Heat transfer (or heat exchanger ) is thermal energy in transit due to a spatial temperature difference. These thermal exchanges are three measure functions of thermal conduction, convective heat transfer coefficient(s), and geometrical parameters.
MODES OF HEAT TRANSFER
Conductivity, convection, and radiation are the three modes of heat transfer. There is an exchange of energy between bodies through one of these modes.
“Conduction may be viewed as the transfer of energy from the more energetic to the less energetic particles of a substance due to interactions between the particles.”
“The convection heat transfer mode comprises two mechanisms. In addition to energy transfer due to random molecular motion (diffusion), energy is also transferred by the bulk, or macroscopic, motion of the fluid.”
” Thermal radiation is energy emitted by matter that is at a non-zero temperature. Although we will focus on radiation from solid surfaces, emission may also occur from liquids and gases.”
Conduction An energy transfer across a system boundary due to a temperature difference by the mechanism of intermolecular interactions. Conduction needs matter and does not require any bulk motion of matter.
Convection An energy transfer across a system boundary due to a temperature difference by the combined mechanisms of intermolecular interactions and bulk transport. Convection needs fluid matter.
Radiation heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of the body. Radiation does not need to matter.
GENERAL HEAT CONDUCTION EQUATION IN CARTESIAN COORDINATES
“The heat transfer is considered, based upon the first law of thermodynamics.”.
From Non-Flow Energy Equation, Q=w+du
Where W=0; Q=du ……eq-1
According to Fourier law; Q=QNX
QX=-KX A dT/dx
QY=-Ky A dT/dy
QZ=-Kz A dT/dz
=-d/dx[-kxdy dz dT/dx]dx
QNx=kx dx dy dz d2T/dx2 (...dv=dx dy dz)
similarly, QNx=k dv d2T/dx2
QNy=k dv d2T/dy2
QNz=k dv d2T/dz2
per unit volume; dv=dx dy dz
dU=mc dT/dx ... dU=⨜dv c dT/dt
The final derivation for HEAT CONDUCTION EQUATION IN CARTESITION CO-ORDINATES is
... kx d2T/dx2 +ky d2T/dy2 +kz d2T/dz2 +qg=⨜ c dT/dt
The above derivation explanation video : (640) HT-EPISODE-19-GENERAL HEAT CONDUCTION EQUATION FOR CARTESIAN CO-ORDINATE – YouTube