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.

This Youtube video explains the equation for better understanding

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 is also called the lambda (λ) value, or k value.

Thermal conductivity is a property of the material and does not take into account thickness. Two different thicknesses of the same material still have the same λ-value.

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(W/mK).

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

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.

Thermal resistance is calculated by dividing the thickness of the material by its thermal conductivity, giving an R-value specific to that thickness

To compare the relative performance of different thicknesses of materials means working out their thermal resistance (units: m2K/W).

U-value

A U-value is a measure of thermal transmittance, or the amount of heat energy that moves through a floor, wall or roof, from the warm (heated) side to the cold side. It is the number of Watts per square metre of the construction, per degree of temperature difference between one side and the other (W/m2K).

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

Specifici heat capacity (symbol c)

Itt is also referred to as massic heat capacity or as the specific heat. The SI unit of specific heat capacity is joule per kelvin per kilogram, J⋅kg⁻¹⋅K⁻¹. Specific heat capacity often varies with temperature, and is different for each state of matter.

For example, the heat required to raise the temperature of 1 kg of water by 1 K is 4184 joules, so the specific heat capacity of water is 4184 J⋅kg⁻¹⋅K⁻¹

Table of specific heat capacities at 25 °C (298 K) unless otherwise noted

Substance	Phase	Isobaric mass heat capacity cPJ⋅g−1⋅K−1	Molar heat capacity, CP,m and CV,m J⋅mol−1⋅K−1		Isobaric volumetric heat capacity CP,v J⋅cm−3⋅K−1	Isochoric molar by atom heat capacity CV,am mol-atom−1
			Isobaric	Isochoric
Air (Sea level, dry, 0 °C (273.15 K))	gas	1.0035	29.07	20.7643	0.001297
Air (typical room conditionsA)	gas	1.012	29.19	20.85	0.00121
Aluminium	solid	0.897	24.2		2.422	2.91 R
Ammonia	liquid	4.700	80.08		3.263	3.21 R
Animal tissue (incl. human)	mixed	3.5			3.7
Antimony	solid	0.207	25.2		1.386	3.03 R
Argon	gas	0.5203	20.7862	12.4717
Arsenic	solid	0.328	24.6		1.878	2.96 R
Beryllium	solid	1.82	16.4		3.367	1.97 R
Bismuth	solid	0.123	25.7		1.20	3.09 R
Cadmium	solid	0.231	26.02		2.00	3.13 R
Carbon dioxide CO2	gas	0.839	36.94	28.46
Chromium	solid	0.449	23.35		3.21	2.81 R
Copper	solid	0.385	24.47		3.45	2.94 R
Diamond	solid	0.5091	6.115		1.782	0.74 R
Ethanol	liquid	2.44	112		1.925
Gasoline (octane)	liquid	2.22	228		1.640
Glass	solid	0.84			2.1
Gold	solid	0.129	25.42		2.492	3.05 R
Granite	solid	0.790			2.17
Graphite	solid	0.710	8.53		1.534	1.03 R
Helium	gas	5.1932	20.7862	12.4717
Hydrogen	gas	14.30	28.82
Hydrogen sulfide H2S	gas	1.015	34.60
Iron	solid	0.449	25.09		3.537	3.02 R
Lead	solid	0.129	26.4		1.440	3.18 R
Lithium	solid	3.58	24.8		1.912	2.98 R
Lithium at 181 °C	solid(?)	4.233
Lithium at 181 °C	liquid	4.379	30.33		2.242	3.65 R
Magnesium	solid	1.02	24.9		1.773	2.99 R
Mercury	liquid	0.1395	27.98		1.888	3.36 R
Methane at 2 °C	gas	2.191	35.69
Methanol	liquid	2.14		68.62	1.695
Molten salt (142–540 °C)	liquid	1.56			2.62
Neon	gas	1.0301	20.7862	12.4717
Nitrogen	gas	1.040	29.12	20.8
Oxygen	gas	0.918	29.38	21.0
Paraffin wax C25H52	solid	2.5 (avg)	900		2.325
Polyethylene (rotomolding grade)	solid	2.3027			2.15
Silica (fused)	solid	0.703	42.2		1.547
Silver	solid	0.233	24.9		2.44	2.99 R
Sodium	solid	1.230	28.23		1.19	3.39 R
Steel	solid	0.466			3.756
Tin	solid	0.227	27.112		1.659	3.26 R
Titanium	solid	0.523	26.060		2.6384	3.13 R
Tungsten	solid	0.134	24.8		2.58	2.98 R
Uranium	solid	0.116	27.7		2.216	3.33 R
Water at −10 °C (ice)	solid	2.05	38.09		1.938
Water at 25 °C	liquid	4.1816	75.34	74.55	4.138
Water at 100 °C	liquid	4.216	75.95	67.9	3.77
Water at 100 °C (steam)	gas	2.03	36.5	27.5	1.53
Zinc	solid	0.387	25.2		2.76	3.03 R

Volumetric heat capacity

The volumetric heat capacity of a material is the heat capacity of a sample of the substance divided by the volume of the sample. It is the amount of energy that must be added, in the form of heat, to one unit of volume of the material in order to cause an increase of one unit in its temperature. The SI unit of volumetric heat capacity is joule per kelvin per cubic meter, J⋅K⁻¹⋅m⁻³.

The volumetric heat capacity can also be expressed as the specific heat capacity (heat capacity per unit of mass, in J⋅K⁻¹⋅kg⁻¹) times the density of the substance (in kg/L, or g/mL).

Thermodynamic Process (Type of transition)

A Thermodynamic process is a process in which the thermodynamic state of a system is changed. A change in a system is defined by a passage from an initial to a final state of thermodynamic equilibrium.

Kinds of process

• Cyclic process
  • Defined by a cycle of transfers into and out of a system. A cycle is a sequence of a small number of thermodynamic processes that indefinitely often, repeatedly returns the system to its original state
• Flow process
  • Defined by flows through a system, a flow process is a steady state of flow into and out of a vessel with definite wall properties. especially the states of the inflow and the outflow materials, and, on the side, the transfers of heat, work, and kinetic and potential energies for the vessel

Kinds of transition

Thermodynamic Process, condition and work done

Type of transition	Condition	Work 1st law of thermodynamics, Q = ΔU + W	Meaning
Isochoric (Isovolumetric)	dV = 0,	So, W = 0 then ΔU = Q = n x Cv x ΔT	volume of the system does not change
Isobaric	dP = 0,	So, ΔU = Q - W ΔU = n x Cv x ΔT W = P x ΔV Q = n x Cp x ΔT	pressure of the system does not change
Isothermal	dT = 0,	So, ΔU = 0 then 0 = Q - W eg, Q = W Where W, P1V1 ln(V2/V1) or P2V2 ln(V2/v1)	system at a constant temperature
Adiabatic	Q = 0	So, ΔU = -W Where W, W = -Cv/R (P2V2 - P1V1) or W = - n x Cv x ΔT	no heat is allowed to enter or leave the system by insulation
cyclic	dE = 0, dH = 0, dP = 0, dV = 0 ΔEint=0		if the state of the system at the end is same as the state at the beginning, state properties such as temperature, pressure, volume, and internal energy of the system do not change over a complete cycle Q=W(cyclic process)

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