Tag: heat transfer

1.Mode of Heat transfer ?

Parameter	Conduction	Convection	Radiation
Definition	Heat transfer through direct contact of molecules in a solid.	Heat transfer due to fluid (liquid or gas) motion.	Heat transfer through electromagnetic waves without any medium.
Medium Required	Solid medium required.	Fluid medium required.	No medium required (can occur in vacuum).
Heat Transfer Mechanism	Molecule-to-molecule vibration.	Bulk movement of fluid particles.	Emission and absorption of thermal radiation.
Example	Heating one end of a metal rod.	Boiling water circulations.	Sun’s heat reaching Earth.
Rate of Transfer	Slow.	Moderate.	Fast.

2.What is the general heat conduction equation in Cartesian, cylindrical, and spherical coordinate systems?

Coordinate System	General Heat Conduction Equation
Cartesian (x, y, z)	$\frac{\mathrm{\partial }T}{\mathrm{\partial }t}=\alpha (\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{x}^2}+\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{y}^2}+\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{z}^2})$
Cylindrical (r, θ, z)	$\frac{\mathrm{\partial }T}{\mathrm{\partial }t}=\alpha (\frac{1}{r}\frac{\mathrm{\partial }}{\mathrm{\partial }r}\left(r\frac{\mathrm{\partial }T}{\mathrm{\partial }r}\right)+\frac{1}{r^2}\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{\theta }^2}+\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{z}^2})$
Spherical (r, θ, φ)	$\frac{\mathrm{\partial }T}{\mathrm{\partial }t}=\alpha (\frac{1}{r^2}\frac{\mathrm{\partial }}{\mathrm{\partial }r}\left(r^2\frac{\mathrm{\partial }T}{\mathrm{\partial }r}\right)+\frac{1}{r^2\sin \theta }\frac{\mathrm{\partial }}{\mathrm{\partial }\theta }(\sin \theta \frac{\mathrm{\partial }T}{\mathrm{\partial }\theta })+\frac{1}{r^2{\sin }^2\theta }\frac{{\mathrm{\partial }}^{2}T}{\mathrm{\partial }{\varphi }^2})$​

3. Thermal Properties ?

Property	Definition	Formula	Unit
Thermal Conductivity (k)	Ability of a material to conduct heat. Higher k means better heat conduction.	$q=-kA\frac{dT}{dx}$	W/m·K
Thermal Resistance (R)	Opposition offered by a material to heat flow. Higher R means lower heat transfer.	$R=\frac{L}{kA}$	K/W
Thermal Diffusivity (α)	Rate at which heat spreads through a material. Indicates how quickly temperature changes.	$\alpha =\frac{k}{\rho C_p}$	m²/s