Heat Flow Rate – Performance in Heating Technology

by Martin Schlobach | Last updated: Jan 9, 2021 | 0 comments

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In this small article I will introduce you to the heat flow rate, also called heat performance, as another basic and important quantity of heating technology. The heat flow rate is given as $\dot{Q}$ (Q point).

Table of Contents

1 Performance P
2 Heat Flow Rate
3 Example calculation – Calculate heat flow rate for a radiator
4 Conclusion

Performance P

In order to understand the heat flow, the performance is used as a basis. The performance $P$ indicates how much work $W$ was converted in a certain time $t$ . The unit for the performance is Watt $[W]$ .

$Performance = \frac{Work}{Time}$ -> $P = \frac{W}{t}$

Heat Flow Rate $\dot{Q}$

In heating technology the heat performance is given as heat flow rate $\dot{Q}$ . This means that the heat flow rate $\dot{Q}$ indicates how much quantity of heat $Q$ was converted in a certain time $t$ . In other words, if 1 joules of heat is converted per second, a heat flow rate of one watt is produced.

The heat flow rate can be calculated using the following formulas:

$Heat~Flow~Rate = \frac{Quantity~ of~ heat}{Time}$

$\dot{Q} = \frac{Q}{t}}$

$Heat~Flow~Rate = Volume~flow~rate \cdot Density \cdot \ Specific~heat~capacity \cdot temperature~difference$

$\dot Q=\dot V \cdot \rho \cdot c \cdot \Delta\vartheta}$

Example calculation – Calculate heat flow rate for a radiator

To better understand the topic of heat flow rate, I will show you in the following example calculation how you can apply the formulas. In this example we calculate the output of a radiator.

Task:

In a room with two radiators, a radiator is to be replaced, but the craftsman cannot determine the performance of the old radiators. In old hydraulic balancing documents, he finds the system temperatures of 75/55/20, a room heating load of 900 W and the calculated volumetric flow rates for the radiators of: Radiator 1 = 14.4 l/h and radiator 2 = 26.2 l/h

To what extent can the room heating load help to determine the radiator output?
Radiator 1 is to be replaced. What is the radiator output at the given volumetric flow rate?
Is the calculated radiator output appropriate for radiator 1 and should the craftsman choose a radiator of this size? If not, what is the appropriate radiator output?

Important: For the calculation of the radiator output we need the density of water $\rho$ , the specific heat capacity of water $c$ and the temperature spread $\Delta\vartheta$ .

Given:

Room heating load $\Phi_{HL,i}$ = $900 W$
Flow rate radiator 1: $\dot V$ = $14.4 l/h$ at 75/55/20
Flow rate radiator 2: $\dot V$ = $26,2 l/h$ at 75/55/20
Temperature spread Delta Theta: $75 - 55 = 20 K$
Specific heat capacity: $c = 1.16\frac{Wh}{kg\cdot K}$
Density: $\rho = 1\frac{kg}{l}$

Wanted:

Radiator output $\dot Q$ for radiators 1 and 2

Solution:

To what extent can the room heating load help to determine the radiator output?

After the calculation, the room heating load helps the craftsman to estimate whether the installed radiators are oversized or undersized. He can then adapt the radiator to be replaced to the real demand.

The reason for this is as follows: many radiators in old and renovated buildings are far oversized. If we now replaced the radiator with the oversized radiator output, we would supply more energy to the room than it needs according to the calculated room heating load.

Calculation of radiator output (heat flow rate) $\dot Q$ :

To calculate the radiator output we use the following formula:

$\dot Q=\dot V \cdot \rho \cdot c \cdot \Delta\vartheta}$

To understand how the unit Watt $W$ results, you can shorten the units of the given sizes below.

$\dot Q=\frac{l \cdot kg \cdot Wh \cdot K}{h \cdot l \cdot kg \cdot K} = W}$

With the given formula we can now calculate the heat flow rate and use the given values.

$\dot Q=14,1 \frac{l}{h} \cdot 1\frac{kg}{l} \cdot 1,16\frac{Wh}{kg\cdot K} \cdot 20 K = \underline{\underline{327,12 W}}$

The radiator output $\dot Q$ for radiator 1 is thus 327.12 W.

Is the calculated radiator output appropriate for radiator 1 and should the craftsman choose a radiator of this size?

To answer this question, we have to calculate the radiator output for radiator 2 because by adding up the calculated output values, we can compare the result with the room heating load. To do this, we insert the given values into the formula:

$\dot Q=26,2 \frac{l}{h} \cdot 1\frac{kg}{l} \cdot 1,16\frac{Wh}{kg\cdot K} \cdot 20 K = \underline{\underline{607,84 W}}$

The radiator output $\dot Q$ for radiator 2 is thus 607.84 W.

In total, we would have a total radiator output of:

$\dot Q_{ges} = 327.12 W + 607.84 W = \underline{\underline{934.96 W}}$

This results in a total radiator output of 934.96 W. The calculated room heating load is 900 W. It is therefore sufficient for the craftsman to install a radiator with an output of 300 W for radiator 1.

Conclusion

I hope I could bring you a little closer to the heat flow rate with these example calculations. If you have questions, suggestions or criticism to this contribution, I’m looking forward to read your comments.

Greetings! Martin

About Me

Hi, my name is Martin and I’m a passionate engineer in the field of buildings technology. Here you can read who I am and why I write this blog.

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Heat Flow Rate – Performance in Heating Technology

Performance P

Heat Flow Rate $\dot{Q}$