Heat Exchanger Calculator
Calculate heat duty, LMTD, and required area for shell-and-tube heat exchangers. Enter values for instant results with step-by-step formulas.
Formula
Q = U x A x LMTD | LMTD = (dT1 - dT2) / ln(dT1/dT2)
Where Q is heat duty (BTU/hr), U is the overall heat transfer coefficient (BTU/hr-ft^2-F), A is heat transfer area (sq ft), and LMTD is the Log Mean Temperature Difference. For counterflow: dT1 = T_hot_in - T_cold_out, dT2 = T_hot_out - T_cold_in.
Worked Examples
Example 1: Process Water Heater Design
Problem: Hot process fluid (10,000 lb/hr, cp=1.0) enters at 200F and exits at 120F. Cold water enters at 70F and exits at 140F. Counterflow with U = 150 BTU/hr-ft^2-F. Find heat duty, LMTD, and required area.
Solution: Q = m_dot x cp x (T1i - T1o) = 10000 x 1.0 x (200 - 120) = 800,000 BTU/hr\n\nCounterflow LMTD:\ndeltaT1 = T1i - T2o = 200 - 140 = 60F\ndeltaT2 = T1o - T2i = 120 - 70 = 50F\nLMTD = (60 - 50) / ln(60/50) = 10 / 0.1823 = 54.85F\n\nA = Q / (U x LMTD) = 800,000 / (150 x 54.85) = 97.2 sq ft\n\nEffectiveness = 800000 / (10000 x 1.0 x (200-70)) = 800000/1300000 = 61.5%
Result: Q = 800,000 BTU/hr | LMTD = 54.85F | Area = 97.2 sq ft | Effectiveness = 61.5%
Example 2: Steam Condenser Sizing
Problem: Condense steam at 212F (enters and exits at 212F, effectively) to heat water from 60F to 180F. Hot side flow 5,000 lb/hr, cp=1.0 BTU/lb-F equivalent duty. U = 250 BTU/hr-ft^2-F.
Solution: Q = 5000 x 1.0 x (212 - 180) = 160,000 BTU/hr (approximate for comparison)\n\nUsing given temps with hot: 212in/200out, cold: 60in/180out counterflow:\ndeltaT1 = 212 - 180 = 32F\ndeltaT2 = 200 - 60 = 140F\nLMTD = (32 - 140) / ln(32/140) = -108 / -1.476 = 73.17F\n\nFor Q = 5000 x 1.0 x 12 = 60000 BTU/hr:\nA = 60000 / (250 x 73.17) = 3.28 sq ft
Result: Q = 60,000 BTU/hr | LMTD = 73.17F | Area = 3.28 sq ft
Frequently Asked Questions
What is the overall heat transfer coefficient U and what factors affect it?
The overall heat transfer coefficient U (BTU/hr-ft^2-F or W/m^2-K) represents the combined thermal resistance of all heat transfer paths between the two fluids. It includes the convective resistance on the hot side (1/h_hot), the tube wall conduction resistance (t/k_wall), the convective resistance on the cold side (1/h_cold), and fouling resistances on both sides (R_f). The overall relationship is 1/U = 1/h_hot + R_f_hot + t/k + R_f_cold + 1/h_cold. Typical U values range from 10-30 BTU/hr-ft^2-F for gas-to-gas exchangers, 50-150 for gas-to-liquid, 150-300 for liquid-to-liquid with water, and 500-1000 for condensing steam to water. The individual convective coefficients depend on fluid velocity, fluid properties (viscosity, thermal conductivity, density), and geometry. Higher velocities increase h but also increase pressure drop, requiring optimization of tube diameter, baffle spacing, and flow velocity.
What is the difference between counterflow and parallel flow heat exchangers?
In counterflow (countercurrent) configuration, the hot and cold fluids flow in opposite directions, while in parallel flow (cocurrent), they flow in the same direction. Counterflow is almost always preferred because it achieves a higher LMTD for the same inlet and outlet temperatures, requiring less heat transfer area and thus lower capital cost. Counterflow is the only arrangement that can heat the cold fluid above the hot fluid outlet temperature, and it can achieve closer approach temperatures (smaller temperature difference between fluids at one end). The maximum effectiveness of a counterflow exchanger approaches 1.0 as the area increases, while a parallel flow exchanger is limited to an effectiveness of 1/(1+Cr) where Cr is the capacity ratio. Parallel flow is occasionally preferred when it is important to limit the cold fluid outlet temperature (to prevent thermal decomposition), for rapid quenching applications, or when the temperature cross in counterflow would require multiple shell passes.
What is fouling and how does it affect heat exchanger performance?
Fouling is the accumulation of unwanted deposits on heat transfer surfaces that increases thermal resistance and reduces heat exchanger performance over time. Common fouling mechanisms include scaling (precipitation of dissolved minerals like calcium carbonate), biological fouling (growth of algae, bacteria, or marine organisms), corrosion fouling (oxide layer buildup), particulate fouling (deposition of suspended solids), and chemical reaction fouling (polymerization or coking). Design fouling factors (resistances) are added to the clean overall coefficient to account for expected fouling: typical values range from 0.0005 hr-ft^2-F/BTU for clean river water to 0.003 for heavy fuel oil. Fouling can reduce heat transfer by 10-30% or more and increase pressure drop significantly. Mitigation strategies include proper water treatment, regular cleaning schedules (chemical or mechanical), maintaining adequate flow velocities (to prevent settling), and selecting appropriate materials. Over-designing for fouling increases capital cost but extends cleaning intervals.
How is the effectiveness-NTU method used for heat exchanger design?
The effectiveness-NTU method is an alternative to the LMTD method that is particularly useful when outlet temperatures are unknown (rating problems) or when the heat exchanger configuration is complex. Effectiveness (epsilon) is defined as the ratio of actual heat transfer to the maximum possible heat transfer: epsilon = Q / Q_max, where Q_max = C_min x (T_hot_in - T_cold_in) and C_min is the smaller of the two heat capacity rates (m_dot x cp). NTU (Number of Transfer Units) = U x A / C_min represents the dimensionless size of the exchanger. The capacity ratio Cr = C_min / C_max. For each flow configuration, there is a unique relationship between effectiveness, NTU, and Cr. For counterflow: epsilon = [1 - exp(-NTU(1-Cr))] / [1 - Cr x exp(-NTU(1-Cr))]. The effectiveness-NTU method avoids iteration when solving for outlet temperatures and provides physical insight into heat exchanger performance limits.
How do you select the right type of heat exchanger for a given application?
Heat exchanger selection depends on operating conditions, fluid properties, space constraints, maintenance requirements, and cost. Shell-and-tube exchangers handle the widest range of temperatures (up to 1000+ degrees F) and pressures (up to thousands of psi) and are the standard choice for most process applications. Plate heat exchangers are more compact (3-5 times less area) and easier to clean but are limited to lower pressures (typically under 300 psi) and temperatures (under 400 degrees F). Double-pipe exchangers are simple and inexpensive for small duties (under 50 sq ft). Air-cooled exchangers eliminate the need for cooling water but require large plot space. Spiral exchangers handle slurries and fouling fluids well due to their single-channel design. Plate-fin exchangers provide extremely high area density for cryogenic and aerospace applications. The selection process typically starts with the fluid properties and operating conditions, narrows to feasible types, then optimizes based on total cost of ownership.
What is the approach temperature and why is it important in heat exchanger design?
Approach temperature is the minimum temperature difference between the hot and cold fluids at any point in the heat exchanger. In a counterflow exchanger, the approach occurs at one end where the temperatures are closest. A smaller approach temperature means more heat is recovered but requires a larger (and more expensive) heat exchanger area, since Q = U x A x LMTD and a smaller approach reduces the LMTD. Typical minimum approach temperatures range from 10-20 degrees F for liquid-liquid exchangers, 20-30 degrees F for gas-liquid, and 30-50 degrees F for gas-gas. In heat integration (pinch analysis), the minimum approach temperature (delta T_min) determines the maximum possible heat recovery and the minimum heating and cooling utility requirements. Reducing delta T_min below 15-20 degrees F usually becomes uneconomical because the area increases exponentially while the energy savings increase only linearly. The optimal approach temperature balances capital cost against energy cost.