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where α is the convection heat transfer coefficient, k is the conduction heat transfer coefficient, L is the thickness of the wall, m is the mass of the wall and cp is the specific heat of the metal in the wall. These equations describe the dynamics of the temperature in the wall. The heat transfer is approximated to the 1-dimensional case, but since the wall is very thin compared to the length, it is a justified approximation. We also want to define the efficiency of a heat exchanger, so that we know how good it is compared to an ideal heat exchanger. In order to do so we start by defining the maximum possible heat transfer rate: where q=Cmin(Tfluegas,in −Tair,in) (5.5.1) Cmin =min{(cpm&)air,(cpm&)fluegas} (5.5.2) Cmin is minimum heat capacity flow of the two involved fluids. The subscripts in and out refer to the inlet and outlet of the heat exchanger and the subscript air and flue gas refer to the cold and hot fluid of the heat exchanger respectively. The maximum heat transfer can only be achieved in an ideal counterflow heat exchanger of infinite length. The actual heat transfer can thus be stated as: q=Cair(Tair,out −Tair,in) (5.5.3) which gives us a formal definition on the efficiency: (5.5.4) In the T100 microturbine, the fluids are air and flue gas. The only differences between the substances are somewhat lower percentage oxygen and higher percentage carbon dioxide and water vapor. When the fuel is added, the total mass flow is increased, but only with 1 % due to the large air/fuel ratio. The exhaust gas has also higher temperature than the air, which also gives a little larger cp. Then Cmin = Cair and we get the right had side of equation (5.5.4). The equation above gives the efficiency of the heat exchanger based on temperature measurements. It is used to evaluate the efficiency of a recuperator in use. It does not, however, say anything in advance about what the efficiency a designed recuperator will have and what factors that can improve the efficiency. Another useful expression for the efficiency is therefore taken from DeWitt (1996). The following equation is only valid when the heat capacity flows of the fluids are equal, which is a justified approximation in the case of the T100 microturbine. (5.5.5) The variable NTU (number of thermal units) is a dimensionless parameter that is widely used for heat exchangers. It shows how well the heat exchanger can transfer heat due to its geometry, mass flow, mediums and heat transfer coefficients. (5.5.6) where A is the heat exchanger surface area and U [W/m2 K] is the overall heat transfer coefficient defined as (5.5.7) The variable α is the convection heat transfer coefficient; L is the thickness of the wall and k is the thermal conductivity (conduction heat transfer coefficient). The wall between the fluids is ε = q = Cair (Tair,out −Tair,in ) = Tair,out −Tair,in qmax Cmin (Tflue gas,in −Tair,in ) Tflue gas,in −Tair,in ε= NTU 1+ NTU NTU =U⋅A C min U=1 (1+L+1) αair kwall α fluegas 35PDF Image | Modelling of Microturbine Systems
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