | 0,124 | 272 | 0,54 |
| 1500 | 0,132 | 297 | 0,53 |
| 1600 | 0,14 | 323 | 0,52 |
Heat transfer under laminar flow regime
An approximate estimate of the average heat transfer coefficient is most often carried out using the criterion equation of M.A. Mikheev (for Re ≤ 2200):
á to= 0.15 ⋅ ⋅ Re 0.33 ⋅ Pr av 0.33 (Gr av ⋅ Pr av) 0.1 ⋅ () 0.25 ⋅ ϕ ,
which, in addition to those previously presented, includes one more criterion - Gr, called the Grashof criterion, which characterizes the lifting force of gases (gravity for liquids).
â ⋅ g ⋅ d 3 ⋅ ∆t
where: â is the coefficient of volumetric expansion of a liquid or gases, for gases â = 273, 1 deg.
g - free fall acceleration (acceleration of gravity), m / s 2;
d - reduced diameter or for vertical walls - wall height, m;
∆t is the temperature difference between the heated walls and the medium (t st - t cf) or (t cf - t st);
í - coefficient of kinematic viscosity, m 2 / s
ϕ - coefficient taking into account the relative length of pipes, equal to
Heat transfer during forced transverse washing of tube bundles
Heat transfer coefficient by convection in a transversely washed in-line pipe bundle (Fig. 7.10):
á to\u003d 0.206С z ⋅ С s ⋅ d í 0.65 ⋅ Pr 0.33, W / (m 2 K),
where: С z is the coefficient taking into account the number of rows of pipes z along the gas flow in the gas duct, at z<10 С z = 0,91+0,0125 (z-2), а при z>10 C z = 1;
C s - coefficient taking into account the geometric layout of the tube bundle - depends on the longitudinal S 2 and transverse S 1 steps,
C s \u003d 1+ 2S 1 - 3 1 - S 2 3 -2
ë is the coefficient of thermal conductivity of gases at the average temperature of the flow, W/(m⋅K) or kcal/m⋅h⋅gr.;
d is the outer diameter of the pipes, m;
w is the average gas velocity, m/s;
í is the coefficient of kinematic viscosity of gases at the average flow temperature, m 2 /s.
Heat transfer coefficient by convection in a transversely washed tube bundle (Fig. 7.9.):
á to\u003d С s ⋅ С z ⋅ d í 0.6 ⋅ Pr 0.33, W / (m 2 ⋅ K),
where: С s depends on S 1 and ϕ s ;
ϕ s \u003d (S 1 / d - 1) (S ′ 2 / d), S ′ 2 - the average diagonal pitch of the pipes (Fig. 7.9.);
at 0.1< ϕ s ≤ 1,7 и при S 1 /d ≥ 3,0 С s = 0,34 ⋅ ϕ s 0,1 ;
at 1.7< ϕ s ≤ 4,5 и при S 1 /d < 3,0 С s = 0,275 ⋅ ϕ s 0,5 ;
With z = 4 at z< 10 и S 1 /d ≥ 3.
Heat transfer during forced longitudinal washing of tubular heating surfaces
Heat transfer coefficient by convection:
á to\u003d 0.023 d eq í 0.8 ⋅ Pr 0.4 ⋅ С t ⋅ С d ⋅ С l, W / (m 2 ⋅K),
where: C t - temperature coefficient depending on the temperature of the medium and the wall - for water and steam, as well as when cooling gases C t \u003d 1.0, when heating combustion products and air C t \u003d (T / T st) 0.5 , where T and T st - the temperature of the gas, air and wall, in degrees K;
С d – coefficient introduced during flow in annular channels, with one-sided surface heating 0.85 ≤ С d ≤ 1.5, with two-sided С d = 1;
C l is a coefficient depending on the length of the channel; with longitudinal washing of pipes 1 ≤ С l ≤ 2, with l > 50d С l = 1.0.
Partial formulas for determining the heat transfer coefficients by convection
For high-temperature thermal units (according to N.N. Dobrokhotov):
á to\u003d 10.5W 0, W / m 2 K (or á to\u003d 9W 0, kcal / m 2 hour deg), where: W 0 - gas velocity in the furnace space, referred to 0 ° C, i.e. nm 3 /s.
For the movement of flue gases (air) through brick channels with dimensions from 40 × 40 to 90 × 90 mm (according to M.S. Mamykin):
W 0 0.8 4 W 0.8 4
á to\u003d 0.9 √ T, W / m 2 K (or 0.74 √ T, kcal / m 2 hour deg),
where: T is the absolute temperature of gases, °K; d is the reduced diameter in m;
For the free movement of air along the vertical surfaces of the walls at low temperatures (according to M.S. Mamykin):
á to\u003d 2.56 √ t 1 - t 2, W / m 2 K (or 2.2 √ t 1 - t 2, kcal / m 2 hour deg), where:
(t 1 - t 2) - the temperature difference between the surfaces of the walls and gas. For a horizontal surface facing upwards, instead of a coefficient of 2.56 (2.2), 3.26 (2.8) is taken and for a downward facing 1.63 (1.4).
For nozzles of regenerative heat exchangers (according to M.S. Mamykin):
á to\u003d 8.72, W / m 2 ⋅K (or á to\u003d 7.5, kcal / m 2 ⋅ hour ⋅ deg).
Calm water - metal wall (according to H. Kuhling):
á to\u003d 350 ÷ 580, W / (m 2 ⋅K);
Flowing water - a metal wall (according to H. Kuhling):
á to\u003d 350 + 2100 √ W, W / (m 2 ⋅K), where W is the speed in m / s.
Air is a smooth surface (according to H. Kuhling):
á to\u003d 5.6 + 4W, W / (m 2 ⋅ K), where W is the speed in m / s.
On fig. 7.17.–7.22. nomograms are given to determine á to graphic method.
Rice. 7.17. Heat transfer coefficient by convection during transverse washing of in-line smooth-tube bundles, αc = Cz⋅Cf⋅αn, W/m2⋅K (kcal/m2⋅h⋅deg) (rH2O is the volume fraction of water vapor)
Rice. 7.18. Heat transfer coefficient by convection during transverse washing of staggered smooth-tube bundles, αc = Cz⋅Cf⋅αn, W/m2⋅K (kcal/m2⋅h⋅deg), (rH2O is the volume fraction of water vapor)
Rice. 7.19. Heat transfer coefficient by convection during longitudinal washing of smooth pipes with air and flue gases
Rice. 7.20. Heat transfer coefficient by convection during longitudinal washing of smooth pipes with non-boiling water, α = C ⋅ α , W/m2 ⋅K (kcal/m2 ⋅h⋅deg)
Rice. 7.21. Convection heat transfer coefficient for plate air heaters at Re< 10000, αк = Cф⋅ αн, Вт/м2⋅К (ккал/м2⋅ч⋅град)
Rice. 7.22. Heat transfer coefficient by convection for regenerative air heaters at Re ≤ 5200, αk = Cf⋅ αn, W/m2⋅K (kcal/m2⋅h⋅deg)
α - characterizes the intensity of convective heat transfer and depends on the coolant velocity, heat capacity, viscosity, surface shape, etc.
[W / (m 2 grad)].
The heat transfer coefficient is numerically equal to the power of the heat flow transferred to one square meter of the surface at a temperature difference between the coolant and the surface of 1°C.
The main and most difficult problem in calculating the processes of convective heat transfer is finding the heat transfer coefficient α . Modern methods for describing the process coefficient. thermal conductivity based on the theory boundary layer, make it possible to obtain theoretical (exact or approximate) solutions for some rather simple situations. In most cases encountered in practice, the heat transfer coefficient is determined experimentally. In this case, both the results of theoretical solutions and experimental data are processed by methods theoriessimilarities and are usually represented in the following dimensionless form:
Nu=f(Re, Pr) - for forced convection and
Nu=f(Gr Re, Pr) - for free convection,
where 
- Nusselt number, - dimensionless heat transfer coefficient ( L- typical flow size, λ
- coefficient of thermal conductivity); Re=
-
the Reynolds number characterizing the ratio of the forces of inertia and internal friction in the flow ( u- characteristic velocity of the medium, υ - kinematic coefficient of viscosity);
Pr=
-
the Prandtl number, which determines the ratio of the intensities of thermodynamic processes (α is the coefficient of thermal diffusivity);
Gr=
-
the Grasshof number characterizing the ratio of Archimedean forces, inertial forces and internal friction in the flow ( g- acceleration of gravity, β
- thermal coefficient of volume expansion).
What does the heat transfer coefficient depend on? The order of its magnitude for various cases of heat transfer.
Convective heat transfer coefficient α the greater the higher the thermal conductivity λ and flow rate w, the smaller the coefficient of dynamic viscosity υ and the greater the density ρ and the smaller the reduced channel diameter d.
The most interesting case of convective heat transfer from the point of view of technical applications is convective heat transfer, that is, the process of two convective heat transfers occurring at the interface of two phases (solid and liquid, solid and gaseous, liquid and gaseous). In this case, the calculation task is to find the heat flux density at the phase boundary, that is, the value showing how much heat a unit of the phase interface receives or gives off per unit time. In addition to the above factors affecting the process of convective heat transfer, the heat flux density also depends on the shape and size of the body, on the degree of surface roughness, as well as on the temperatures of the surface and the heat-releasing or heat-receiving medium.
The following formula is used to describe convective heat transfer:
q st = α(T 0 -T st ) ,
where q st - heat flux density on the surface, W / m 2 ; α - heat transfer coefficient, W/(m 2 °C); T 0 and T st- temperature of the medium (liquid or gas) and surface, respectively. the value T 0 - T st often denoted Δ T and called temperature difference . Heat transfer coefficient α characterizes the intensity of the heat transfer process; it increases with an increase in the velocity of the medium and during the transition from the laminar to the turbulent mode of motion due to the intensification of the convective transfer. It is also always larger for those media that have a higher thermal conductivity. The heat transfer coefficient increases significantly if a phase transition occurs on the surface (for example, evaporation or condensation), which is always accompanied by the release (absorption) of latent heat. The value of the heat transfer coefficient is strongly influenced by mass transfer on the surface.
1. Basic concepts of convective heat transfer:
convection, convective heat transfer, heat transfer coefficient, thermal resistance of heat transfer, essence of convective heat transfer processes
2. Cyclone furnaces
3. Gaseous fuel
1. Basic concepts of convective heat transfer
Convection, convective heat transfer, heat transfer coefficient, thermal resistance of heat transfer, essence of convective heat transfer processes.
convection called the process of heat transfer during the movement of macroparticles (gas or liquid). Therefore, convection is possible only in a medium whose particles can easily move.
convective called heat transfer due to the combined action of convective and molecular heat transfer. In other words, convective heat transfer is carried out simultaneously in two ways: convection and heat conduction.
Convective heat transfer between a moving medium and its interface with another medium (solid, liquid or gas) is called heat dissipation.
The main task of the theory of convective heat transfer is to determine the amount of heat that passes through the surface of a solid body washed by the flow. The resulting heat flow is always directed in the direction of decreasing temperature,
In practical calculations of heat transfer, Newton's law is used:
Q = b F(t w -tct) (15-1)
i.e., the heat flux Q from the liquid to the wall or from the wall to the liquid is proportional to the surface F, involved in heat transfer, and temperature difference ( t w - t st, where t st is the temperature of the wall surface, and tzh is the temperature of the medium surrounding the wall surface. The coefficient of proportionality b, which takes into account the specific conditions of heat exchange between the liquid and the surface of the body, is called heat transfer coefficient.
Taking the formula (15-1) F = 1m², and f = 1 sec, we obtain the heat flux density in watts per square meter;
q= b (t w -tct) (15-2)
The value 1/b reciprocal of the heat transfer coefficient is called thermal resistance to heat transfer.
b = q: (t w -tct) (15-3)
From equality (15-3) it follows that the heat transfer coefficient, and is the heat flux density q, referred to the temperature difference between the surface of the body and the environment.
With a temperature difference equal to 1 ° (t w -tct = 1 °), the heat transfer coefficient is numerically equal to the heat flux density b = q
Heat transfer is a rather complex process and the heat transfer coefficient depends on many factors, the main of which are:
a) the cause of the fluid flow;
b) fluid flow regime (laminar or turbulent);
c) physical properties of the liquid;
d) the shape and dimensions of the heat-releasing surface.
Due to the occurrence of fluid movement, it can be free and forced.
Free movement (thermal) occurs in an unevenly heated liquid. The resulting temperature difference leads to a difference in density and the emergence of less dense (lighter) elements of the liquid, which causes movement. In this case, free movement is called natural or thermal convection . So, for example, heat exchange between the inner and outer panes of a window frame is carried out by natural convection (provided that the distance between the panes is sufficient for air circulation).
2. Cyclone furnaces
Cyclone furnaces are designed for burning crushed coal. Scheme such a furnace is shown in Fig. 19-8. Crushed coal with primary air is supplied through the fitting I in cyclone chamber 2. Secondary air is tangentially supplied to it, which enters through the fitting 3 at a speed of about 100 m/s, A rotating flow of combustion products is created in the chamber, throwing large particles of fuel onto its walls, where they are gasified under the action of hot air flows.
From the cyclone chamber, the combustion products with unburned fuel particles enter the afterburner 4. The slag from the cyclone chamber through the afterburner enters the slag bath, where it is granulated with water.
The advantages of cyclone furnaces are:
1) the possibility of burning fuel with a small excess of air 1.05-1.1, which reduces heat loss with exhaust gases;
2) increased specific thermal power of the furnace volume;
3) the ability to work on crushed coal (instead of pulverized coal);
4) capture of fuel ash in the furnace up to 80-90%.
The disadvantages of a cyclone furnace include:
1) the difficulty of burning high-moisture coals and coals with a low yield of volatile substances;
2) increased energy consumption for blasting.
3. Gaseous fuel
Natural. Natural (natural) gas is found in many places around the world.
Gas fuel reserves in some fields reach hundreds of billions of cubic meters. It is extracted not only from special gas wells, but also as a by-product of oil production. This natural gas is called associated petroleum gas.
The main component of natural gas is methane CH 4 .
Natural gas has a high calorific value. It is used as a fuel for industrial furnaces, vehicles, as well as for domestic needs.
Part of natural gas is subjected to chemical processing to obtain liquid fuel, process gas, chemical raw materials.
In the USSR, large gas-bearing regions are located in the Volga region, in the North Caucasus, Ukraine, in the Trans-Urals, etc.
Artificial. Artificial gas fuel (coke, black oil, generator gases) is obtained during the processing of oil and natural solid fuels, as well as a by-product in raw materials. industries such as blast furnaces.
Blast furnace gas formed in blast furnaces during iron smelting. Approximately half of the gas produced is used for the blast furnace's own needs. The other half of the gas can be used as fuel.
Task
Condition: How much heat must be brought to 1 kg. air with t \u003d 20 ° C, so that its volume at constant pressure doubles.
Question: Determine the air temperature at the end of the process, the heat capacity of the air is constant.
1) t = 25C - according to IS-chart.
2) T \u003d t + 273 \u003d 298K
3) T \u003d t + 273 \u003d 293K
Calculate the final volume as follows:
Vk \u003d Vn x 2 \u003d 0.058x2 \u003d 0.116 m²
Determine the amount of heat by the formula:
Q \u003d mc (T -T) \u003d 1.5x1.005 (298-293) \u003d \u003d 7.537
where m is the mass of kg. - on assignment 1.5kg, c-heat capacity kJ (kgC) from the table - 1.005kJ / kg.
Answer: it is necessary to supply heat in the amount of Q = 7.537, the air temperature at the end of the process will be 25C.
Page 1
The coefficients of convective heat transfer in this case are of the order of 10 kcal / m2 h deg. It has been found that the coefficients of radiant heat transfer at temperatures approximately equal to the temperature of the atmosphere are of the order of 2 kcal/m2 - h - deg. This means that under such conditions no accurate measurement with a conventional thermometer is possible.
The coefficient of convective heat transfer a is a function of thermophysical properties, temperature and velocity of the coolant, as well as the configuration and dimensions of the heat exchange surface.
Coefficients of convective heat transfer on the inner surfaces of the sgen and windows: P 3 and pr 4 kcal / m1 hour grid.
The coefficients of convective heat transfer between gases and pipes in heat exchangers or packing in regenerators are determined by the formulas given in reference books and special manuals. A number of them are given in the relevant sections of this book. In all cases, to increase the intensity of convective heat transfer, it is necessary to strive for the greatest uniformity in washing off all heating surfaces with gases, to reduce to the optimal dimensions the cross sections of the channels formed by the material in the layer through which the coolant flows, to increase the flow rate to values justified by technical and economic calculations.
The coefficient of convective heat transfer in the layer of air (outside) is much less than in the layer of water or steam (inside the device), so the resistance to external heat transfer RH for the heater is relatively high. Therefore, to increase the heat flow, it is necessary to develop the outer surface of the heater. In devices, this is done by creating special protrusions, tides and fins. However, this reduces the heat transfer coefficient.
The coefficient of convective heat transfer between the medium and the body placed in it at the same speed for liquids is many times greater than for gases. Liquids are opaque to heat rays, gases are transparent. Therefore, when measuring the temperature of gases, it is necessary to take into account the influence on the temperature of the meter of radiant heat transfer between the surface of the meter and the walls of the pipe.
The coefficients of convective heat transfer between the packing and hot gas or air are determined from experimental data.
The convective heat transfer coefficient ak strongly depends on the fiber diameter and the relative velocity of the medium due to a sharp change in the thickness of the laminar boundary layer comparable to the fiber diameter.
The coefficients of convective heat transfer of the packing and hot gases or air are determined from experimental data.
The coefficient of convective heat exchange of the walls of the room with the air contained in it is 11 36 W / m2 - deg.
Consequently, the coefficient of convective heat transfer depends on the method of heat supply, and with complex heat transfer (convection and radiation) it is much higher compared to only convective heat transfer, all other things being equal.
The average values of the coefficient of convective heat transfer on the vertical surfaces of the fences in the room without much error can be determined by the formula (1.64), since the temperature drops and the geometric dimensions of the heated and cooled surfaces that take place in reality usually correspond mainly to the turbulent regime. All considered formulas, including (1.64), are written for a vertical freely located surface.
Criteria equations are usually used to determine the coefficient of convective heat transfer. These equations for heat transfer conditions typical for the room are given in Table. 5 for forced and free convection. They refer to the conditions of motion near the surface of the plate. They are characterized by unidirectionality and uniformity, in a word, orderliness of movement.
The average value of the coefficient of convective heat transfer c, (sometimes denoted as oc) in the range from 0 to an arbitrary section / can be determined on the basis of the mean integral theorem.
