Kinetics [rate] and Thermodynamics of heat exchangers

This note attempts to highlight when the rate of heat transfer becomes a dominating factor over simple thermodynamics.

Generalized facts

The?kinetics work predominantly when there are resistances to heat flow. Resistance determines the rate of heat transfer in these situations, Q = U A dT. In processes where resistances do not play a critical role , Q = m Cp dT, thermodynamics may become more important in determining the behavior of the system. Examples of such processes include cooling towers and refrigerators, where thermodynamic principles govern the efficiency and effectiveness of heat transfer. In a heat exchanger, there is an approach temperature that arises from the unequal resistances in a heat exchanger. The interplay of the resistances with the heat transfer process to get the maximum pinch temperature and no temperature cross is a very critical factor. The resistances in the path of heat transfer are kinetics-controlled factors.

Basic facts

Simple cold and hot fluid mixing

When hot and cold miscible fluids are mixed, heat transfer occurs from the hot fluid to the cold fluid. During the process, the temperature difference between hot and cold fluids drives the heat transfer until both fluids reach the same temperature. The rate of heat transfer is dependent in addition to the temperature difference between the fluids, on the specific heat capacity of the fluids, and the mass or volume of the fluids being mixed. In such a process the specific heat is the only resistance. In such cases, Q = m Cp dT

Heat transfer in a heat exchanger

The same process as above becomes different when hot and cold fluid are separated by a metal plate. The problem is multiple resistances in the path of heat flow with nonlinear thermal properties

The temperature gradient in forced convection

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?Simply count the resistances along the heat flow path. Each resistance provides its barrier to heat flow. The specific heats of the fluids on either side, cold and hot, differ. The thermal conductivities of the boundary layers on either side of the metal plate where conduction is the mode of heat transfer differ. Furthermore, the metal has its thermal resistance. Besides all these resistances there are fouling on both in and outside of the tube surfaces that heat has to overcome. As a result, heat transfer in a heat exchanger is a rather complex process.

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Nonlinear response of thermal conductivity and specific heat with temperature further compounds heat transfer. In such cases, Q = U A dT.? U represents the inverse of the sum of all resistances.

To summarize, in heat transfer, the two main forms of heat transfer resistance that need to be overcome are convection and conduction, with a metal wall serving as a barrier between them. Heat, Q moves from hot to cold. For a fluid flow, when there is no external resistance to heat flow, only Cp [specific heat] offers the internal resistance to heat flow.?Cp takes away Q /mass- degc and supplies it for molecular motions, the equation is Q = m Cp dt.

When there are external resistances like the metal wall between the hot and cold fluid in a heat exchanger with boundary layers, the equation gets modified to, Q= U A dt, "U" is called the overall heat transfer coefficient. In the equation Q = U A dt, the overall heat transfer coefficient U takes into account various modes of heat transfer, such as conduction, convection, and radiation.

Thermodynamics and Kinetics in heat exchangers

Both kinetics and thermodynamics play a role in controlling a heat exchanger. Thermodynamics determines the overall energy transfer and heat exchange in the system, while kinetics governs the rate at which these processes occur. The design and operation of a heat exchanger must consider both thermodynamic principles, such as heat transfer efficiency and temperature gradients, as well as kinetic factors, like flow rates and reaction rates, to optimize performance.

Role of kinetics [rate] in heat transfer

In a heat exchanger with multiple resistances Q = U A dT

The overall heat transfer coefficient, U takes into account all resistances contributing to the heat transfer rate in the path of heat transfer and U is inversely proportional to dT

The resistances in a heat exchanger, including those across solid walls and fluid boundary layers, are expressed in units of watts per meter per Kelvin, reflecting the relationship between temperature difference, heat transfer rate, and material/flow properties in determining the efficiency of heat transfer processes.

In this concept, the overall heat transfer resistance in a heat exchanger is typically expressed in terms of thermal conductivity (W/m*K) and thickness (m) for solid walls and convective heat transfer coefficients (W/m^2*K) for fluid streams.

The thermal resistance for conduction through a solid wall can be calculated using the equation:

R_wall = L_wall / (k_wall A) where:

- R_wall is the thermal resistance of the solid wall (in K/W),

- L_wall is the thickness of the wall (in meters),

- k_wall is the thermal conductivity of the wall material (in W/mK), and

- A is the surface area of the wall (in square meters).

Similarly, the thermal resistance for convection across a fluid boundary layer can be calculated as:

R_fluid = 1 / (h*A) where:

- R_fluid is the thermal resistance of the fluid boundary layer (in K/W),

- h is the convective heat transfer coefficient (in W/m^2*K), and

- A is the surface area for convective heat transfer (in square meters).

The overall thermal resistance in a heat exchanger is obtained by summing up the individual resistances for conduction through solid walls and convection across fluid boundary layers. This concept helps in analyzing and optimizing heat exchanger performance by identifying and minimizing the dominant resistances to heat transfer.

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