LECUTRE 32: Steady state heat flow in furnaces and heat exchangers
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1 LECUTRE 32: Steady state heat flow in furnaces and heat exchangers Contents Estimation of heat losses in furnaces Heat exchanger Performance of a heat exchanger Regenerator Key words: Heat exchanger, Regenerator, Recuperator, Heat recovery, Furnaces Estimation of heat losses in furnaces In furnaces operating at high temperatures, heat losses from the outer wall of the shell are important to estimate, when the furnace operates at steady state. These losses correspond to loss in energy. In order to estimate the heat losses, wall temperature should be known. Shell temperature can either be calculated or measured. In the following lecture a method is discussed to calculate the shell temperature of the furnace. Consider wall of the furnace at temperaturet which is lined with refractory material of thickness Δx, thermal conductivity K as shown in the figure. Figure 32.1: Furnace wall showing heat balance Surrounding temperature is T. Let the shell temperature facing the surrounding is T. T is unknown. Heat balance of the furnace is [Heat flow by conduction to the outer shell = Heat loss from the shell to the surrounding by convection and radiation] (1) Q C Q C Q R. (2)
2 K AV AT T h A T T 5.67 F A T T (3) h is heat transfer coefficient for natural convection. F is view factor, is emissivity of the shell and A is the area of the furnace. Heat transfer coefficient h can be evaluated by h C T 0.25 D (4) Heat exchanger Heat exchanger, as the name indicates is an equipment used to capture the heat of products of combustion and to preheat the air simultaneously. Recuperators and regenerators are commonly used to capture and reuse the heat. A recuperator is a continuous type of heat exchanger in which both hot and cold streams flow continuously. Both streams are separated by a wall. Transfer of heat from hot stream to cold stream is through the separating wall. Both streams may flow parallel flow as shown in figure (a) or counter current (as shown in b) or cross flow (as in c). Metallic heat exchangers are used at low temperatures whereas ceramic heat exchangers can be used at high temperatures Figure 32.2: Types of recuperator (a) parallel flow, (b) counter current and (c) cross flow Another type of heat exchanger for high temperature purposes is the regenerator. A regenerator contains heat storage elements which alternately absorb heat from hot products of combustion and preheat the incoming air. Two types of regenerators are in use: (a) Continuous gas flow, moving element for heat storage and (b) Intermittent gas flow, stationary heat storage element.
3 In the continuous gas flow type the two gas streams flow continuously through own compartments and the heat storage elements move from hot stream to cold stream. They are normally constructed of metal and are primarily used for low temperature like boiler. For high temperature applications, the regenerator contains stationary heat storage elements. It consists of a chamber filled with brick chequework to give a multiple vertical gas passage. The hot products of combustion and cold air flow alternately through the same chamber and same passage in a cyclic fashion. In all the above types of heat exchangers, the residence of the stream is important for the heat transfer efficiency which is turn controlled by the flow rate of the stream, cross section area of the vessel and thermal conductivity of the material Performance of a heat exchanger A heat exchanger captures and uses the heat of flue gases simultaneously. Performance of a heat exchanger can be evaluated in terms of its ability to capture and to preheat the air to the maximum possible temperature. Consider a co axial type heat exchanger in which hot stream enters at T and exits at T. Cold stream say air enters at temperature T and pre heated stream exists at T as shown in the figure. Figure 32.3: Heat exchanger under consideration for macroscopic heat balance Length of the heat exchanger is L. Macroscopic heat balance can be used to evaluate the performance. In the macroscopic balance, we are concerned with the initial and final states of the flue gas and air i.e. at plane 1 and 2. Assumptions: i) Flow of flue gases and air are at steady state.
4 ii) Flow is adiabatic which means no loss of heat, which means heat lost by flue gas is completely absorbed by air Q Q, i.e. (5) Heat lost by flue gas Q m H H (6) Heat taken by air Q m H H (7) Q and Q are he at content in hot and cold stream, m and m mass flow rate of hot and cold stream and is the enthalpy. There is no heat loss to surrounding, so Q Q. For ideal gases and in compressible fluids ΔH C P ΔT m C T T Q (8) m C T T Q Q (9) Heat balance over a length dl of heat exchanger m C dt U 2π r T T dl. (10) P r outside radius of the inner tube. U over all heat tranfer coefficient U is an overall coefficient for heat flow path consisting of a series of thermal resistances such that U (11) K Here and are convective thermal resistance and is thermal resistance of the wall of thickness Δx K and of thermal conductivi ty K due to conduction. Re arrangement of equations 9 and 10 gives T TT U M CP (12) And T U T T M C (13) Adding equations 12 and 3
5 T T U T T C C 2π r dl (14) By assuming U as independent of l and integrating over the length l we get. ln T T U T T C C 2π r l (15) Expression rela tes terminal temperatures of the heat exchanger to stream rates and heat exchanger dimensions. It can be used to describe the performance of the exchanger By equation 8, 9 and 15 T T T T QU 2 π r L (16) T T T T U A T T ln (17) The equations 16 and 17 describe the rate of heat flow as a function of the terminal temperatures of the heat exchanger and do not contain the manner in which streams are flowing. Therefore, the equations 16 or 17 are general equations to evaluate the performance of the heat exchanger Application to regenerator Regenerators are unsteady heat flow system to which steady state heat, flow is not strictly applicable. For most engineering applications, a regenerator can be considered in terms of heat flow analogous to a continuous recuperator as hot flue gas brick surface conduction through brick brick air and to deal with average temperature to eliminate time. By this analogy brick surfaces are at higher temperature during flue gas cycle than during cold gas cycle and temperature difference corresponds to that across the separating wall in a recuperator. Also heat flow in and out from brick is equivalent to resistance to heat flow across the separating wall in a recuperator. With this analogy we can define the overall heat transfer coefficient as applicable to regenerator as U S f K (18) In the equation 18
6 h f and h are he at transfer coefficient from flue gas to brick surface and from brick surface to air respectively. S is the thermal resistance of the separating wall which is analogous to that of brick in K the regenerator. S Estimat ion of is relatively difficult to estimate in unsteady state flow. The equivalent thermal K resistance varies with the thickness of the brick and the time of contact. Its contribution is 15 to 20% of the total resistance to flow of heat from hot to cold stream. Equation 17 can be used for regenerators keeping in mind the above limitations.
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