This article provides an in-depth exploration of the overall heat transfer coefficient, a crucial parameter in understanding heat exchange processes in various engineering systems. It discusses the formula for calculating this coefficient in different scenarios, including multi-layered systems and cylindrical tubes, along with practical considerations such as surface fouling and the inclusion of fins. Representative values and factors influencing the overall heat transfer coefficient are also outlined, offering valuable insights for engineers and researchers.
What is the overall heat transfer coefficient?
This coefficient is defined as the total thermal resistance to heat transfer between two fluids.
Figure 1.
Overall heat transfer coefficient formula
The overall heat transfer coefficient for a multi-layered system (see Figure 1), such as a wall, pipe, or heat exchanger, with fluid flow on each side of the wall, can be calculated using the following formula:
Where U is the overall heat transfer coefficient (W/(m2K)), kn thermal conductivity of the material in layer n (W/(m K)), hi and ho are convection heat transfer coefficients (W/(m2K)) between inside and outside walls and fluids, respectively. Heat transfer (W) through a system such as the system in figure 1 can be calculated as:
Where ΔT is the temperature difference of the fluids and A is the area of the heat transfer.
Thermal equivalent circuit
A simple approach to calculate the overall heat transfer coefficient is a thermal equivalent circuit. For instance, the system in Figure 2 can be presented as a circuit illustrated in Figure 3.
Figure 2. Heat transfer between two fluids through a composite wall. Note that A1 and A4 are equal, and L2 and L3 are equal.
Figure 3. The thermal equivalent circuit of the system is in Figure 2.
Conductive and convective thermal resistances are indicated in equations 3 and 4, respectively.
If thermal resistances are in series, the total thermal resistance is:
If thermal resistances are in parallel, the total thermal resistance is:
Therefor the total thermal resistance for the circuit in Figure 3 is:
Finally, the rate of heat transfer through the circuit is:
Based on equation 1, equation 8 can be rewritten as:
For the system in Figure 2, A1 and A2 can be replaced with A in equation 9. Note that all the mentioned equations are for steady state condition.
Overall heat transfer coefficient for cylindrical tubes
The Conductive and convective thermal resistances are indicated for cylindrical coordinates in equations 10 and 11, respectively.
H is the tube length, r is the radius of the contact surface between the solid and the fluid, and rinner and router are the radii of the tube’s inner and outer surfaces.
In cylindrical coordinates, the calculation of an overall heat transfer coefficient depends on whether it is based on the cold or hot side, because inner and outer surface area of a tube are different, unlike the system in Figure 1, U1A1 is not equal to U2A2.
Overall heat transfer coefficient units
The units of overall heat transfer coefficient expressed in various systems:
- International System of Unit (SI): Watts per square meter per Kelvin (W/(m2.K))
- Imperial Units (British Engineering Unit): BTU per hour per square foot per degree Fahrenheit (BTU/(h.ft2.°F))
- Metric Unit: Joule per second per square meter per Kelvin (J/(s.m2.K)) or Watt per square meter per degree Celsius (W/(m2.°C))
- International Unit: Kilocalorie (IT) per hour per square meter per degree Celsius (kcal/(h.m2.°C))
The overall heat transfer coefficient for heat exchangers
Equation 1 is designed for clean, unfinned surfaces, yet real-world heat exchangers commonly face fouling due to fluid impurities, rust, or chemical reactions with the wall material. This fouling results in the buildup of films or scales on the surface, notably raising the resistance to heat transfer between fluids. Moreover, in heat exchaners usually fins are added into surfaces, which increase overall heat transfer coefficient.
The overall heat transfer coefficient formula for heat exchangers
To accommodate fouling effects, Equation 1 incorporates an additional thermal resistance known as the fouling factor (Rf ). This factor’s magnitude depends on various factors like operating temperature, fluid velocity, and the duration of heat exchanger service.
While representative fouling factors are provided in Table 1, it’s crucial to note that the fouling factor is dynamic during heat exchanger operation, beginning at zero for a clean surface and increasing as deposits accumulate.
Table 1. Representative fouling factors, from fundamentals of heat and mass transfer by Frank P. Incropera et al.
| Fluid | Rf (m2.K/W) |
| Seawater and treated boiler feedwater (below 50_C) | 0.0001 |
| Seawater and treated boiler feedwater (above 50_C) | 0.0002 |
| River water (below 50_C) | 0.0002– 0.001 |
| Fuel oil | 0.0009 |
| Refrigerating liquids | 0.0002 |
| Steam (nonoil bearing) | 0.0001 |
Furthermore, fins are commonly incorporated into surfaces exposed to one or both fluids. By increasing the surface area, fins decrease the overall resistance to heat transfer. Consequently, when considering both surface fouling and fin effects, the overall heat transfer coefficient undergoes modification as follows:
The quantity ηo in Equation 13 is termed the overall surface efficiency or temperature effectiveness of a finned surface. ηo is expressed in equation 14.
where Af is the entire fin surface area, and ηf is the efficiency of a single fin.
Overall heat transfer coefficient table
TABLE 2 Representative Values of the overall heat transfer coefficient, from fundamentals of heat and mass transfer by Frank P. Incropera et al.
| Fluid Combination | U (W/m2 K) |
| Water to water
Water to oil Steam condenser (water in tubes) Ammonia condenser (water in tubes) Alcohol condenser (water in tubes) Finned-tube heat exchanger (water in tubes, air in cross flow) |
850-1700
110-350 1000-6000 800-1400 250-700 25-50 |
Typical values of the overall heat-transfer coefficient for various types of heat exchanger are given in Table 3. The reference values of Table 3 have been taken from Coulson & Richardson’s Chemical Engineering Vol. 6, 2nd Edition & 3rd Edition, R K Sinnot.
Table 3. Typical overall heat transfer coefficients
|
Shell and tube exchangers |
|||||
| Hot fluid | Cold fluid | U (W/(m2.K)) | |||
| Heat exchangers
Water Organic solvents Light oils Heavy oils Gases Coolers Organic solvents Light oils Heavy oils Gases Organic solvents Water Gases Heaters Steam Steam Steam Steam Steam Dowtherm Dowtherm Flue gases Flue Condensers Aqueous vapours Organic vapours Organics (some non-condensables) Vacuum condensers Vaporisers Steam Steam Steam |
Water Organic solvents Light oils Heavy oils Gases
Water Water Water Water Brine Brine Brine
Water Organic solvents Light oils Heavy oils Gases Heavy oils Gases Steam Hydrocarbon vapours
Water Water Water Water
Aqueous solutions Light organics Heavy organics |
800-1500 100-300 100-400 50-300 10-50
250-750 350_ 900 60-300 20-300 150-500 600-1200 15-250
1500-4000 500-1000 300_ 900 60-450 30-300 50-300 20-200 30-100 30-100
1000-1500 700-1000 500-700 200-500
1000-1500 900-1200 600_ 900 |
|||
|
Air-cooled exchangers |
|||||
| Process fluid | |||||
| Water
Light organics Heavy organics Gases, 5-10 bar 10-30 bar Condensing hydrocarbons |
300—450
300-700 50-150 50-100 100-300 300-600 |
||||
|
Immersed coils |
|||||
| Coil | Pool | ||||
| Natural circulation Steam
Steam Steam Water Water Agitated Steam Steam Steam Water Water |
Dilute aqueous solutions Light oils Heavy oils Aqueous solutions Light oils Dilute aqueous solutions Light oils Heavy oils Aqueous solutions Light oils |
500-1000 200-300 70-150 200-500 100-150 800-1500 300-500 200-400 400-700 200-300 |
|||
|
Jacketed vessels |
|||||
| Jacket | Vessel | ||||
| Steam
Steam Water Water |
Dilute aqueous solutions
Light organics Dilute aqueous solutions Light organics |
500-700
250-500 200-500 200-300 |
|||
|
Gasketed-plate exchangers |
|||||
| Hot fluid | Cold fluid | ||||
| Light organic
Light organic Viscous organic Light organic Viscous organic Light organic Viscous organic Condensing steam Condensing steam Process water Process water Dilute aqueous solutions Condensing steam |
Light organic
Viscous organic Viscous organic Process water Process water Cooling water Cooling water Light organic Viscous organic Process water Cooling water Cooling water Process water |
2500-5000
250-500 100-200 2500-3500 250-500 2000-4500 250-450 2500-3500 250-500 5000-7500 5000-7000 5000-7000 3500-4500 |
|||
Overall heat transfer coefficient of water
The overall heat transfer coefficient for water systems varies depending on numerous factors such as the flow regime, system geometry, materials involved, and the presence of fouling. In applications like heat exchangers or pipes carrying water, this coefficient is influenced by parameters such as flow rates, temperatures, and the design of the system. The exact value necessitates detailed analysis or experimental determination due to the variability introduced by different operating conditions and configurations.
Overall heat transfer coefficient in ANSYS Fluent
In a heat transfer simulation using ANSYS Fluent, you do not need to manually enter the value of the overall heat transfer coefficient. The software calculates heat transfer and mass transfer directly based on the defined boundary conditions, material properties, and the governing equations.
After running an ANSYS Fluent simulation, the overall heat transfer coefficient value can indeed be extracted as an output from the software. However, the software takes the reference temperature (T∞) from a predefined value, which is sometimes unsuitable and needs to be changed. Therefore, it is often necessary to set the reference value manually. By extracting heat fluxes and temperature differences and calculating the heat transfer coefficient outside the software, using equation 2, sometimes a more accurate overall heat transfer coefficient may be achieved.
Figure 4. Reference values in ANSYS Fluent
Conclusion
In conclusion, grasping the significance of the overall heat transfer coefficient is vital for enhancing the effectiveness of heat exchange processes in engineering systems. By incorporating factors such as surface fouling, fin utilization, and system geometry, engineers can precisely forecast and optimize heat transfer rates. The equations and representative values presented herein serve as valuable resources for designing and evaluating a wide array of engineering applications, from heat exchangers to structural components like pipes and walls.
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