## Heat Transfer

Boilers are devices used to transfer heat. As defined in Chapter 2, heat is thermal energy that is transferred across the boundary of systems with differing temperatures, always in the direction of the lower temperature. Heat transfer occurs when two adjacent bodies of mass are not in equilibrium due to a difference in temperature.

There are three general modes of heat transfer: conduction, convection, and radiation. One or more of these accounts for heat transfer in all applications. All three methods are important in the process of steam generation.

Conduction is the transfer of heat energy through a material due to a temperature difference across it. This is consistent with the second law of thermodynamics statement that heat flows in the direction of decreasing temperature. For fluids, conduction takes place by molecular impact; for solid nonconductors, by molecular vibration;

Where:

Rate of heat transfer by conduction Area normal to the direction of heat flow Temperature

Distance along the direction of heat flow A property of the material called thermal conductivity Temperature gradient

Consistent with the second law, the flow of heat is positive when the temperature gradient, AT/L, is negative. The minus sign indicates that heat flow is in the direction of decreasing temperature.

The discrete form of Fourier's law derived by integrating the differential form with a constant temperature gradient is shown as Figure 7-7 and is expressed as:

Where:

L = Length in the direction of heat flow

T1 & T2 = Temperatures of the two surfaces

 Fluid Flow Tf J /5 -Solid Surface Qf

Fig. 7-8 Convection Heat Transfer.

Fig 7-7 Conduction Heat Transfer.

### Fig. 7-8 Convection Heat Transfer.

Thermal conductivity (k), a property of the material, quantifies its ability to conduct heat. It is expressed as Btu/ h •ft • °F (W/m • °K). Boilers are designed to optimize conduction of heat from combustion gases to liquids or vapors via a metal medium. Generally, thermal conductivities are highest for solids, lower for liquid, and lower still for gases. For metals, k is extremely high: k for pure metals ranges from 30 to 240 (52 to 415) and for alloys from 8 to 70 (14 to 121). Copper, for example, has a k value of223 (386), while iron and carbon steel are 42 and 25 (73 and 43), respectively. For gases, k is extremely small. Air, for example, has a k value of 0.014 (0.024). For nonmetallic liquids, k ranges from 0.05 to 0.40 (0.087 to 0.69). Water, for example, has a k value of 0.32 (0.55).

Convection is the transfer of heat within a fluid (gas or liquid) due to a combination of molecular conduction and macroscopic fluid motion. Convection occurs adjacent to heated surfaces as a result of fluid motion past the surfaces. As a fluid is heated, its density typically decreases. If part of a fluid mass is heated, the cooler, denser portion acts to displace the heated portion. A convection current is the continuous flow of cooler fluid to, and heated fluid from, the heated area. Natural convection occurs when the fluid motion is due to these local density differences alone. Forced convection occurs when mechanical forces from devices such as fans give motion to the fluids. The rate of heat transfer by convection can be shown as Figure 7-8 and expressed as:

Where:

Qf = Rate of heat transfer by convection h = Local heat transfer coefficient

A = Surface area

Ts = Surface temperature

Tf = Fluid temperature

Like thermal conductivity, the heat transfer coefficient (h) ranges widely between substances and may depend on the temperature of the fluid and surface. It is expressed as Btu per hour per square foot per °F (Btu/h • ft2 • °F) or Watt per square meter per °K (W/m2 • °K). For air (free convection), h ranges from 1 to 5 (6 to 28) and for forced convection, h typically ranges from 5 to 50 (28 to 280). For steam (forced convection), h ranges from 300 to 800 (1,700 to 4,500). For water (forced convection), h ranges from 50 to 2,000 (280 to 11,000) and for water (boiling), h ranges from 500 to 20,000 (2,800 to 114,000).

Radiation is the transfer of energy between bodies by electromagnetic waves. Solely the temperature of a body produces electromagnetic radiation and, unlike conduction and convection, radiative transfer requires no intervening medium. All surfaces whose temperatures are above absolute zero continuously emit thermal radiation. Electromagnetic waves that result from conversion of energy at the body's surface emanate from the surface and strike another body. Some of the thermal radiation is absorbed by the receiving body and converted into internal energy. The remaining portion is reflected from or transmitted through the body. For a perfect radiator, radiant energy transfer is expressed, based on the Stefan-Boltzmann law, as:

Where:

QR = Rate of heat transfer by radiation A = Surface area

0 = Stefan-Boltzmann constant (in English engineering units = 0.1713 x 10-8 Btu/h • ft2 • °R4 and in SI units 0 = 5.67 x 10-8 W/m2 • °K4) T44 = Absolute surface temperature

The rate of radiant energy transfer from a body is a function of the temperature as given above and the nature of the surface. A perfect radiator, or blackbody, absorbs all of the radiant energy reaching its surface and emits radiant energy at the maximum theoretical rate. The net radiation heat transfer between two blackbody surfaces in a vacuum or non-interactive gas is expressed as:

Where F is the configuration factor and represents the fraction of radiant energy leaving surface 1 that directly strikes surface 2, and Ti and T2 are the absolute surface temperatures. Radiation heat transfer is shown diagram-matically in Figure 7-9.

Surface 1 alTi

Surface 2 at To

A real radiator, or graybody, absorbs less than 100% of the energy incident on it. The heat transfer by radiation of a graybody is expressed as:

where £ is emissivity, or the emittance of the surface, and can be expressed as:

Energy actually radiated by the system

Energy radiated if the system were a blackbody

Like k and h, £ values also vary widely among materials. For polished metals £ ranges from 0.01 to 0.08. For oxidized metals, £ ranges from 0.25 to 0.7. For special paints, £ can be 0.98 or even higher, though it is always less than 1.

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### Responses

• stefan
How civil engineering related with heat and energy transfer?
2 years ago