How to Calculate the Rate of Heating on Any Material at Various Conditions?

[physwil90]

I was wondering if anyone knows of an equation that will properly calculate the rate of heating on any material, at any altitude, at any speed, and with air hitting that surface at any angle.

The equation will be somewhere similar to
(DT/dt)t=0=(Tr-Tinitial)h/(cρz)
Where:
T=temperature
t=time
Tr=T0(1+0.2rM^2) where r=recovery factor~0.84 for laminar air flow~0.89 for
turbulent air flow
Tinitial=initial temperature
h=kNNu/x
k=3.58E-6[717/(T0+225)](T0/492)^3/2
NNu=0.0271Re^0.8
x=boundary layer distance from the nose
Re=ρVL/μ
ρ=density of fluid
V=mean fluid velocity
L=travel length of fluid
μ=the dynamic viscosity of the fluid
c=specific heat
z=thickness

However, this equation is for (specifically) heating on a thin rocket airframe.

Any help would be greatly appreciated.

 

[eljose79]

Thank you for your question. I am always interested in finding equations that can accurately calculate physical phenomena. In response to your query, I have some suggestions for you to consider.

Firstly, the equation you have provided seems to be specifically for heating on a thin rocket airframe. If you are looking for a more general equation that can calculate the rate of heating on any material, at any altitude, at any speed, and with air hitting the surface at any angle, you may need to consider a more complex and comprehensive equation.

One possible equation that could be used is the Newton's law of cooling, which states that the rate of heat transfer is proportional to the temperature difference between the object and its surroundings. However, this equation may not take into account the effects of altitude, speed, and air angle.

Another approach could be to use the heat transfer coefficient, which is a measure of how easily heat can be transferred between a material and its surrounding medium. This coefficient can be affected by factors such as altitude, speed, and air angle, and can be calculated using empirical equations or through experiments.

In addition, you may also want to consider the effects of convection, radiation, and conduction in your equation, as these can also impact the rate of heating on a material.

In conclusion, there is no single equation that can accurately calculate the rate of heating on any material, at any altitude, at any speed, and with air hitting the surface at any angle. It may be necessary to combine multiple equations and factors to get a more comprehensive and accurate result. I hope this helps in your research. Good luck!