Thermodynamics

Heat transfer and heat dissipation

Heat can be transferred through objects and spaces. Transfer of heat means that the thermal energy is transferred from one place to another.

Generated heat is dissipated to the ambient air via various paths through the conduction, radiation, and convection.

Thermal conduction

Heat is transferred from a high temperature point to a low temperature point within an identical object due to movement of molecules composing the material. No movement of the material is involved

Convection (heat transmission):

Heat is transferred by flow of a fluid when there is a temperature difference between the surface of a solid and a fluid, such as air or water, that is in contact with the surfaces.

Types of convection

• Fluid  : Material that flows, such as gas or liquid
• Convection : Heat transfer phenomenon where heat is transferred by a fluid that receives the heat. Note: No heat transfer through convection is expected to occur without any fluid (in a vacuum).
• Natural convection : Upward flow generated by temperature difference in fluid
• Forced convection  : Flow generated by an external factor, such as a fan or pump

Heat radiation:

From the surface of an object, an electromagnetic wave is emitted with a wavelength corresponding to the surface temperature.

The electromagnetic wave is transmitted through a space and hits the destination object. The vibration energy of the electromagnetic wave causes vibration of molecules on the surface of the destination object, transferring heat and changing the temperature of the destination object. Through the heat radiation, heat may be transferred without any medium between objects (even in a vacuum)

Heat Flux

Heat flux is the amount of heat energy transferred through a surface in a unit area in unit time. The heat flux can be the amount of heat transferred from or dissipated on the surface of consideration. 

Heat flux is also known as thermal flux, heat flow density, heat flux density, or heat flow rate intensity. Its SI units are watts per square metre (W/m²)

heat flux(q) is based on these two quantities : q = Q / A

1. The amount of heat transfer per unit area (Q)
2. The area where the heat transfer takes place (A)

Heat Flux is dependent on,

1. Temperature difference - The temperature difference or gradient is necessary for any heat transfer to take place. The heat flux shares a direct relationship with the temperature gradient. As the temperature gradient increases, the heat flux magnitude increases.
2. Thermal transfer coefficient or heat transfer coefficient - The thermal transfer coefficient is introduced through Newton’s law of cooling, the heat flux associated with a surface is linearly related to the temperature gradient. The proportionality constant linking heat flux and temperature gradient is called the heat transfer coefficient.

Mathematically, the heat flux equation on one dimension can be expressed as (According to Fourier’s law, the heat flux is directly proportional to the thermal or temperature gradient):

heat transfer rate in Watts	q = -K x A x (∆T / ∆x ) = K x A x (T2 - T1 / L)
heat flux in Watts per square meter	q'' = - K x (∆T / ∆x )
	q is the heat flux in Watts K is the heat transfer coefficient A is the area of the cross-section of the surface ∆T / ∆x is the temperature gradient T2 is higher temperature T1 is lower temperature L is length of one dimensional distance

Thermal conductivity

Thermal conductivity is a fundamental concept in heat transfer and is crucial in multiple industries and scientific disciplines. It refers to the ability of a material to conduct heat or the rate at which heat transfers through a substance. Understanding heat and its relationship to thermal conductivity is essential for designing efficient thermal systems, optimizing energy usage, and ensuring the safety and performance of various materials and products. Thermal conductivity is determined by various physical factors that govern the flow of heat energy.

The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly measured in W·m⁻¹·K⁻¹.

The defining equation for thermal conductivity is calculated by known as Fourier's Law for heat conduction.

This Youtube video explains the equation for better understanding

Thermal resistance

Thermal resistance is a quantification of how difficult it is for heat to be conduct. The higher the thermal resistance, the more difficult it is for heat to be conducted, and vice vers.

The thermal resistance can be considered in the same way as the electric resistance. The basic formulas of thermal calculation can be treated in the same way as Ohm's law. R is used as the symbol for the electric resistance, while θ (theta) is used for the thermal resistance.

Electric		Thermal
Voltage difference ΔV (V)	∆𝑉 = 𝑅 × 𝐼	Temperature difference ΔT (°C)	∆𝑇 = 𝑅𝑡ℎ × 𝑃
Electric resistance R (Ω)	𝑅 = ∆𝑉 / 𝐼	Thermal resistance Rth (°C/W)	𝑅𝑡ℎ = ∆𝑇 / 𝑃
Current I (A)	𝐼 = ∆𝑉 / 𝑅	Heat flow P (W)	𝑃 = ∆𝑇 / 𝑅𝑡ℎ

The radiation heat transfer emissivity coefficients for some common materials

Surface Material	Emissivity Coefficient - ε -
Alloy 24ST Polished	0.09
Alumina, Flame sprayed	0.8
Aluminum Commercial sheet	0.09
Aluminum Foil	0.04
Aluminum Commercial Sheet	0.09
Aluminum Heavily Oxidized	0.2 - 0.31
Aluminum Highly Polished	0.039 - 0.057
Aluminum Anodized	0.77
Aluminum Rough	0.07
Aluminum paint	0.27 - 0.67
Anodize black	0.88
Antimony, polished	0.28 - 0.31
Asbestos board	0.96
Asbestos paper	0.93 - 0.945
Asphalt	0.93
Basalt	0.72
Beryllium	0.18
Beryllium, Anodized	0.9
Bismuth, bright	0.34
Black Body Matt	1.00
Black lacquer on iron	0.875
Black Parson Optical	0.95
Black Silicone Paint	0.93
Black Epoxy Paint	0.89
Black Enamel Paint	0.80
Brass Dull Plate	0.22
Brass Rolled Plate Natural Surface	0.06
Brass Polished	0.03
Brass Oxidized 600oC	0.6
Brick, red rough	0.93
Brick, fire-clay	0.75
Cadmium	0.02
Carbon, not oxidized	0.81
Carbon filament	0.77
Carbon pressed filled surface	0.98
Cast Iron, newly turned	0.44
Cast Iron, turned and heated	0.60 - 0.70
Cement	0.54
Cromium polished	0.058
Clay	0.91
Coal	0.80
Concrete	0.85
Concrete, rough	0.94
Concrete tiles	0.63
Cotton cloth	0.77
Copper electroplated	0.03
Copper heated and covered with thick oxide layer	0.78
Copper Polished	0.023 - 0.052
Copper Nickel Alloy, polished	0.059
Glass smooth	0.92 - 0.94
Glass, pyrex	0.85 - 0.95
Glass, opal	0.87
Gold not polished	0.47
Gold highly polished	0.02 - 0.04
Granite, natural surface	0.96
Gravel	0.28
Gypsum	0.85
Ice smooth	0.966
Ice rough	0.985
Inconel X Oxidized	0.71
Iron polished	0.14 - 0.38
Iron, plate rusted red	0.61
Iron, dark gray surface	0.31
Iron, rough ingot	0.87 - 0.95
Lampblack paint	0.96
Lead pure unoxidized	0.057 - 0.075
Lead Oxidized	0.43
Limestone	0.90 - 0.93
Lime wash	0.91
Magnesia	0.72
Magnesite	0.38
Magnesium Oxide	0.20 - 0.55
Magnesium Polished	0.07 - 0.13
Marble White	0.95
Masonry Plastered	0.93
Mercury liquid	0.1
Mild Steel	0.20 - 0.32
Molybdenum polished	0.05 - 0.18
Mortar	0.87
Nickel, elctroplated	0.03
Nickel, polished	0.072
Nickel, oxidized	0.59 - 0.86
Nichrome wire, bright	0.65 - 0.79
Oak, planed	0.89
Oil paints, all colors	0.92 - 0.96
Paper offset	0.55
Plaster	0.98
Platinum, polished plate	0.054 - 0.104
Pine	0.84
Plaster board	0.91
Porcelain, glazed	0.92
Paint	0.96
Paper	0.93
Plaster, rough	0.91
Plastics	0.90 - 0.97
Polypropylene	0.97
Polytetrafluoroethylene (PTFE)	0.92
Polyethylene, black plastic	0.92
Porcelain glazed	0.93
Pyrex	0.92
PVC	0.91 - 0.93
Quartz glass	0.93
Roofing paper	0.91
Rubber, foam	0.90
Rubber, hard glossy plate	0.94
Rubber, natural hard	0.91
Rubber, natural oft	0.86
Salt	0.34
Sand	0.9
Sandstone	0.59
Sapphire	0.48
Sawdust	0.75
Silica	0.79
Silicon Carbide	0.83 - 0.96
Silver Polished	0.02 - 0.03
Snow	0.96 - 0.98
Soil	0.90 - 0.95
Steel Oxidized	0.79
Steel Polished	0.07
Stainless Steel, weathered	0.85
Stainless Steel, polished	0.075
Stainless Steel, type 301	0.54 - 0.63
Steel Galvanized Old	0.88
Steel Galvanized New	0.23
Thoria	0.28
Tile	0.97
Tin unoxidized	0.04
Titanium polished	0.19
Tungsten polished	0.04
Tungsten aged filament	0.032 - 0.35
Water (0 - 100oC)	0.95 - 0.963
Wood Beech, planned	0.935
Wood Oak, planned	0.885
Wood, Pine	0.95
Wrought Iron	0.94
Zinc Tarnished	0.25
Zinc polished	0.045

https://fscdn.rohm.com/en/products/databook/applinote/common/basics_of_thermal_resistance_and_heat_dissipation_an-e.pdf

Measurement thermal conductivity

• Experimental methods
  • Steady-State Heat Flow
  • Transient Hot Wire Method
  • Laser Flash Analysis

• Non-Destructive methods
  • infrared thermography, ultrasound, and thermal wave analysis

Temperature gradient

A temperature gradient refers to the difference in temperature between two points in a material or between two adjacent materials. Heat transfer occurs when there is a temperature gradient, with heat flowing from regions of higher temperature to regions of lower temperature. When there is a temperature difference, the system will naturally attempt to balance the temperatures, leading to heat transfer and thermal conductivity