Heat Transfer (Basics)

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Learning Objectives

• Explain the difference between Energy and Power
• Calculate the heat transfer through Conduction, Convectionon and Radiation
• Calculate heat storage

If you can complete the above tasks then scroll to the exercises at the bottom of the page

Energy and Power

Energy is a measure of capcity: e.g. The building has stored 100kWh of Energy. Power is a measure of Energy Transfer e.g. The building is loosing 1kW of Energy to the outside.

This can be compared with a bucket filling up with water. The amount of water is the "Energy" and the rate at which the bucket is filling up is the "Power".

Power and Energy can be mathematically formulated like so:

$P=E/t$

Heat Transfer

Heat Transfer is one type of Power. It is the transfer of Heat Energy from one source to another. It can be achieved through either Conduction, Convection, or Radiation.

Conduction

Conduction is the transfer of heat through a solid medium, for example a building wall. It is mathematicall defined by

$Q_{condunction}=\frac{kA(T_h-T_c)}{d}$

Where

• $A$ is the area of the surface

• $T_h$ is the temperature of the hot side

• $T_c$ is the temperature of the cold side

• $k$ is the thermal conductance of the material

• $d$ is the thickness of the material

Convection

Convection is the transfer of energy through a liquid or gaseous medium. For example the flow of heat from the radiator, to the room air. It is mathematically defined by:

$Q_{convection}=h_cA$

Where A is the area of the surface

$h_c$ is the convective coefficient

The convection coefficient can be obtained either through Tables, or for air, it can be approximated through the following forumla

$h_c = 10.45 - v + 10 v^{1/2}$

where $v$ is the velocity of the air

Radiation

Radiation is the transfer of heat through electromagnetic waves. For example, the transfer of energy from the sun to the building facade. It can be mathematically defined as

$Q_{radiation} = \epsilon \sigma (T_h^4 - T_c^4) A$

where:

• $\epsilon$ is the emissivity of the object (1 for a black body, 0 for a perfect reflector)
• $\sigma$ is the Boltzman's constant = $5.670367(13)×10^{−8} W m^{−2} K^{−4}$
• $A$ is the area of the object $.$

Heat Storage

Energy can be stored in a material by raising its temperature. The amount of Thermal Energy stored is mathematically defined by:

$E= mc_p dT$

Where: m is the mass of the object

$c_p$ is the heat storage capacity, obtained from tables

$dT$ is the temperature change

Test

A south facing wall of a house has a surface area of $100m^2$. It is made of a 36.5cm thick insulated wooded wall with a thermal conductance of $0.054\frac{W}{mK}$. The outside air temperature is $10^{\circ}C$ and the interior air temperature is $24^{\circ}C$.

var x = 10;

assert(x == 10);

// This is context code available everywhere
// The user will be able to call magicFunc in his code
function magicFunc() {
    return 3;
}