Rates of Heat Transfer

The rate of heat transfer depends on the overall heat transfer coefficient, the surface area, and the temperature difference between the fluid and surrounding. Mathematically, the average rate of heat transfer is defined as 

The heat transfer to/from the fluid to the surroundings depends on the total thermal resistances or overall heat transfer coefficient. The thermal resistances depend on a large number of factors including the physical properties of the fluid and the environmental conditions. In general, tiie total thermal resistance is the summation of the following resistances  

Mathematically, the overall heat transfer coefficient is defined as 

Typical overall heat transfer coefficients are presented in Table 2.8. 

The resistance due to the film can be calculated using the following equation  

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Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

However, if high rates of heat transfer are required or the catalyst requires frequent regeneration, then fixed beds are not suitable, and under these circumstances, a fluidized bed is preferred, as we shall discuss later. 

LOW RATE OF HEAT TRANSFER AND/OR HIGH HEAT OF REACTION... 

Fixing the rate of heat transfer in a batch reactor is often not the best way to control the reaction. The heating or cooling characteristics can be varied with time to suit the characteristics of the reaction. Because of the complexity of hatch operation and the fact that operation is usually small scale, it is rare for any attempt to be made... 

If condensation requires gas stream cooling of more than 40—50°C, the rate of heat transfer may appreciably exceed the rate of mass transfer and a condensate fog may form. Fog seldom occurs in direct-contact condensers because of the close proximity of the bulk of the gas to the cold-Hquid droplets. When fog formation is unavoidable, it may be removed with a high efficiency mist collector designed for 0.5—5-p.m droplets. Collectors using Brownian diffusion are usually quite economical. If atmospheric condensation and a visible plume are to be avoided, the condenser must cool the gas sufftciendy to preclude further condensation in the atmosphere. 

The ideal high level heat-transfer medium would have excellent heat-transfer capabiUty over a wide temperature range, be low in cost, noncorrosive to common materials of constmction, nondammable, ecologically safe, and thermally stable. It also would remain Hquid at winter ambient temperatures and afford high rates of heat transfer. In practice, the value of a heat-transfer medium depends on several factors its physical properties in relation to system efficiency its thermal stabiUty at the service temperature its adaptabiUty to various systems and certain of its physical properties. 

If the rate of moisture vaporization is controlled bv the rate of heat transfer to the wet soHd, then for convection dominated heat transfer, h, at the boiling poiat of water, the characteristic time is... 

The rate of heat-transfer q through the jacket or cod heat-transfer areaM is estimated from log mean temperature difference AT by = UAAT The overall heat-transfer coefficient U depends on thermal conductivity of metal, fouling factors, and heat-transfer coefficients on service and process sides. The process side heat-transfer coefficient depends on the mixing system design (17) and can be calculated from the correlations for turbines in Figure 35a. 

It is important that the rate of circulation within the waterwaH tubes be great enough to carry heat away from the metal tube walls fast enough to prevent the walls from overheating. Because the circulation is dependent on the difference ia density between the cooler water found ia the downcomers and the hotter water and steam located ia the waterwaHs, the rate of circulation iacreases as this differential pressure iacreases. Thus, the rate of heat transfer from the combustion 2one to waterwaHs, the height of the boiler, and its operating pressure all combine to determine the rate of circulation. 

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). 

Enclosed Spaces The rate of heat transfer across an enclosed space is calculated from a special coefficient h based upon the temperature difference between the two surfaces, where h = (q/A)/ (Li 2)- The value of h L/k may be predicted from Eq. (5-32) by using the values of a and m given in Table 5-3. 

Heat transfer by nucleate boiling is an important mechanism in the vaporization of liqmds. It occurs in the vaporization of liquids in kettle-type and natural-circulation reboilers commonly usea in the process industries. High rates of heat transfer per unit of area (heat flux) are obtained as a result of bubble formation at the liquid-solid interface rather than from mechanical devices external to the heat exchanger. There are available several expressions from which reasonable values of the film coefficients may be obtained. 

Fouling refers to any change in the sohd boundaiy separating two heat transfer fluids, whether by dirt accumulation or other means, which results in a decrease in the rate of heat transfer occurring across that boundaiy. Fouling may be classified by mechanism into six basic categories ... 

Principal advantages are high rate of heat transfer, no internal pressure drop, short time of contact (very important for heat-sensitive materials/ easy accessibihty to tubes for cleaning, and, in some cases, prevention of leakage from one side to another. 

Wet-bulb temperature is the dynamic equilibrium temperature attained by a water surface when the rate of heat transfer to the surface by convection equals the rate of mass transfer away from the surface. At equilibrium, if neghgible change in the dry-bulb temperature is assumed, a heat balance on the surface is... 

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