Mass Flow Rate And Temperature: Effect, Relation ,Problem Examples

This article discusses about relation between mass flow rate and temperature. For incompressible fluids, volume rate and mass flow rate go side by side.

We will narrow the discussion by defining the system and science happening there. We will consider a system where heat transfer is taking place, lets say water flowing in a pipe. The entire discussion in this article will revolve around this system.

What is heat transfer?

Heat transfer in simple terms is the transfer of energy (or entropy) from one point to other. It is measured by the temperature change taking place between unit length of system.

We can say that heat transfer is directly proportional to temperature change and inversely proportional to length of the system. Mathematically, heat transfer can be given by-

What are different modes/types of heat transfer?

Heat transfer from one substance to another can take place by many means. Sometimes, it needs a medium for transfer and sometimes it doesn’t.

Lets see what are different types of heat transfer-

• Conduction–  Heat is transferred between two points when the molecules between them collide with each other. The vibrational energy of the atoms is transferred from on atom/molecule to other. This way the heat propagates. This implies, for heat transfer to take place by conduction it needs a medium.
• Convection– The heat is transferred by the movement of fluid. This fluid can be air or water.
• Radiation- The heat transfer can take place in absence of a medium. Radiation heat transfer takes place in the form of electromagnetic waves.

Mass flow rate and temperature relation

Lets consider water flowing through a pipe. Water being a incompressible fluid means that volumetric flow and mass flow rate are proportional.

Lets consider two cases-

• Low mass flow rate/volumetric flow rate: The volumetric flow rate of the water is low that means volume/mass of water flowing through the pipe section per second is less hence the water molecules will get heated up faster.
• High mass flow rate/volumetric flow rate: If the number of molecules of water flowing through a point is more then it will take more time to heat them up. Hence, we can say that temperature difference in this case will be lesser.

Mass flow rate and temperature equation

As we have discussed above, the temperature difference in the system is inversely proportional to the mass flow rate in the system. That is, as mass flow rate increases the temperature difference decreases.

The relation between mass flow rate and temperature difference is given below-

For same value of heat transfer we can say that the temperature difference is inversely proportional to the mass flow rate.

How does temperature affect mass flow rate?

The temperature increases the velocity of the molecules flowing hence the kinetic energy of the fluid increases with increase in temperature.

How to calculate pressure from mass flow rate?

Hagen Pouisuille law equation says that pressure is directly proportional to the flow rate.

Q is the flow rate and it is the rate of change of volume. For fluids whose density is constant that is incompressible fluids, mass flow rate is directly proportional to volume flow rate. Hence we can say that pressure increases with mass flow rate.

The Hagen Pouisueille equation is given below-

where,

mu is the dynamic viscosity

Q is the flow rate in liters per second

What is a heat exchanger?

As the name suggests, heat exchangers is a device used for exchanging heat between two substances. It can be used to cool or heat the other substance by using a working substance.

Evaporator and condensers are also types of heat exchangers. Condenser and evaporators are discussed in below sections. Heat exchangers find their applications in refrigeration systems, power plants, air conditioning systems etc.

Types of heat exchangers

On the basis of direction of cold fluid and hot fluid the heat exchangers can be classified into three types. They are given below-

• Parallel flow heat exchanger- In this type of heat exchanger, both the cold and hot fluid flow in the same direction.
• Counter flow heat exchanger– In this type of heat exchanger, both hot and cold fluids move in opposite direction to each other.
• Cross flow heat exchanger– In this type of heat exchanger , hot and cold fluids move perpendicular to each other.

Different applications require different types flow directions between the hot and cold fluids. The governing principle is same in all the three types.

What is an evaporator?

An evaporator is a type of heat exchanger used for converting the liquid phase of a substance to its gaseous form. For example, water gets converted into vapor. Entire phase change process occurs with no temperature change.

The heat transferred from the hot fluid is equal to the heat absorbed by the colder fluid. Evaporator is used in refrigeration systems to remove the heat from the food and beverages kept inside the refrigerator.

What is condenser?

A condenser is a type of heat exchanger which used for converting a gaseous phase of a substance to liquid phase of that substance. For example, vapor converting back to liquid form. Entire phase change process occurs with no temperature change.

The heat transferred to the cold fluid is equal to the heat absorbed by the hotter fluid. Condensers are used in power plants where the exhaust steam from the turbine is converted into liquid

What is LMTD?

LMTD also known as Logarithmic Mean Temperature Difference is a term used in heat exchangers. It is the logarithmic average of temperatures of cold fluid and hot fluid.

LMTD is used for finding the overall heat transfer taking place inside the system. It takes into account initial and final temperatures of both hot fluid and cold fluid. The formula for LMTD is given below-

Where,

Delta T1 is the temperature difference between the initial temperatures of both hot and cold fluids.

Delta T2 is the temperature difference between the final temperatures of both hot and cold fluids.