![]() The extent of this temperature drop depends on the characteristics of the boundary layer. There is a temperature drop from $T_1$ to $T_2$ across the convective boundary layer. The bulk temperature of the hot fluid is represented by the black dot labelled $T_1$. The orange lines in Figure 4-7 represent relative temperature changes. In some cases, additional thermal resistance effects called “fouling factors” are also included in the mathematical definition of the $U$-value.įigure 4-7 shows how the $U$-value for a heat exchanger where the two fluids are separated by a flat plate can be viewed as a sum of several thermal resistances. The $U$-value of a heat exchanger involves knowing the convection coefficient for both fluid-to-surface interfaces, as well as the thermal conductivity of the wall separating the fluids. The value of $U$ is the rate of heat transfer through the heat exchanger (in Btu/hr), per square foot of internal surface area, per ✯ of log mean temperature difference. To make the units in Formula 4-5 consistent, $U$ must have units of Btu/hr/ft 2/✯. The constant $U$ is called the overall heat transfer coefficient of the heat exchanger. This proportionality can be changed to a formula (e.g., an equality with an = sign, rather than a proportionality) by introducing a constant called $U$. $LMTD$ = log mean temperature difference established by the current conditions (✯) ![]() $A$ = internal surface area separating the two fluids within the heat exchanger (ft 2) $q$ = rate of heat transfer across the heat exchanger (Btu/hr) ![]() This can be expressed as the proportionality: Thus, the heat transfer rate is proportional to the multiplication of internal surface area ($A$) times the log mean temperature difference ($LMTD$). It is also directly proportional to the surface area that separates the two fluids. The heat transfer rate through a heat exchanger is directly proportional to the $LMTD$. This concept should always be observed when planning and documenting the design of any hydronic system using heat exchangers. This implies that to attain the highest possible rate of heat transfer, heat exchangers should always be configured for counterflow rather than parallel flow. The higher the $LMTD$, the higher the rate of heat transfer. Namely that the $LMTD $ of a heat exchanger configured for counterflow will always be higher than that of the same heat exchanger configured for parallel flow and having the same entering conditions for both flow streams. Heat transfer theory can also be used to prove a very important concept in the application of heat exchangers. However, when the inertial forces become dominant over the viscous forces, which would be characterized by higher Reynolds numbers, the dampening effects of viscosity are not able to prevent turbulent flow from being established and maintained.įor flow through a round pipe, the $Re\#$ is calculated using Formula 4-1.įormula 4-1: $$ Re\# = 40.3^o F $$ Any disturbance to the flow stream that might otherwise induce turbulence is quickly dampened out by viscous forces, and thus sustained turbulence cannot exist. ![]() When the Reynolds number is low, the inertial forces are relatively weak compared to the viscous forces. It also accounts for the speed of the fluid and the geometry of surfaces in contact with the fluid. It takes several physical characteristics of the flowing fluid into account, including the fluid’s density and viscosity, both of which are dependent on the fluid’s temperature. The Reynolds number is a ratio of the inertial forces existing in a flow stream compared to the viscous forces in that flow stream. It’s based on calculating a dimensionless quantity called the Reynolds number of the fluid (abbreviated as $Re\#$). It’s possible to predict if flow through a pipe or across a smooth plate will be laminar or turbulent. ![]()
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