In this example, a simple heat exchanger with single shell pass and single tube pass is considered. We use cookies to help provide and enhance our service and tailor content and ads. For heat exchanger that has two ends (which we call “A” and “B”) at which the hot and cold streams enter or exit on either side, the LMTD is defined as: This holds both for parallel-flow arrangement, where the streams enter from the same end, and for counter-flow arrangement, where they enter from different ends. It is a measure of the heat exchanger’s departure from the ideal behavior of a counter flow heat exchanger having the same terminal temperatures. It can be readily noticed that for co-current heat exchanger the logarithmic mean temperature difference is lower compared to counter-current heat exchanger. What design should we adopt? This parameter can be found in Ref [24,25], and is taken as 0.0002 m2 K/W. For the parallel flow arrangement, the state is reached when both streams attain the same temperature at outlet. (Tsay et al., 2017) to estimate the tube side heat transfer coefficient αijknmtube and the shell side heat transfer coefficient αijknmShell of the MHEX. LMTD is introduced due to the fact, the temperature change that takes place across the heat exchanger from the entrance to the exit is not linear. This can be achieved with the use of proper metallurgy for cold end heat transfer surface area (i.e., LP economizer; also known as “preheater” or “feedwater heater”). Figure 1 - Typical PFD for an Instrument Air Supply System. Representative surface temperature distributions are also shown: these will be closer to the hot stream temperatures if the heat transfer coefficient is higher for the hot stream, a point which will be further developed later. For multiple shell and tube passes, the LMTD calculated has to be multiplied by a correction factor to account for geometric changes. ΔT2 = TH2 - TC2 = 90 - 50 = 400Ceval(ez_write_tag([[300,250],'enggcyclopedia_com-medrectangle-4','ezslot_2',106,'0','0'])); It can be readily noticed that for co-current heat exchanger the logarithmic mean temperature difference is lower compared to counter-current heat exchanger. Theodore L. Bergman, Adrienne S. Lavine, Frank P. Incropera. That is, /},Tlm, CF > /},Tlm, PF, and thus a smaller surface area (and thus a smaller heat exchanger) is needed to achieve a specified heat transfer rate in a counter-flow heat exchanger. Sufficient superheater and reheater surface area must be selected to achieve the desired steam temperatures. The amount of heat transferred, therefore, is directly a function of the total amount of heat transfer surface area included in the HRSG. Reach out to our reader base of engineering professionals. This location allows the HRSG designer to balance the amount of superheater and reheater surface areas upstream and downstream of the duct burner for steam temperature control. The flow pattern in a shell and tube heat exchanger with a single tube . A double pipe heat exchanger is usually operated as a counter flow heat exchanger, as shown in the diagram at the left. F factor is calculated as per equations (1) & (2). (10), the tube layout constant and tube count constant depend on heat exchanger geometry and can be found in Ref. 23–14. In order to determine the total heat flow, either the heat flow should be summed up using elemental areas and the temperature difference at the location or more conveniently engineers can average the value of temperature difference. HRSGs in combined cycle power plants are an amazing bridge between the Brayton and Rankine cycles. ΔT1 = TH1 - TC2 = 100 - 50 = 500C (At one end hot fluid enters and cold fluid exits.) Copyright © 1984, McGraw-Hill Inc., reproduced by permission of Krieger Publishing Company, Malabar, Florida, USA. Log mean temperature difference for an exchanger with straight-line heat release curves. Because the temperature of the process fluid changes as it flows, a mean temperature difference (MTD) must be used. Figure 3.10. ISBN: 9781118137253. In this equation, Pt is the tube pitch, which changes according to the tube diameter [24]: The Reynolds number of the shell side can be found using Eq. Surface area sequencing refers to how the different sections within a pressure level (economizer, evaporator, superheater) are arranged between the different pressure levels. (11.23) which can be expressed as, A. Castell, C. Solé, in Advances in Thermal Energy Storage Systems, 2015. This section provides the modeling equations for the shell and tube heat exchanger and baffle configuration calculations. This calculator is used to calculate LMTD for parallel flow (i.e. Reference: As discussed in an earlier chapter, one of the most important functions of the cardiovascular system is to maintain the temperature of the body. This is represented as, where To is the mean outlet temperature and Ti is the mean inlet temperature. Even if the HRSG has three pressure levels and one stage of reheat, without sufficient surface area, energy will be wasted up the stack and lost. In this equation, As is the cross-sectional area of the shell perpendicular to the flow direction, according to the segmental, continuous, or noncontinuous baffle type; it can be calculated using Eqs. Heat and Mass Transfer. This is given by. McGraw-Hill Education, 2011. Addison-Wesley Pub. The log-mean temperature difference of heat exchanger 1 can be expressed as, Similarly for the heat exchanger in loop 2, Knowing, Ui,2, Ai,2, and Qh, ΔTlm,2 can be evaluated from Eq. Note that some information about velocity is needed to solve for the temperature because this is a coupled convection problem. Earlier, we mentioned that the temperature difference between the hot and cold fluids varies along the heat exchanger, and it is convenient to have a mean temperature difference /},Tm for use in the relation Q = UAs /},Tm. Note that for a shell-and-tube heat exchanger, T and t represent the shell- and tube-side temperatures, respectively, as shown in the correction factor charts. The determination of the correction factor F requires the availability of the inlet and the outlet temperatures for both the cold and hot fluids. (ii) ■ THE LOG MEAN TEMPERATURE DIFFERENCE METHOD. DOE Fundamentals Handbook, Volume 1 and 2. Heat transfer through a capillary. The capillary can be considered to provide the blood with a constant surface heat flux of −1000 W/m2. U.S. Department of Energy, Thermodynamics, Heat Transfer and Fluid Flow. The required area of this heat exchanger can be then directly calculated using general heat transfer equation: We hope, this article, Logarithmic Mean Temperature Difference – LMTD, helps you. But there are other HRSG design decisions that also affect heat recovery, and hence, cycle efficiency. On the other hand the temperature difference continuously varies with location (especially in counter-flow arrangement). There is mainly two different flow arrangement in heat exchangers, Your email address will not be published. The most common are counterflow and crossflow (both streams unmixed) and these are shown below. Your email address will not be published. When we have multipass parallel flow or counter flow or cross flow exchangers, LMTD is first calculated for single pass counter flow exchanger and the mean temperature difference is obtained by multiplying the LMTD with a correction factor F which takes care of the actual flow arrangement of the exchanger. Heat transfer rate in the exchanger is represented by. Joseph Miller, in Heat Recovery Steam Generator Technology, 2017. The LMTD is based only on temperature values, therefore it does not account for the energy stored during a phase change, since the process occurs at almost constant temperature, but with important variations in the enthalpy. Therefore, using /},Tam in calculations instead of /},Tlm will overestimate the rate of heat transfer in a heat ex- changer between the two fluids. 23–15). Knowing Ui,1, Ai,1, and Qh, the log-mean temperature difference ΔTlm,1 can be evaluated from Eq. The evaporation rate is obtained from the energy conservation in the evaporator: The heat transfer and energy conservation in the condenser is modeled as, where U is the overall heat transfer coefficient, A is the condenser surface area, and LMTD is the log-mean temperature difference in the condenser defined as.