6.5 Heat exchangers

Heat exchangers are crucial devices in chemical engineering, transferring heat between fluids efficiently. They come in various types, each suited for specific applications. Understanding their design and operation is key to optimizing heat transfer processes.

This section dives into heat exchanger types, LMTD calculations, and overall heat transfer coefficients. We'll explore how to determine heat exchanger effectiveness and efficiency, essential for designing and analyzing these vital components in chemical engineering systems.

Heat exchanger types and applications

Classification and main types of heat exchangers

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• Heat exchangers are devices used to transfer heat between two or more fluids, which can be in direct contact or separated by a solid wall
• The main types of heat exchangers are shell and tube, plate, extended surface, and regenerative heat exchangers, each with specific advantages and applications

Shell and tube heat exchangers

• Shell and tube heat exchangers consist of a bundle of tubes enclosed within a cylindrical shell, with one fluid flowing through the tubes and the other flowing through the shell
• They are commonly used in chemical processing, power generation, and oil refining due to their robustness and ability to handle high pressures and temperatures

Plate and extended surface heat exchangers

• Plate heat exchangers are composed of a series of corrugated plates stacked together, forming channels for fluid flow
• They are compact, easy to clean, and often used in food processing and pharmaceutical industries where hygiene is critical
• Extended surface heat exchangers, such as fin-tube or plate-fin heat exchangers, have fins attached to the heat transfer surfaces to increase the surface area and enhance heat transfer
• They are used in air conditioning, refrigeration, and gas processing applications where high heat transfer rates are required in a compact space

Regenerative heat exchangers

• Regenerative heat exchangers, such as rotary or fixed matrix types, involve a periodic flow reversal of the fluids, allowing for efficient heat recovery
• They are used in high-temperature applications, such as glass and steel manufacturing, where heat recovery is essential for energy efficiency

LMTD calculations for heat exchangers

Log mean temperature difference (LMTD) method

• The LMTD method is used to determine the heat transfer rate and the required heat transfer area in a heat exchanger, given the inlet and outlet temperatures of the hot and cold fluids
• The LMTD is a logarithmic average of the temperature differences between the hot and cold fluids at the inlet and outlet of the heat exchanger, accounting for the non-linear temperature profile along the heat exchanger length
• The LMTD is calculated using the following equation: $LMTD = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)$, where ΔT1 and ΔT2 are the temperature differences between the hot and cold fluids at the two ends of the heat exchanger

Heat transfer rate calculation

• The heat transfer rate (Q) is calculated using the equation: $Q = U × A × LMTD$, where U is the overall heat transfer coefficient, and A is the heat transfer area
• The overall heat transfer coefficient (U) depends on the fluid properties, flow conditions, and the geometry of the heat exchanger, and is determined separately

LMTD correction factor for multi-pass and cross-flow heat exchangers

• For heat exchangers with multiple passes or cross-flow arrangements, a correction factor (F) is applied to the LMTD to account for the deviation from counter-current flow
• The corrected LMTD is then used in the heat transfer rate equation: $Q = U × A × F × LMTD$
• The correction factor (F) is typically obtained from charts or empirical correlations based on the heat exchanger geometry and the temperature ratios of the fluids

Overall heat transfer coefficient

Definition and calculation

• The overall heat transfer coefficient (U) is a measure of the heat transfer performance of a heat exchanger, considering the resistances to heat transfer on both the hot and cold fluid sides, as well as the resistance of the separating wall
• The overall heat transfer coefficient is calculated using the equation: $1/U = 1/h1 + 1/h2 + Rw$, where h1 and h2 are the individual heat transfer coefficients for the hot and cold fluids, respectively, and Rw is the thermal resistance of the separating wall

Individual heat transfer coefficients

• The individual heat transfer coefficients (h) depend on the fluid properties, flow conditions, and the geometry of the heat exchanger
• They can be determined using empirical correlations, such as the Dittus-Boelter or Sieder-Tate equations for turbulent flow in tubes: $Nu = 0.023 × Re^{0.8} × Pr^{0.4}$ (Dittus-Boelter) or $Nu = 0.027 × Re^{0.8} × Pr^{1/3} × (μ/μ_w)^{0.14}$ (Sieder-Tate), where Nu is the Nusselt number, Re is the Reynolds number, Pr is the Prandtl number, and μ/μ_w is the viscosity ratio

Fouling factors

• Fouling, which is the accumulation of deposits on the heat transfer surfaces, can significantly reduce the overall heat transfer coefficient over time
• Fouling factors are often included in the overall heat transfer coefficient calculation to account for this effect: $1/U = 1/h1 + 1/h2 + Rw + Rf1 + Rf2$, where Rf1 and Rf2 are the fouling factors for the hot and cold fluid sides, respectively
• Fouling factors are determined experimentally or from published data for different fluids and heat exchanger materials

Heat exchanger effectiveness vs efficiency

NTU-effectiveness method

• The NTU-effectiveness method is an alternative approach to analyze heat exchanger performance, particularly when the outlet temperatures of the fluids are not known
• NTU stands for "Number of Transfer Units," which is a dimensionless parameter that represents the size of the heat exchanger relative to its heat transfer capacity
• NTU is calculated using the equation: $NTU = UA / Cmin$, where Cmin is the smaller of the two fluid heat capacity rates (m × cp)

Effectiveness calculation

• The effectiveness (ε) of a heat exchanger is defined as the ratio of the actual heat transfer rate to the maximum possible heat transfer rate
• It is a function of the NTU and the heat capacity rate ratio (Cr = Cmin / Cmax)
• Effectiveness is calculated using different equations depending on the flow arrangement (counter-flow, parallel-flow, cross-flow, etc.) and the heat capacity rate ratio, such as: $ε = (1 - exp(-NTU × (1 - Cr))) / (1 - Cr × exp(-NTU × (1 - Cr)))$ for counter-flow heat exchangers

Efficiency determination

• The efficiency of a heat exchanger can be determined by comparing the actual heat transfer rate (calculated using the effectiveness) to the theoretical maximum heat transfer rate for a given inlet temperature difference and flow rates
• The actual heat transfer rate is calculated as: $Q_actual = ε × Cmin × (Th_in - Tc_in)$, where Th_in and Tc_in are the inlet temperatures of the hot and cold fluids, respectively
• The theoretical maximum heat transfer rate is calculated as: $Q_max = Cmin × (Th_in - Tc_in)$
• The efficiency is then determined as: $η = Q_actual / Q_max = ε$

Application in heat exchanger design and analysis

• The NTU-effectiveness method is particularly useful for designing heat exchangers and evaluating their performance under different operating conditions
• It allows for the determination of the required heat transfer area or the outlet temperatures of the fluids, given the desired effectiveness or heat transfer rate
• The method is also used to compare the performance of different heat exchanger configurations and to optimize the design for a specific application