Solution Equations for Lumped Mass Capacitance | Derivation for Temperature & Total Heat Transfer

The whole purpose of Lumped Mass Capacitance is to simplify the second order partial differential equations in time and space in Heat Diffusion equation ( or heat conduction equation of Fourier's law ) to a much simpler single order complete differential equation in time coordinate only. This differential equation can be easily solved and the solution gives us temperature change with time based on the material characteristics (or material properties) and size and shape of structure. Also, we can integrate to get the total heat transfer which will happen in a given time duration t.
The temperature and total heat transfer is a function of:
U - Overall Heat Transfer Coefficient of the building envelope
A - Wall, Window, Glass, etc. Area of the building
UA factor - U*A
rho - density of material of the building
V - total volume of the material used
c - specific heat capacity of the building material
t - time duration of interest
T - temperature of the building as a function of time t
Q - total heat transfer happening in time t
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In this course on Energy Management in Commercial Buildings, I am going to bring up the trending topics and technology used in our homes, offices and industry to keep them cool and warm as per the comfort requirement. The course is a complete and an extended version of what I studied at Texas A&M University under Dr. David Claridge. All course content credits goes to my professor Dr. David Claridge.
The content included in this course are:
Overview of energy issues around the world
Building energy performance overview
Concept of Continuous Commissioning
Historical Methods for Load Calculations
Bin method energy calculations
Building load calculations
Buildings as a Lumped Capacitance
Modified Bin Method
Fans, Coils, Dampers, Valves
Different types of AHU
Model Calibration
Chillers and Cooling Towers
Furnace and Boilers
Building Hydronic Loops
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For new viewers, this channel is for spreading knowledge and educational purposes.
Educator : Dhyan Patel
Education : Mechanical Engineering @ BITS Pilani - K. K. Birla Goa Campus
Texas A&M University - MS Thesis Mechanical Engineering
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