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## Steady-state and transient heat transfer through fins of complex geometry

### Abstract

Various methods for steady-state and transient analysis of temperature distribution and efficiency of continuous-plate fins are presented. For a constant heat transfer coefficient over the fin surface, the plate fin can be divided into imaginary rectangular or hexangular fins. At first approximate methods for determining the steady-state fin efficiency like the method of equivalent circular fin and the sector method are discussed. When the fin geometry is complex, thus transient temperature distribution and fin efficiency can be determined using numerical methods. A numerical method for transient analysis of fins with complex geometry is developed. Transient temperature distributions in continuous fins attached to oval tubes is computed using the finite volume - finite element methods. The developed method can be used in the transient analysis of compact heat exchangers to calculate correctly the heat flow rate transferred from the finned tubes to the fluid.
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## Mathematical modelling of tube heat exchangers with complex flow arrangement

### Abstract

General principles of mathematical modelling of transient heat transfer in cross-flow tube heat exchangers with complex flow arrangements which allow a simulation of multipass heat exchangers with many tube rows are presented. First, a system of differential equations for the transient temperature of both fluids and the tube wall with appropriate boundary and initial conditions is formulated. Two methods for modelling heat exchangers are developed using the finite difference method and finite volume method. A numerical model of multipass steam superheater with twelve passes is presented. The calculation results are compared with the experimental data.
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## Measurement of heat flux density and heat transfer coefficient

### Abstract

The paper presents the solution to a problem of determining the heat flux density and the heat transfer coefficient, on the basis of temperature measurement at three locations in the flat sensor, with the assumption that the heat conductivity of the sensor material is temperature dependent. Three different methods for determining the heat flux and heat transfer coefficient, with their practical applications, are presented. The uncertainties in the determined values are also estimated.
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## Measurements of absorbed heat flux and water-side heat transfer coefficient in water wall tubes

### Abstract

The tubular type instrument (flux tube) was developed to identify boundary conditions in water wall tubes of steam boilers. The meter is constructed from a short length of eccentric tube containing four thermocouples on the fire side below the inner and outer surfaces of the tube. The fifth thermocouple is located at the rear of the tube on the casing side of the water-wall tube. The boundary conditions on the outer and inner surfaces of the water flux-tube are determined based on temperature measurements at the interior locations. Four K-type sheathed thermocouples of 1 mm in diameter, are inserted into holes, which are parallel to the tube axis. The non-linear least squares problem is solved numerically using the Levenberg-Marquardt method. The heat transfer conditions in adjacent boiler tubes have no impact on the temperature distribution in the flux tubes.
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## Verification of heat flux and temperature calculation on the control rod outer surface

### Abstract

The paper presents heat transfer calculation results concerning a control rod of Forsmark Nuclear Power Plant (NPP). The part of the control rod, which is the object of interest, is surrounded by a mixing region of hot and cold flows and, as a consequence, is subjected to thermal fluctuations. The paper describes a numerical test which validates the method based on the solution of the inverse heat conduction problem (IHCP). The comparison of the results achieved by two methods, computational fluid dynamics (CFD) simulations and IHCP, including a description of the IHCP method used in the calculation process, shows a very good agreement between the methods.
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## Optimum heating of cylindrical pressure components weakened by holes

### Abstract

A method for determining time-optimum medium temperature changes is presented. The heating of the pressure elements will be conducted so that the circumferential stress caused by pressure and fluid temperature variations at the edge of the opening at the point of stress concentration, do not exceed the allowable value. In contrast to present standards, two points at the edge of the opening are taken into consideration. The first point, P1, is located at the cross section and the second, P2, at the longitudinal section of the vessel. It will be shown that the optimum temperature courses should be determined with respect to the total circumferential stress at the point P2, and not, as in the existing standards due to the stress at the point P1. Optimum fluid temperature changes are assumed in the form of simple time functions. For practical reasons the optimum temperature in the ramp form is preferred. It is possible to increase the fluid temperature stepwise at the beginning of the heating process and then increase the fluid temperature with the constant rate. Allowing stepwise fluid temperature increase at the beginning of heating ensures that the heating time of a thick-walled component is shorter than heating time resulting from the calculations according to EN 12952-3 European Standard.
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## Effect of scale deposits on the internal surfaces of the tubes on the superheater operation

### Abstract

A mathematical model of the steam superheater exchanger with distributed parameters has been developed. Scale deposits were assumed to be present on the internal tube surfaces. It was assumed that the inner tube surfaces are covered by a thin layer of scale deposits. The finite volume method was used to solve partial differential equations describing flue gas, tube wall and steam temperature. The developed modeling technique can especially be used for modeling tube heat exchangers when detail information on the tube wall temperature distribution is needed. The numerical model of the superheater developed in the paper can be used for modeling of the superheaters with complex flow arrangement accounting scales on the internal tube surfaces. Using the model proposed the detailed steam, wall and flue gas temperature distribution over the entire superheater can be determined. The steam pressure distribution along its path flow and the total heat transfer rate can also be obtained. The calculations showed that the presence of scale on the internal surfaces of the tubes cause the steam temperature decrease and the heat flow rate transferred from the flue gas to the steam. Scale deposits on the inner surfaces of the tubes cause the tube wall temperature growth and can lead to premature wear of tubes due to overheating.
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## Improving flexibility characteristics of 200 MW unit

### Abstract

Calculations were performed of the thermal system of a power plant with installed water pressure tanks. The maximum rise in the block electric power resulting from the shut-off of low-pressure regenerative heaters is determined. At that time, the boiler is fed with hot water from water pressure tanks acting as heat accumulators. Accumulation of hot water in water tanks is also proposed in the periods of the power unit small load. In order to lower the plant electric power in the off-peak night hours, water heated in low-pressure regenerative heaters and feed water tank to the nominal temperature is directed to water pressure tanks. The water accumulated during the night is used to feed the boiler during the period of peak demand for electricity. Drops in the power block electric power were determined for different capacities of the tanks and periods when they are charged. A financial and economic profitability analysis (of costs and benefits) is made of the use of tanks for a 200 MW power unit. Operating in the automatic system of frequency and power control, the tanks may also be used to ensure a sudden increase in the electric power of the unit. The results of the performed calculations and analyses indicate that installation of water pressure tanks is well justified. The investment is profitable. Water pressure tanks may not only be used to reduce the power unit power during the off-peak night hours and raise it in the periods of peak demand, but also to increase the power capacity fast at any time. They may also be used to fill the boiler evaporator with hot water during the power unit start-up from the cold state.
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## New technique of the local heat flux measurement in combustion chambers of steam boilers

### Abstract

A new method for measurement of local heat flux to water-walls of steam boilers was developed. A flux meter tube was made from an eccentric tube of short length to which two longitudinal fins were attached. These two fins prevent the boiler setting from heating by a thermal radiation from the combustion chamber. The fins are not welded to the adjacent water-wall tubes, so that the temperature distribution in the heat flux meter is not influenced by neighbouring water-wall tubes. The thickness of the heat flux tube wall is larger on the fireside to obtain a greater distance between the thermocouples located inside the wall which increases the accuracy of heat flux determination. Based on the temperature measurements at selected points inside the heat flux meter, the heat flux absorbed by the water-wall, heat transfer coefficient on the inner tube surface and temperature of the water-steam mixture was determined.
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