132 lines
4.8 KiB
Markdown
132 lines
4.8 KiB
Markdown
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title = "Heat Transfer"
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author = ["Dehaeze Thomas"]
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draft = false
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## Conduction (diffusion) {#conduction--diffusion}
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The _conduction_ corresponds to the heat transfer \\(P\\) (in watt) through molecular agitation within a material and is specified with:
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\\[ P = \frac{\lambda \cdot A \cdot \Delta T}{L} \quad [W] \\]
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with:
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- \\(\lambda\\) the thermal conductivity in \\([W/m \cdot K]\\)
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- \\(A\\) the surface area in \\([m^2]\\)
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- \\(\Delta T\\) the temperature difference in \\([K]\\)
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- \\(L\\) the length of the barrier in \\([m]\\)
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## Convection {#convection}
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The convection corresponds to the heat transfer through flow of a fluid.
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It can be either _natural_ or _forced_.
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The _forced convection_ \\(P\\) (in watt) can be described with:
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\\[ P = h A (T\_0 - T\_f) \quad [W] \\]
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with:
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- \\(h\\) the convection heat transfer coefficient in \\([W/m^2 \cdot K]\\).
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\\(h \approx 10.5 - v + 10\sqrt{v}\\) with \\(v\\) the velocity of the object through the fluid in \\([m/s]\\)
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- \\(A\\) the surface area in \\([m^2]\\)
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- \\(T\_0\\) the temperature of the object in \\([K]\\)
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- \\(T\_f\\) the temperature of the convecting fluid in \\([K]\\)
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Note that clean-room air flow should be considered as forced convection.
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## Radiation {#radiation}
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_Radiation_ corresponds to the heat transfer \\(P\\) (in watt) through the emission of electromagnetic waves from the emitter to its surroundings is:
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\\[ P = \epsilon \cdot \sigma \cdot A \cdot (T\_r^4 - T\_s^4) \\]
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with:
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- \\(\epsilon\\) the emissivity which corresponds to the ability of a surface to emit energy through radiation relative to a black body surface at equal temperature.
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It is between 0 (no emissivity) and 1 (maximum emissivity)
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- \\(\sigma\\) the Stefan-Boltzmann constant: \\(\sigma = 5.67 \cdot 10^{-8} \\, \frac{W}{m^2 K^4}\\)
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- \\(A\\) the surface in \\([m^2]\\)
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- \\(T\_r\\) the temperature of the emitter in \\([K]\\)
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- \\(T\_s\\) the temperature of the surrounding in \\([K]\\)
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The emissivity of materials highly depend on the surface finish (the more polished, the lower the emissivity).
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Some examples are given in <tab:emissivity_examples>.
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<a id="table--tab:emissivity-examples"></a>
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<div class="table-caption">
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<span class="table-number"><a href="#table--tab:emissivity-examples">Table 1</a>:</span>
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Some examples of emissivity (specified at 25 degrees)
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</div>
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| Substance | Emissivity |
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|----------------------------|------------|
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| Silver (polished) | 0.005 |
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| Silver (oxidized) | 0.04 |
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| Stainless Steel (polished) | 0.02 |
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| Aluminium (polished) | 0.02 |
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| Aluminium (oxidized) | 0.2 |
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| Aluminium (anodized) | 0.9 |
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| Copper (polished) | 0.03 |
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| Copper (oxidized) | 0.87 |
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<div class="exampl">
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Let's take a polished aluminum plate (20 by 20 cm) at 125K (temperature of zero thermal expansion coefficient of silicon) surrounded by elements are 25 degrees (300 K):
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\\[ P = \epsilon \cdot \sigma \cdot A \cdot (T\_r^4 - T\_s^4) = 0.36\\, J \\]
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</div>
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## Heat {#heat}
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The _heat_ \\(Q\\) (in Joules) corresponds to the energy necessary to change the temperature of the mass with a certain material specific heat capacity:
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\\[ Q = m \cdot c \cdot \Delta T \\]
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with:
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- \\(m\\) the mass in \\([kg]\\)
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- \\(c\\) the specific heat capacity in \\([J/kg \cdot K]\\)
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- \\(\Delta T\\) the temperature different \\([K]\\)
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<div class="exampl">
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Let's compute the heat (i.e. energy) necessary to increase a 1kg granite by 1 degree.
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The specific heat capacity of granite is \\(c = 790\\,[J/kg\cdot K]\\).
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The required heat is then:
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\\[ Q = m\cdot c \cdot \Delta T = 790 \\,J \\]
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</div>
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<a id="table--tab:specific-heat-capacity"></a>
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<div class="table-caption">
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<span class="table-number"><a href="#table--tab:specific-heat-capacity">Table 2</a>:</span>
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Some examples of specific heat capacity
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</div>
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| Substance | Specific heat capacity [J/kg.K] |
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|---------------------|---------------------------------|
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| Air | 1012 |
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| Aluminium | 897 |
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| Copper | 385 |
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| Granite | 790 |
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| Steel | 466 |
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| Water at 25 degrees | 4182 |
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## Heat flow {#heat-flow}
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The heat flow \\(P\\) (in watt) is the derivative of the heat:
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\\[ P = \cdot{Q} = \frac{dQ}{dt} = \frac{dT}{R\_T} = C\_T \cdot dT \\]
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with:
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- \\(Q\\) the heat in [W]
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- \\(R\_T\\) the thermal resistance in \\([K/W]\\)
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- \\(C\_T\\) the thermal conductance in \\([W/K]\\)
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## Bibliography {#bibliography}
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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</div>
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