**TABLE OF CONTENT**

**WHAT IS THE OVERALL HEAT TRANSFER COEFFICIENT? **

*In industry, heat transfer problems are usually resolved for composite materials or systems with different layers which involve different modes of heat transfer such as conduction, convection, and radiation.* *The thermal resistance that is offered by the different layers in a system is referred to as the Overall Heat Transfer Coefficient. It is also known as the U-factor.*

*The U-factor that is used in calculating overall heat transfer is analogous to the convection heat transfer coefficient used in Newton’s law of cooling.**The overall heat transfer coefficient is dependant on the geometry of the object or surface. For example, in a wall, we can observe different modes of heat transfer, the outer surface of the wall experiences convection heat transfer while the space between the walls undergoes conduction mode of heat transfer.*

The overall heat transfer coefficient of the wall is taken to be a sum of the convective heat transfer coefficient and the conductive heat transfer coefficient. In short, the overall heat transfer coefficient is the summation of the individual heat transfer coefficient. Further explanation on the derivation of the overall heat transfer coefficient and using it for composite heat transfer problems are explained below.

**SIGNIFICANCE OF OVERALL HEAT TRANSFER COEFFICIENT**

In industrial applications, it is essential to know the overall heat transfer coefficient, especially in cases where the heat transfer rate needs to be optimized for better performance of a system. To calculate the heat transfer rate Q(dot) for any system with different fluids or different layers, it is essential to know the overall heat transfer coefficient.

From the value of the overall heat transfer coefficient and the rate of heat transfer, it is possible to calculate the individual heat transfer coefficient. This would help in modifying a particular portion of the thermal system for better performance as per the requirements.

Under steady-state conditions, the rate of heat transfer from a fluid at bulk temperature T1 to solid at bulk temperature T2 over an incremental area dA is given by the rate of heat transfer dQ(dot) i.e.

**dQ(dot) = U*(T _{2 }– T_{1})*A**

Here the overall heat transfer coefficient is represented by the letter U.

**FORMULA FOR OVERALL HEAT TRANSFER COEFFICIENT | HOW TO FIND OVERALL HEAT TRANSFER COEFFICIENT | OVERALL HEAT TRANSFER COEFFICIENT FORMULA | HOW TO CALCULATE OVERALL HEAT TRANSFER COEFFICIENT | OVERALL HEAT TRANSFER COEFFICIENT DERIVATION**

The formula for the Overall Heat Transfer coefficient is given by

**Qdot = U*(T _{1 }+ T_{2})*A**

Derivation for the Overall Heat Transfer coefficient for Wall given below

Consider a composite wall that is exposed to the external environment at temperature T1, and the conduction coefficient is noted to be H_{1}. The ambient temperature inside the room is T2 and the convection coefficient is H_{2}. Here the heat transfer is using conduction and convection. Either side of the wall experiences heat transfer using convection at different magnitudes.

The temperature inside the wall varies and is a value between T1 and T2 if there is no source of heat generation from within the wall. The conduction coefficient of the wall is taken to be K in this case unless the wall is made up of different layers which is the usual case. In real life scenario, the wall is made up of different layers such as plastering, bricks, cement, etc. In such cases, it is essential to take into consideration the thermal resistance offered by each layer of the wall.

The overall heat transfer coefficient for the above system is as given below:

And the rate of heat transfer **Q(dot) = UAΔT**

It is evident that U is not a thermophysical property and depends on the flow, velocity, and also on the material through which the heat transfer takes place.

**OVERALL HEAT TRANSFER COEFFICIENT WITH FOULING**

Fouling is a usual problem that is encountered in heat exchangers. It is an additional layer that is formed on the inner surface of the heat exchanger. Several factors contribute to the fouling of the surfaces of heat exchangers. The rate of heat transfer is reduced because of fouling which in turn affects the heat transfer efficiency.

The decrease in heat transfer efficiency is accounted for in calculations using the fouling factor. It is often referred to as the dirt factor. The fouling factor is dependent on the fluid on either side of the heat exchanger.

The overall heat transfer coefficient with fouling is given by

In the above equation,

U represents the overall heat transfer coefficient

h_{0 }is the heat transfer coefficient on the shell side

h_{i} is the heat transfer coefficient on the tube side

R_{do} is the fouling factor on the shell side

R_{di} is the fouling factor on the tube side

OD is the outer diameter of the tube

ID is the inner diameter of the tube

A_{0} is the outer area of the tube

A_{i }is the inner area of the tube

K_{w }is the value of resistance offered by the tube wall

From the equation, it is evident that the value of the overall heat transfer coefficient decreases with an increase in either or both values of fouling factor (i.e., tube side or shell side). This decrease in the overall heat transfer coefficient will in turn reduce the rate of heat transfer.

**OVERALL HEAT TRANSFER COEFFICIENT UNITS | OVERALL HEAT TRANSFER COEFFICIENT UNIT CONVERSION | OVERALL HEAT TRANSFER COEFFICIENT CONVERSION**

The S.I. unit of overall heat transfer coefficient is W/m^{2} K. Another unit that is used for representing the overall heat transfer coefficient is Btu/(hr.ft^{2 0}F).

The unit conversion from SI unit to English units is follows:

*1 *W/m^{2} K* = = 0.1761 *Btu/(hr.ft^{2 0}F).*)*

**EFFECT OF FLOW RATE ON OVERALL HEAT TRANSFER COEFFICIENT | OVERALL HEAT TRANSFER COEFFICIENT VS FLOW RATE**

The flow rate has an impact on the overall heat transfer coefficient. It is noted that there is a 10% decrease in heat transfer coefficient when the mass flow rate increases by three times. This estimation of the heat transfer coefficient is based on the Dittus-Boelter correlation.

While keeping the area constant, it is observed that the heat transfer coefficient increases by increasing the mass flow rate. A 90% increase in heat transfer coefficient is expected by doubling the mass flow rate. With this increase, there is an expected increase of pressure drop which is proportional to the mass flow rate.

For cases where the velocity is constant, the pressure drop decreases and is inversely proportional to the mass flow rate. The positive aspects that are attained from a higher heat transfer coefficient are lost due to the increased pressure drop when the area is kept constant.

**OVERALL COEFFICIENT OF HEAT TRANSFER TABLE**

The table below provides the overall heat transfer coefficient for a few equipment that are very often used in the industry. The range is provided because the overall heat transfer coefficient is dependent on the fluid that is used in the equipment. For gases, the value of the heat transfer coefficient is very low and that of liquids is much higher.

Equipment | U (W/m^{2)} |

Heat Exchanger | 5-1500 |

Coolers | 5-1200 |

Heaters | 20-4000 |

Condensers | 200-1500 |

Air Cooled Heat Exchangers | 50-600 |

**Table 1:**Overall Coefficient of Heat Transfer for different Equipment

**AVERAGE OVERALL HEAT TRANSFER COEFFICIENT**

In heat transfer problems which consist of two different fluids which could be water and alcohol at two different temperatures, in such cases the average of the temperatures of the two fluids is used for solving the heat transfer problem which is termed as the average overall heat transfer coefficient.

Let’s take Q to be the heat flowing through the surface at an average temperature ΔT_{avg}, and the area across which the heat transfer takes place is taken to be A. The average overall heat transfer coefficient for this heat flow is as given below

**OVERALL HEAT TRANSFER COEFFICIENT BASED ON INSIDE AREA**

For heat exchangers, the overall heat transfer coefficient can be based on either the inside area or on the outside area

When the overall heat transfer coefficient is calculated based on the inside area, the convection coefficient at the inside is taken to be 1/h_{i}, while the conduction coefficient at the interface is taken to be 1/ln(r_{0}/r_{i})/2πkL and the convection coefficient on the outer surface of the heat exchanger is taken to be 1/h_{0}.

Therefore, the overall heat transfer coefficient based on the inside area is given as

When the overall heat transfer coefficient is calculated based on the outside area, the convection coefficient at the inside is taken to be 1/h_{i}, while the conduction coefficient at the interface is taken to be 1/ln(r_{0}/r_{i})/2πkL and the convection coefficient on the outer surface of the heat exchanger is taken to be 1/h_{0}.

Therefore, the overall heat transfer coefficient based on the inside area is given as

The significant difference between the two-equation is in the area, when the overall heat transfer coefficient is based on the inside area, the inner area of the heat exchanger is used in the equation. While when the overall heat transfer coefficient is based on the outside area, the outer area is taken in the equation.

**DIFFERENCE BETWEEN INDIVIDUAL AND OVERALL HEAT TRANSFER COEFFICIENT**

When heat is flowing through a composite material, the thermal resistance offered by different layers of the material which can be due to heat conduction or convection is referred to as the overall heat transfer coefficient. The overall heat transfer coefficient is the summation of the individual heat transfer coefficient. The thermal resistance is analogous to the electrical resistance in a circuit. Here the heat transfer coefficient is dependent on the material in series or parallel arrangement.

It is of great interest to determine the individual heat transfer coefficient from the overall heat transfer coefficient. For example, for a heat exchanger, the overall heat transfer coefficient can be measured experimentally, from this overall coefficient, extracting the thermal resistance offered by the hot and cold fluid individually is the problem to be solved.

**OVERALL HEAT TRANSFER COEFFICIENT PROBLEMS **

**Consider a wall of thickness 5cm is made of bricks which has a thermal conductivity K=20 W/m K. The inner surface of the wall is exposed to room temperature of 25 ^{0}C while the external surface is exposed to the hot atmospheric temperature of 40^{0}C. What is the overall heat transfer coefficient, given the convection coefficient of air 25 **

**W/m**

^{2}K?*From the above problem, we can conclude that the system is exposed to convection on either side of the wall and conduction heat transfer within the wall. The thermal conductivity of the wall is given to be 20W/mK while the convection coefficient of air is noted to be 25 W/m ^{2}K.*

*= 12.12 W/m^{2}K*

**FREQUENTLY ASKED INTERVIEW QUESTIONS AND ANSWERS**

**1. overall heat transfer coefficient equation heat exchanger **

**2. overall heat transfer coefficient double pipe | double pipe heat exchanger overall heat transfer coefficient**

1/U = D_{o}/h_{i}.D_{i} + D_{o}.ln(D_{o}/D_{i})/2k_{t} + 1/h_{o}+ R_{i}.D_{o}/D_{i} + R_{o}

**3. overall heat transfer coefficient formula for cylinder**

*The overall heat transfer coefficient for a cylinder is given by the formula below which experiences both conduction and convection mode of heat transfer*

**4. overall heat transfer coefficient for evaporator**

Type | U (W/m^{2}K) |

Natural circulation – steam flowing outside and highly viscous fluid flowing inside | 300-900 |

Natural circulation – steam flowing outside and low viscous fluid flowing inside | 600-1700 |

Forced circulation – steam flowing outside and liquid flowing inside | 900-3000 |

**Table 2:**Overall Heat Transfer Coefficient for Evaporators

**5. Overall heat transfer coefficient shell and tube | overall heat transfer coefficient for shell and tube heat exchanger | how to calculate overall heat transfer coefficient for heat exchanger | How do you calculate the overall heat transfer coefficient of an evaporator?**

*The overall heat transfer coefficient for any heat exchanger can be calculated using the below equation the method used might vary. One can choose the LMTD method as well*

**6. Graphite heat exchanger overall heat transfer coefficient**

*The overall heat transfer coefficient for heat exchangers which are molded graphite to graphite is about 1000W/m ^{2}K while the overall heat transfer coefficient for graphite to air is observed to be 12 W/m^{2}K*

**7. Aluminium overall heat transfer coefficient**

*The overall heat transfer coefficient for aluminum is noted to be 200W/m ^{2}K*

**8. Air to air heat exchanger overall heat transfer coefficient**

*The overall heat transfer coefficient of air-to-air heat transfer coefficient is noted to be between 350 to 500 W/m ^{2}K.*

**9. Area of the heat exchanger from overall heat transfer coefficient**

*The area of a heat exchanger can be calculated from the overall heat transfer coefficient using the following formula*

**10. In which heat exchange process the value of the overall heat transfer coefficient will be highest?**

*The overall heat transfer coefficient is the highest for tubular heat exchangers used for evaporation with steam flowing outside the tubes and liquid flowing inside. They are noted to have an overall heat transfer coefficient in the range between 900 to 3000 W/m ^{2}K.*

**11. Can the overall heat transfer coefficient be negative?**

*In cases where the reference temperature is taken as the adiabatic wall temperature, the overall heat transfer coefficient will be negative which indicates that the heat flux is in the opposite direction with a definite temperature gradient.*

**12. Does the overall heat transfer coefficient change with temperature?**

*Overall heat transfer coefficient is dependent on the temperature gradient; therefore, temperature changes can result in changes in a temperature gradient. So, yes overall heat transfer coefficient changes with temperature.*

**13. What is the overall heat transfer coefficient and its application?**

*The thermal resistance that is offered by the different layers in a system is referred to as the Overall Heat Transfer Coefficient. It is also known as the U-factor. It is used in extracting the individual heat transfer coefficient of the different layers of a system.*

*The overall heat transfer coefficient of a system can be measured but the individual heat transfer coefficient of a system is difficult to obtain. In such situations, the overall heat transfer coefficient along with the rate of heat transfer will help in determining the individual heat transfer coefficient*

**14. What are the factors affecting the overall heat transfer coefficient?**

*The factors affecting the overall heat transfer coefficient are thermophysical properties such as the density, viscosity, and thermal conductivity of the fluid. Further, it is affected by the geometry and area across which the heat transfer is taking place. The velocity of fluids affects the overall heat transfer coefficient to a large extend. In heat exchanges, the type of flow also has a significant impact on the overall heat transfer coefficient.*

**15. What is the overall heat transfer coefficient in round tubes? | overall heat transfer coefficient pipe**

*A fluid flowing through a round tube experiences convective heat transfer between the fluid flowing on the outside and the outer surface of the tube, and also between the fluid flowing in the inside and the inner surface of the tube. There is conduction heat transfer between the outer surface and inner surface of the tube. Hence the overall heat transfer coefficient is given as follow:*

*(1/UA) overall = (L/kA) inner + (1/hA) + (L/kA) outer*

Where k is the thermal conductivity of the tube and h is the convective heat transfer coefficient

Click Here, for latest reads on Thermostatic Expansion Valve.

For more post on Mechanical, please follow us.

I am Veena Parthan, completed my master’s in Thermal Engineering. I am working as a Solar Operation and Maintenance Engineer for the UK Solar sector. I have more than 5 years’ experience in the field of Energy and Utilities. I have a profound interest in renewable energy and their optimization. I have published an article in AIP conference proceedings which is based on Cummins Genset and its flow optimization.

During my free hours, I engage in freelance technical writing and would love to offer my expertise on LambdaGeeks platform. Apart from that, I spend my free hours reading, engaging in some sport activities and trying to evolve into a better person.

Looking forward to connect you through LinkedIn –