Equations heat exchangers

The equation for forced-convective heat transfer in conduits can be used for plate heat exchangers equation 12.10. 

In designing and evaluating heat exchangers. Equation 5.1 cannot be used directly, as the temperatures ofthe wall surface and are usually unknown. Thus, the usual practice is to use the overall heat transfer coefficient U (kcal h m 2 °C or Wm K" ), which is based on the overall temperature difference - that is, the difference between the bulk temperatures of two... 

Constant liquid density and physical properties are assumed, so the volume of liquid in the reactor is constant with time, as is the volume in the cooling system (jacket or external heat exchanger). Equations (4.4)-(4.6) become... 

Solving the heat exchanger equations using spatial finite differences... 

In this system the thermal model of the secondary circuit contains the heat exchanger part model Mg and the drya- part model Mj. Using the heat exchanger Equation 14.41, the inlet air temperature of the dryer can be determined the solution of the MEN model equation system in Eigure 14.34b gives the mass flow rate of the drying air rh. Thickness and initial state of the material in the dryer can be considered as given. Eor the simulation of static bed dryers, different methods are used [128-130]. 

Replace the Heat Exchangers Equation rE19.4bI shows that a new heat exchanger with half of... 

The shell-and-tube heat exchanger is probably the most common type of exchanger used in the chemical and process industries. The simplest type of such device is the 1-1 design (1 shell pass, 1 tube pass), as illustrated in Fig. 7.7a. Of all shell-and-tube types, this comes closest to pure countercurrent flow and is designed using the basic coimtercurrent equation ... 

Heat exchanger cost data can usually be manipulated such that fixed costs, represented by the coefficient a in Eqs. (F.2) to (F.4), do not vary with exchanger specification. Equations (F.3) and (F.4) can now be rearranged to give the modified exchanger area A as a function of actual area A and the cost law coefficients ... 

Basic Heat-Transfer Equations. Consider a simple, single-pass, parallel-flow heat exchanger in which both hot (heating) and cold (heated) fluids are flowing in the same direction. The temperature profiles of the fluid streams in such a heat exchanger are shown in Figure 2a. 

Assuming that U, and are invariant with respect to temperature and space, one can integrate equation 14 subject to equation 19, and obtain, after rearrangement, a basic heat-transfer equation for a parallel-flow heat exchanger (4). 

A similar derivation can be made for a siagle-pass counterflow heat exchanger ia which the hot and cold fluids ate flowing ia the opposite direction (see Fig. 2b). The resultiag heat-transfer equation is still... 

The equations for counterflow ate identical to equations for parallel flow except for the definitions of the terminal temperature differences. Counterflow heat exchangers ate much mote efficient, ie, these requite less area, than the parallel flow heat exchangers. Thus the counterflow heat exchangers ate always preferred ia practice. 

For heat exchangers other than the parallel and counterflow types, the basic heat-transfer equations, and particularly the effective fluid-to-fluid temperature differences, become very complex (5). For simplicity, however, the basic heat-transfer equation for general flow arrangement may be written as... 

The importance of equations 37—39 is that once the heat-exchanger effectiveness, S, is known for a given heat exchanger, one can compute the actual heat-transfer rate and outlet stream temperatures from specified inlet conditions. This process is known as rating a given heat exchanger. 

The expressions for S can be obtained usiag basic governing heat-transfer equations, such as equations 14 and 19 with proper substitutions of equation 36. For simple, siagle-pass, parallel- and counterflow heat exchangers, the foUowiag expressions result ... 

Entrance andExit SpanXireas. The thermal design methods presented assume that the temperature of the sheUside fluid at the entrance end of aU tubes is uniform and the same as the inlet temperature, except for cross-flow heat exchangers. This phenomenon results from the one-dimensional analysis method used in the development of the design equations. In reaUty, the temperature of the sheUside fluid away from the bundle entrance is different from the inlet temperature because heat transfer takes place between the sheUside and tubeside fluids, as the sheUside fluid flows over the tubes to reach the region away from the bundle entrance in the entrance span of the tube bundle. A similar effect takes place in the exit span of the tube bundle (12). 

Published Cost Correla.tions. Purchased cost of an equipment item, ie, fob at seller s site or other base point, is correlated as a function of one or more equipment—size parameters. A size parameter is some elementary measure of the size or capacity, such as the heat-transfer area for a heat exchanger (see HeaT-EXCHANGETECHNOLOGy). Historically the cost—size correlations were graphical log—log plots, but the use of arbitrary equation forms for correlation has become quite common. If cost—size equations are used in computer databases, some limit logic must be included so that the equation is not used outside of the appHcable size range. 

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