Q = m Cp dT – Energy Basics

Energy Basics is a series covering fundamental energy concepts.

Posts in this series include kW vs kWh and First & Second Law of Thermodynamics.

A hot water loop is a common way to transfer heat.  Hot water loops are often found in district heating networks and on industrial sites.

But do you know that often these loops are not operated optimally?

Figure 1 – A simple hot water loop

This post will explain how the CAPEX & OPEX costs of many hot water loops are higher than they should be.  We explore this by introducing one of the most useful equations in energy engineering.

The equation below shows how to calculate heat transferred in our hot water loop.

Q = m Cp dT

The mass flow rate (m, kg/s) is a measurement of the amount of water flowing around the hot water loop.

The specific heat capacity (CP,  kJ/kg.°C) is a thermodynamic property specific to the material. We could manipulate the specific heat capacity only by changing the fluid used in the loop.  Water is a good fluid choice for cost and safety considerations.  The specific heat capacity of water does vary with temperature but for the scope of liquid water heating it can be estimated as constant.

The temperature difference (dT ,°C) is the change in temperature of the hot water.  It is the difference in temperature before and after heat transfer.

As engineers we are able to manipulate two of the three variables in our equation – flow rate and temperature difference.  We can optimize these through the design and operation of our hot water loops.

We could use two distinct methods to deliver the same amount of heat in our hot water loop:

  1. High mass flow rate + low temperature difference
  2. Low mass flow rate  + high temperature difference

The second method is optimal and will reduce our scheme CAPEX & OPEX costs.

A low mass flow rate minimizes the amount of electricity required to pump water around the loop.

A high temperature difference means:

  • Increase in the maximum capacity of the loop to deliver heat.  Pipe size limits the capacity of the loop by limiting the maximum flow rate.  More heat can be transferred at the maximum flow rate by using a larger temperature difference.
  • Maximises heat recovery from CHP heat sources such as jacket water or exhaust.
  • Maximises electric output from steam turbine based systems by allowing a lower condenser pressure.

The CAPEX benefit comes from being able to transfer more heat for the same amount of investment.

OPEX benefits arise from reduced pump electricity consumption and increased CHP system efficiency.

Thanks for reading!