A 1-2 shell-and-tube heat exchanger is illustrated in Figure. Table 5.1 Summary of shell-and-tube heat exchangers. Basic Equations.
Heat lost by the hot fluid = -Q = m H × Cp H × (To H - Ti H) (1)Heat gained by the cold side = Q = m C × Cp C × (To C - Ti C) (2)Comparing equations (1) and (2),m H × Cp H × (Ti H - To H) = m C × Cp C × (To C - Ti C) (3)This energy balance equation can be solved for one variable for any given case. Out of total six variables in the equation (3), five should be fixed to determine the unknown variable.It should also be noted that the mass balance equation is already applied in this case to develop equation (3).The fact that m Hin = m Hout = m H and m Cin = m Cout = m C is already considered while writing equations (1) and (2). Hence application of mass balance equation for heat exchanger does not present any new information here.
IntroductionThe heat exchanger design equation can be used to calculate the required heat transfer surface area for a variety of specified fluids, inlet and outlet temperatures and types and configurations of heat exchangers, including counterflow or parallel flow. A value is needed for the overall heat transfer coefficient for the given heat exchanger, fluids, and temperatures. Heat exchanger calculations could be made for the required heat transfer area, or the rate of heat transfer for a heat exchanger of given area. Of average temperature difference is needed. Many heat transfer textbooks have a derivation showing that the log mean temperature difference is the right average temperature to use for heat exchanger calculations. That log mean temperature is defined in terms of the temperature differences as shown in the equation at the right.
T Hin and T Hout are the inlet and outlet temperatures of the hot fluid and T Cin and T Cout are the inlet and outlet temperatures of the cold fluid. Those four temperatures are shown in the diagram at the left for a straight tube, two pass shell and tube heat exchanger with the cold fluid as the shell side fluid and the hot fluid as the tube side fluid.
Heat Transfer Rate, QHeat exchanger calculations with the heat exchanger design equation require a value for the heat transfer rate, Q, which can be calculated from the known flow rate of one of the fluids, its heat capacity, and the required temperature change. Following is the equation to be used:Q = m H C pH (T Hin – T Hout) = m C C pC (T Cout – T Cin), wherem H = mass flow rate of hot fluid, slugs/hr,C pH = heat capacity of the hot fluid, Btu/slug- oFm C = mass flow rate of cold fluid, slugs/hr,Cp C = heat capacity of the cold fluid, Btu/slug- oF,and the temperatures are as defined in the previous section.The required heat transfer rate can be determined from known flow rate, heat capacity and temperature change for either the hot fluid or the cold fluid. Then either the flow rate of the other fluid for a specified temperature change, or the outlet temperature for known flow rate and inlet temperature can be calculated. Overall Heat Transfer Coefficient, UThe overall heat transfer coefficient, U, depends on the conductivity through the heat transfer wall separating the two fluids, and the. Convection coefficients on both sides of the heat transfer wall.
For a shell and tube heat exchanger, for example, there would be an inside convective coefficient for the tube side fluid and an outside convective coefficient for the shell side fluid. The heat transfer coefficient for a given heat exchanger is often determined empirically by measuring all of the other parameters in the basic heat exchanger equation and calculating U. Typical ranges of U values for various heat exchanger/fluid combinations are available in textbooks, handbooks and on websites. A sampling is given in the table at the right for shell and tube heat exchangers: SummaryPreliminary heat exchanger design to estimate the required heat exchanger surface area can be done using the basic heat exchanger equation, Q = U A ΔT lm, if values are known or can be estimated for Q, U and ΔT lm. Heat exchanger theory tells us that ΔT lm is the right average temperature difference to use.For example preliminary heat exchanger design calculations, see the article, '.'
For Excel spreadsheet templates that can be downloaded to make preliminary heat exchanger design calculations, see the article: '.' References and Image CreditReferences for Further Information:1. Bengtson, H., an online, continuing course for PDH credit2.
And Liu, H., Heat Exchangers: Selection, Rating and Thermal Design, CRC Press, 2002.3. Kuppan, T., Heat Exchanger Design Handbook, CRC Press, 2000.Image Credit:Straight tube, two pass, shell and tube heat exchanger: This post is part of the series: Heat Exchanger Design.