**1. Introduction to heat conduction through a pipe**

### What is heat conduction used for ?

When a cylindrical wall is submitted to a differential of temperature in between the inside and the outside of the wall, heat is conducted through the material. The most specific case of cylindrical wall and most useful is **the pipe**, however the concepts exposed in this page can be applied to any cylindrical geometry (chimney...).

**Pipe heat conduction** is key in many aspects of industry but also find many applications in day to day life :

**Building design :**calculation of heat flux through radiators / heaters in rooms**Heat exchanger design :**calculation of heat flux through pipes in order to size tube shell heat exchangers, air conditioners...**Piping design :**design of pipe insulation to avoid heat losses, condensation, safety...

The heat flux can be calculated for both cooling and heating applications.

Each material is characterized by an ability to conduct heat. **It is translated in a thermal conductivity coefficient commonly noted λ** . One must be careful asλ can vary a lot from one material to another and can also vary with the temperature. When conducting heat is a priority, like in the design of heat exchanger,λ must be high, while when isolating is a priority, like designing a building or insulating pipes in between process units, λ must be low. **It is possible also to associate different materials, especially in insulation applications, in order to reach a targetλ while optimizing cost and width of the layers of material.**

Figure 1 : Heat flux through a pipe made of a material of conductivity λ

**2. Heat conduction through a pipe**

### How to calculate the heat conduction through a pipe ?

In general, engineers are looking for a high heat conduction through pipes as they are most of the time used to transfer heat within heat exchanger units, thus the thickness of the pipe is reduced as much as mechanically reasonable and a material with good - which means high - thermal conductivityλ is chosen.

The heat transferred by conduction can be expressed the following general way :

**Q = U.A.ΔT**

With :

Q = heat transferred in W

U = overall heat transfer coefficient in W/m2.°c

A = heat transfer area in m2

ΔT = temperature difference on each surface of the wall in °c

The heat flux, which is the heat transferred expressed as a function of the heat exchange area, can be calculated the following way :

**Φ = Q/A = U.ΔT**

With :

Φ= heat flux in W/m2

Q = heat transferred in W

U = overall heat transfer coefficient in W/m2.°c

A = heat transfer area in m2

ΔT = temperature difference on each surface of the wall in °c

**In the case of a simple pipe**, monomaterial without insulation, the overall heat transfer coefficient can be expressed by :

**U = 1/R = 1/(****(**D_{o}/2**λ)*ln****(D _{o}/D_{i})**)

With :

U = overall heat transfer coefficient in W/m^{2}.°c

R = heat transfer resistance in m^{2}.°c/W

D_{o} = outside pipe diameter in m

D_{i} = inside pipe diameter in m

λ = material thermal conductivity in W/m.°c

ln = log neperian

It is very important to remark that the expression must be standardized regarding the reference surface as the surface area inside and outside the pipe is different. Most of the time, the reference is taken on the outside surface, which is the convention taken in this page.

For a simple pipe, the expressions can then be summarized as :

**Φ = Q/A = ****Q/**** (π.D_{o}.L) **= (

**T**

_{i}-T_{o})/R = (T_{i}-T_{o})/**(**

**(**D_{o}/2**λ)*ln**

**(D**)_{o}/D_{i})With :

T_{i} = temperature on the inside surface of the pipe in °c

T_{o} = temperature on the outside surface of the pipe in °c

L = pipe length considered in m

**Example of heat conduction through a pipe :** in a factory, a chilled water pipe is going through a room at 30c before reaching its point of consumption in another room. The factory operator would like to know what is the additional heat load transferred from the room to the chilled water and that the chiller has to handle. The chiller is supplying water at 4c, the factory operator is measuring the temperature on the pipe at 4.5c. He assumes that the temperature inside the pipe is 4c. The pipe is 81 mm inside diameter and has a thickness of 2.3 mm. It is made of steel with a thermal conductivity of 30 W/m/K. The pipe has a length of 3.5 m.

Φ = Q/A = = (T_{i}-T_{o})/((D_{o}/2λ)*ln(D_{o}/D_{i}))= (4-4.5)/((0.0856/(2*30))*ln(85.6/81)) = -6345 W/m2.°c

Q = Φ*A = -6345*π.85.6/1000*3.5 = -6 kW

**This value is very high and explains why this kind of pipe needs to be insulated. **

**3. Heat conduction through a composite pipe**

### How to insulate a pipe with a layer of low thermal conductivity material ?

**In order to avoid heat losses (or gain if the fluid is cold), or for safety reasons, pipes are often insulated with a layer of low conductivity material put around the pipe.** The pipe wall becomes then composite as it is made of more than 1 material.

**Figure 2 : Heat flux through a composite pipe made of a layer of insulating material**

The resistance of each layer can be expressed using the formula developed for a single wall. However, attention must be brought to the expression for the global resistance as care must be taken **to refer to the right surface to calculate the heat flux**. In the case of a composite walls, **resistances are additive.**

Considering a wall made of n layers of thickness e_{i} and conductivity λ_{i}, the total resistance of the composite wall will be :

With :

R_{total} = heat transfer resistance of the composite wall in m2.°c/W

D_{o} = outside composite pipe diameter in m

D_{i} = inside diameter of layer i in m

D_{i+1} = outside diameter of layer i in m

λ_{i} = material thermal conductivity in W/m.°c of the layer i

It is then possible to calculate the heat flux through the composite wall, knowing the surface temperatures on the surface of each side of the wall.

With :

T_{inside} = temperature on the surface of the wall 1 in °c

T_{outside} = temperature on the surface of the wall 2 in °c

These expressions are particularly useful when working on insulation of pipes.

**Example of heat conduction through a wall composite wall :** the factory operator we introduced in the example of paragraph 2 is thinking that the heat gain coming from the environment crossed by the pipe is too high, he then decides to add a layer of 1 in (2.5 cm) of elastomeric material in order to insulate the pipe . The pipe is, as seen above, made of steel with a thermal conductivity of 30 W/m/K. The insulating material has a thermal conductivity of 0.035W/m/K. The pipe is 3.5 m. He measures now 4 degrees on the inside **surface** and 15 degrees on the **surface** of the insulating material outside the pipe.

D1 = 81 mm, D2 = 81+2.3*2 = 85.6 mm, D3 = Do = 85.6+25*2 = 135.6 mm

Rtotal =135.6/1000 * (1/(2*30)*ln(85.6/81) + 1/(2*0.035)*ln(135.6/85.6)) = 0.89

Φ = Q/A = (T_{skin1}-T_{skin2})/R = (4-15)/(0.89) = -12.34 W/m2.°c

Q = Φ*A = -12.34*π.135.6/1000*3.5 = -18.4W = -**0.018 kW**

**The heat gain has been drastically reduced thanks to the insulation. This will lead to energy savings. **

**4. Free Excel calculation tool for pipe heat conduction**

The heat flux through a pipe or a pipe with insulation can be calculated thanks to this free Excel calculator : Calculation Tool - heat conduction through a pipe

*Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.*

## FAQs

### What is the conduction equation for pipe? ›

It is expressed as **R=lk** R = l k where R is the R-value, l is the thickness, and k is the thermal conductivity.

**How do you calculate heat loss through insulated pipes? ›**

Summing up these two equations we get **dQloss/dx = Uins Tm Tair) Π dins**, Π dins dx being the area of external insulation of the dx element. This dQloss/dx is considered below as being the heat loss [W/m] from the dx element of metallic pipe.

**How do I calculate how much insulation I need for a pipe? ›**

The sheet length required is based on the OD of the pipe to be insulated. The formula to estimate the sheet stretch out in the attached table is: **(pipe OD + 2X insulation thickness) X 3.14 = sheet length**. This formula can be used for other pipe sizes and / or insulation thicknesses.

**How do you calculate heat transfer through a pipe? ›**

Effectiveness of a heat pipe can be represented by a system of thermal resistance. The thermal resistance 𝑅 can be represented by 𝑇 𝑅 = 𝑒 − 𝑇 𝑐 𝑄 ∘ C / W . ( 1 ) The overall heat transfer coefficient, ℎ of the heat pipe can be given by **𝑄 ℎ = 𝐴 𝑇 𝑒 − 𝑇 𝑐 W / m 2 ⋅ ∘ C** .

**How do you calculate thermal conduction? ›**

What is the formula of thermal conductivity? The formula of thermal conductivity is **K = (QL) / (AΔT)**.

**What is conduction from fluids through pipes? ›**

Conduction: This refers to **the mechanism whereby an energy exchange occurs between the fluid and the pipe wall, insulation and soil (if the pipe is buried) due to direct contact**.

**What is the thermal conductivity of insulated pipe? ›**

Thermal insulation material usually used is polyurethane foam or similar, with a thermal conductivity λ_{50} of about **0.024–0.033 W/(m·K)**.

**How do you calculate heat loss by conduction? ›**

By adding 10 percent, the general formula for calculating the heat loss of a system via conduction, convection and radiation can be calculated. Conductance is the inverse of resistance, R, and can be expressed as **U = 1/R or U = k/L**.

**What is the thermal conductivity of pipe insulation? ›**

Pipe insulation made from rigid Phenolic, PIR, or PUR foam insulation is common in some countries. Rigid-foam insulation has minimal acoustic performance but can exhibit low thermal-conductivity values of **0.021 W/(m·K) or lower**, allowing energy-saving legislation to be met whilst using reduced insulation thicknesses.

**How much difference does pipe insulation make? ›**

Insulating your hot water pipes **reduces heat loss and can raise water temperature 2°F–4°F hotter than uninsulated pipes can deliver**, allowing you to lower your water temperature setting. You also won't have to wait as long for hot water when you turn on a faucet or showerhead, which helps conserve water.

### What is the formula for thermal insulation? ›

**R = D / λ** Where: D = Material Thickness (m) λ = Thermal Conductivity of the Material (W/K·m) (according to each material)

**What is insulation formula? ›**

In calculating the R-value of a multi-layered installation, the R-values of the individual layers are added: **R-value _{(}_{outside} _{air} _{film}_{)} + R-value_{(}_{brick}_{)} + R-value_{(}_{sheathing}_{)} + R-value_{(}_{insulation}_{)} + R-value_{(}_{plasterboard}_{)} + R-value_{(}_{inside} _{air} _{film}_{)} = R-value_{(}_{total}_{)}**.

**What is the convective heat transfer equation for a pipe? ›**

Many applications involving convective heat transfer take place within pipes, tubes, or some similar cylindrical device. In such circumstances, the surface area of heat transfer normally given in the convection equation ( **˙Q=h A ΔT** ) varies as heat passes through the cylinder.

**How much heat can a heat pipe transfer? ›**

The maximum temperature for long term water heat pipes is **270 °C (518 °F)**, with heat pipes operating up to 300 °C (572 °F) for short term tests. The main reason for the effectiveness of heat pipes is the vaporization and condensation of the working fluid.

**What is the equation to calculate the amount of heat transferred? ›**

The amount of heat gained or lost by a sample (q) can be calculated using the equation **q = mcΔT**, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change.

**What is thermal resistance and how is it calculated for conduction? ›**

Thermal resistance is represented as **the quotient of the temperature difference between two given points by the heat flow between the two points** (amount of heat flow per unit time). This means that the higher the thermal resistance, the more difficult it is for heat to be conducted, and vice versa.

**How do you calculate thermal convection? ›**

Convection can be estimated as follows **H=HLAh(Th−Ta)**(12.15) (12.15) H = H L A h ( T h − T a ) where HL is a convective heat transfer coefficient (Wm−2K−1 W m − 2 K − 1 ).

**How do you calculate heat conduction rate along a rod? ›**

The heat conduction rate along this rod is equal to the **thermal conductivity times the rod's cross sectional area times the difference in temperature between the two ends of the rod divided by the length of the rod**. So, we have area is π times its rods radius or diameter divided by 2 squared.

**Can conduction occur between two liquids? ›**

**Conduction occurs more readily in solids and liquids**, where the particles are closer together than in gases, where particles are further apart. The rate of energy transfer by conduction is higher when there is a large temperature difference between the substances that are in contact.

**What is the convection coefficient for the water inside the pipe? ›**

Flow type | (W/m^{2} K) |
---|---|

Forced convection; moderate speed cross- flow of air over a cylinder | 200 |

Forced convection; moderate flow of water in a pipe | 3000 |

Forced Convection; molten metals | 2000 to 45000 |

Forced convection; boiling water in a pipe | 50,000 |

### What is generated when fluid flows through a pipe? ›

Whenever the fluid is flowing, there will be an energy that causes the fluid to flow. There are three different types of energy within the flowing fluid – **flow energy (pressure head), kinetic energy, and potential energy**.

**What is conduction rate equation? ›**

This equation is called the law of heat conduction. **ΔQ/Δt** is the rate at which heat flows across the area A, in Joules per second or Watts. ΔT/Δx is the change in the temperature over the distance Δx in degrees Kelvin or Celsius per meter.

**What formula is Q MC ∆ T? ›**

The amount of heat gained or lost by a sample (q) can be calculated using the equation **q = mcΔT**, where m is the mass of the sample, c is the specific heat, and ΔT is the temperature change.

**What is the thermal conductivity of a pipe? ›**

The thermal conductivity will vary with the heat pipe length, unlike solid metals. For example, the thermal conductivity of copper is 390 W/m-k, but for heat pipes, it can range from **1,500 W/mk to 50,000W /mk**.

**What is the equation for conduction heat transfer rate? ›**

The equation for conduction tells us that the rate of heat transfer (Q/t) in Joules per second or watts, is equal to the thermal conductivity of the material (k), multiplied by the surface area of the objects in contact (A), multiplied by the difference in temperature between the two materials (T2 - T1), divided by the ...

**What is the rule of conduction? ›**

The law of heat conduction, also known as Fourier's law, states that **the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows**.

**What does rate of conduction mean? ›**

The rate of conductive heat transfer **depends on temperature gradient between the two bodies, the area of contact and the conductive properties of these bodies**. In conductive heat transfer, heat always flows from the warmer body to the cooler one.

**What does Q represent in Q m * C * Δt? ›**

where Q is **the quantity of heat transferred to or from the object**, m is the mass of the object, C is the specific heat capacity of the material the object is composed of, and ΔT is the resulting temperature change of the object.

**What is Q in the formula i Q t? ›**

^{-}

^{19}C.

...

The relationship between current I and quantity of charge Q.

I = | I = Q ÷ t |
---|---|

t = | t = Q ÷ I |

**What is the equation i Q t? ›**

One ampere is equal to one coulomb passing a point in a wire in one second. We can calculate current, 𝐼 , using the formula 𝐼 = 𝑄 𝑡 , where 𝑄 represents an amount of charge passing a point in an amount of time, 𝑡 .

### What is thermal conductivity of insulation? ›

Thermal conductivity **indicates how easily heat will flow through a material**, whether it is a brick or a layer of insulation. This measurement doesn't relate to the thickness of the material; the number is the same whatever the thickness.

**What is thermal conductivity of insulating material? ›**

Thermal conductivity

In simple terms this is **a measure of the capacity of a material to conduct heat through its mass**. Different insulating materials and other types of material have specific thermal conductivity values that can be used to measure their insulating effectiveness.

**What is the thermal conductivity of a good insulator? ›**

In order to be considered as a thermal insulator, a material should have a thermal conductivity value (λ) of **less than 0.1 W m ^{−}^{1} K^{−}^{1}**.