Heat transfer Flashcards
What are the 3 types of heat transfer?
1) Conduction: Main mode of heat transfer inside the material once it is heated up by the source. This is the most relevant mode, the other ones are kinda negligible.
2) Convection: Mainly related to the losses during the process such as the cooling by the ambient air and/or the process gas.
3)Radiation: Heat losses of the processed material at high temperatures
Fourier Law of conduction
qx’’= -k * dT/dx *ix
qx’’ is the heat flow per unit area per unit time
k is the thermal conductivity and it’s a temperature-dependent property
the sign - indicates the temperature decay as the heat flows in the opposite direction.
It can be expressed in different types of coordinates (i.e. cartesian x y z , cylindrical r z φ, spherical r,θ,φ).
In general q’’=-k * gradient(Τ)
Newton’s law of convection
q’‘=h (Ts-Too)
where h is the convection coefficient, Ts is the temperature of the specimen and Too is the environmental temperature.
Newton’s law of cooling
The rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings, or environment.
1st thermodynamic law
The increase in the internal energy of a system is equal to the amount of energy added by heating the system, minus the amount lost as a result of the work done by the system on its surroundings.
Ein+Eg-Eout=Est
g=generated -> it comes from the conversion of other energy forms
st=stored
What is the sensible energy ?
Sensible energy is the temperature variation in time occuring in a mass of interest that’s expressed by the volume by density multiplied by the specific heat.
ΔUsen= ρ* Cp* (θΤ/θt) * dxdydz
ΔU=ΔUsen+ ΔUt
where ΔUt is the latent component indicating the change of phase but for our interest in can be neglected. It’s only important when dealing with phase transformation
What is the thermal diffusivity
Thermal diffusivity is the thermal conductivity divided by the density and specific heat capacity at constant pressure Cp
α= k / r * Cp [m2/s]
the sum of the second derivatives of T at all coordinates = 1/α * θΤ/ θt
What is induction heating ?
Induction heating is the process of heating an electrically conducting object, by electromagnetic induction, through heat generated in the object by eddy currents. Then the induction is switched off and the cooling down happens because of the temperature difference between the object and the environment. Sometimes, oil or water can be used for the quenching.
How does the laser heat treatment process work?
It scopes to harden the material by using a laser source, where the photonic energy is converted into heat. Conduction is the main mechanism for heat transfer.
The objective is to reach the desired temperature at a given thickness and then turn the laser off. Then, the quenching of the piece takes place either by just the air or by using water or oil for more rapid quenching.
How to calculate the ierfc and what does it define?
1) Calculate the error function
2) Calculate the complimentary error function
3)Calculate the integral of the complimentary error function
The ierfc defines the form of the temperature gradient in space and time as a function fo the process inputs.
erf(x) (error function) is the integral function of the normalized Gaussian function (bell curve).
erf(-x)= - erf(x) –> odd function
erfc(x) = 1- erf(x) —> complimentary error function
erfc(oo)=0
erfc(0)=1
erf(-oo)=2
ierfc(x)= integral -x to x of the erfc(x) *dx
ierfc(0)=0.56 where x defines the depth within the material that we heat
Heating of a specimen
At x=0, the temprature increases with increasing irradiation time t, and reaches the maximum when t=τ,on and then when the laser is off the temperature decreases. We can see that with a fixed position in space, the temperature rise is propotional to sqrt(t). Remember that at infinite depth, T=Ti. (semi-infinite condition)
In physical terms, this corresponds to heat dissipation during the heating cycle, which allows the material to heat up in a linear matter.
What is the thermal length D?
D=sqrt(α*t) [m]
It shows how far the heat will propagate for the given material before it is completely dissipated.
α is the thermal diffusivity and describes how quickly a material reacts to a change in temperature.
It can be shown that at x=1D, 90% of the heat input is dissipated. It means that at the thermal length, the temperature raise is 10% of the one in the surface. We can assume that this is negligible and thus the semi-infinite model is applicable if the material thickness is larger than the thermal distance.
At x=2D, 99.9% of the heat is dissipated and thus at x=2D the temperature is 0.1% of the one in the surface.
The higher the conductivity of a material, the more difficult it is to increase its temperature.
How do we model the cooling phase?
We can think of the cooling phase as the superimposition of a heat flux acting for all t and the opposite flux acting after τ.
Thus, the expression of the heat sink after τ changes and instead of sqrt(αt) it becomes sqrt(α(t-τ))
What can be said about the velocity of the heating and the cooling operation?
The velocity of the heating operation is different than the velocity in the cooling direction because at the coooling phase, we model the heat source with a longer thermal length and the heat sink with a shorter thermal length. In physical terms, the effect of the heat sink is stronger.
