Heat transfer: defined

Results on heat transfer are usually presented as over-all coefficients of heat transfer defined by the simple relation... 

Nusselt number for heat transfer, defined in Problem 1.1 dy/dx, defined in Eq. 2.87... 

Prandtl number (Pr, Npd n. A dimensionless group important in the analysis of convection heat transfer, defined as (in consistent units) Cpp/k, where Cp is the specific heat of a fluid at constant pressures, p the viscosity, and k is the thermal conductivity. The Prandtl number is also the ratio of the kinematic viscosity to the thermal diffusivity see both entries). 

Once the initial network structure has been defined, then loops, utility paths, and stream splits offer the degrees of freedom for manipulating network cost in multivariable optimization. During the optimization, there is no constraint that temperature differences should be larger than or that there should not be heat transfer... 

Equation (F.l) shows that each stream makes a contribution to total heat transfer area defined only by its duty, position in the composite curves, and its h value. This contribution to area means also a contribution to capital cost. If, for example, a corrosive stream requires special materials of construction, it will have a greater contribution to capital cost than a similar noncorrosive stream. If only one cost law is to be used for a network comprising mixed materials of construction, the area contribution of streams requiring special materials must somehow increase. One way this may be done is by weighting the heat transfer coefficients to reflect the cost of the material the stream requires. 

Thermodynamic principles govern all air conditioning processes (see Heat exchange technology, heat transfer). Of particular importance are specific thermodynamic appHcations both to equipment performance which influences the energy consumption of a system and to the properties of moist air which determine air conditioning capacity. The concentration of moist air defines a system s load. 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

The subscripts / and o correspond to inner and outer surfaces of tube, respectively. In these equations, Pi is a reference area for which U is defined, and T[ is the total efficiency of a finned heat-transfer surface and is related to the fin efficiency, Tl by... 

For the purpose of network synthesis, the overall heat-transfer coefficient is usually idealized as a constant value. This iadependence of the heat-transfer coefficient makes possible the iterations necessary to solve the network problem. Usually, the overall heat-transfer coefficient for each exchanger (match) is defined as... 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

In fossil fuel-fired boilers there are two regions defined by the mode of heat transfer. Fuel is burned in the furnace or radiant section of the boiler. The walls of this section of the boiler are constmcted of vertical, or near vertical, tubes in which water is boiled. Heat is transferred radiatively from the fire to the waterwaH of the boiler. When the hot gas leaves the radiant section of the boiler, it goes to the convective section. In the convective section, heat is transferred to tubes in the gas path. Superheating and reheating are in the convective section of the boiler. The economizer, which can be considered as a gas-heated feedwater heater, is the last element in the convective zone of the boiler. 

A guarded hot-plate method, ASTM D1518, is used to measure the rate of heat transfer over time from a warm metal plate. The fabric is placed on the constant temperature plate and covered by a second metal plate. After the temperature of the second plate has been allowed to equiUbrate, the thermal transmittance is calculated based on the temperature difference between the two plates and the energy required to maintain the temperature of the bottom plate. The units for thermal transmittance are W/m -K. Thermal resistance is the reciprocal of thermal conductivity (or transmittance). Thermal resistance is often reported as a do value, defined as the insulation required to keep a resting person comfortable at 21°C with air movement of 0.1 m/s. Thermal resistance in m -K/W can be converted to do by multiplying by 0.1548 (121). 

Cooling System Corrosion Corrosion can be defined as the destmction of a metal by chemical or electrochemical reaction with its environment. In cooling systems, corrosion causes two basic problems. The first and most obvious is the failure of equipment with the resultant cost of replacement and plant downtime. The second is decreased plant efficiency to loss of heat transfer, the result of heat exchanger fouling caused by the accumulation of corrosion products. 

Equation 2 defines the basic mode of operation of the dryer. The heat-transfer coefficient is a key property of the dryer configuration. 

Contact Drying. Contact drying occurs when wet material contacts a warm surface in an indirect-heat dryer (15—18). A sphere resting on a flat heated surface is a simple model. The heat-transfer mechanisms across the gap between the surface and the sphere are conduction and radiation. Conduction heat transfer is calculated, approximately, by recognizing that the effective conductivity of a gas approaches 0, as the gap width approaches 0. The gas is no longer a continuum and the rarified gas effect is accounted for in a formula that also defines the conduction heat-transfer coefficient ... 

Specialized heat transfer nomenclature used for radiative heat transfer is defined in the subsection Heat Transmission hy Radiation. Nomenclature for mass transfer is defined in the subsection Mass Transfer. ... 

Individual Coefficient of Heat Transfer Because of the comphcated structure of a turbulent flowing stream and the impracti-cabifity of measuring thicknesses of the several layers and their temperatures, the local rate of beat transfer between fluid and solid is defined by the equations... 

The analogy has been reasonably successful for simple geometries and for fluids of very low Prandtl number (liquid metals). For high-Prandtl-number fluids the empirical analogy of Colburn [Trans. Am. Tn.st. Chem. Ting., 29, 174 (1933)] has been veiy successful. A J factor for momentum transfer is defined asJ =//2, where/is the friction fac tor for the flow. The J factor for heat transfer is assumed to be equal to the J factor for momentum transfer... 

I0-38Z ) is solved to give the temperature distribution from which the heat-transfer coefficient may be determined. The major difficulties in solving Eq. (5-38Z ) are in accurately defining the thickness of the various flow layers (laminar sublayer and buffer layer) and in obtaining a suitable relationship for prediction of the eddy diffusivities. For assistance in predicting eddy diffusivities, see Reichardt (NACA Tech. Memo 1408, 1957) and Strunk and Chao [Am. ln.st. Chem. Eng. J., 10, 269(1964)]. 

Once a plant is built, the conditions of agitation, aeration, oxygen transfer, and heat transfer are more or less set, and sterilization cycles are defined. Those environmental conditions achievable in plant-scale equipment should be scaled down to the pilot plant and laboratoiy equipment (shaken flasks) to insure that results can be translated. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

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