# Sensible heat ratio: Definition, Formula, Diagram, Examples [with Pdf]

## What is sensible heat ratio?

Sensible heat ratio is the ratio of sensible heat to the total heat exchanged by the system. The sensible heat ratio is used to indicate the amount of heat used for sensible heating or cooling.

The total heat supplied to the system is used for sensible heating/cooling and latent heating/cooling. The term sensible heat ratio states the fraction of total heat supplied for sensible heating/cooling.

If the system absorbs or reject Q_{\text{total}} amount of total heat and out of this, Q_{\text{sensible}} amount of sensible heat is used to change the temperature of the system, then the sensible heat ratio is given by,

Sensible heat ratio = \mathbf{\frac{\text{Sensible heat}}{\text{Total heat}}}

= \mathbf{\frac{Q_{\text{sensible}}}{Q_{\text{total}}}}

## Sensible heat ratio equation:

The heating or cooling process on a psychometric diagram is shown below,

Process 1-2 indicates the total heating or cooling process.

While process 1-a indicates the part of heat used for sensible heating/cooling and process a-2 indicates part of heat used for latent heating/cooling.

Therefore the sensible heat ratio (SHR) is given by,

SHR = \frac{\text{Sensible heat}}{\text{Total heat}}

SHR = \frac{\text{Sensible heat}}{\text{Sensible heat}\ +\ \text{Latent heat}}

SHR = \frac{h_{a}-h_{1}}{(h_{a}-h_{1})+(h_{2}-h_{a})}

SHR = \mathbf{\frac{h_{a}-h_{1}}{h_{2}-h_{1}}}

This is the equation for the sensible heat ratio.

## Sensible heat ratio example:

1] The air conditioner rejects the total amount of heat of 13 KJ/Kg to cool the cabin at atmospheric pressure from 35°C to 26°C. The air inside the cabin has an average specific heat of Cp = 1.003 KJ/Kg, Find the sensible heat ratio for the process.

Solution:

Given:
Q_{\text{total}} = 13 KJ/Kg
T_{\text{initial}} = 35°C
T_{\text{final}} = 26°C
C_{P} = 1.003 KJ/Kg

The amount of heat rejected for the cooling of air can be calculated as,

Q_{\text{sensible}} = C_{p} (T_{\text{initial}} – T_{\text{final}})

Q_{\text{sensible}} = 1.003 (35 – 26)

\mathbf{Q_{\text{sensible}}} = 9.027 KJ/Kg

The sensible heat ratio is given by,

SHR = \frac{Q_{\text{sensible}}}{Q_{\text{total}}}

SHR = \frac{9.027}{13}

SHR = 0.694

The sensible heat ratio for the process is 0.694

2] If the air conditioner is rejecting the heat at the rate of 14 KJ/Kg with the sensible heat ratio of 0.75. Find the final temperature if the Cp = 1.003 KJ/Kg and \mathbf{T_{\text{initial}} = 34.5°C.

Solution:

Given:
Q_{\text{total}} = 14 KJ/Kg
T_{\text{initial}} = 34.5°C
SHR = 0.75
C_{p} = 1.003 KJ/Kg

The amount of the sensible heat is given by,

SHR = \frac{Q_{\text{sensible}}}{Q_{\text{total}}}

0.75 = \frac{Q_{\text{sensible}}}{14}

\mathbf{Q_{\text{sensible}}} = 10.5 KJ/Kg

The final temperature of the air is given by,

Q_{\text{sensible}} = C_{p} (T_{\text{initial}} – T_{\text{final}})

10.5 = 1.003 x (34.5 – T_{\text{final}})

\mathbf{T_{\text{final}}} = 24.03°C

The final temperature of the air is 24.03°C

FAQ:

How do you calculate sensible heat ratio?

The sensible heat ratio is calculated by taking the ratio of sensible heat and total heat.