# Calculating the amount of emitted heat

## Main Question or Discussion Point

Imagine that some object (a long rod for example) is flying in atmosphere very quickly. If we know its speed, altitude and also amount of time spent during flight-can we calculate the amount of heat emitted during this quick motion (due to atmospheric drag)? I would like to know if that object is melted/boiled or no the temperature can be calculated by means of this online-calculator here: http://www.grc.nasa.gov/WWW/BGH/stagtmp.html Now, how the emitted heat should be calculated? The temperature should be multiplied to time? And should we compare the received result to materials heat capacity?

## Answers and Replies

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I know you can solve for the convection heat transfer coefficient and just do q=hA deltaT (convection heat trans equation) to get the heat transfer into the object (rod in this case). Whether or not you can do this using this calculator, I'm not sure.

I know you can solve for the convection heat transfer coefficient and just do q=hA deltaT (convection heat trans equation) to get the heat transfer into the object (rod in this case). Whether or not you can do this using this calculator, I'm not sure.
Q-is amount of heat as I know, but what are h, A and deltaT? T is Temperature obviously

In this case, q is the rate of heat exchange (energy per time), but h is the coefficient of convection heat transfer and A is the surface area that the fluid (air) is in contact with, usually the surface area of the object. The deltaT is temperature, but if I remember my supersonic flow equations, the temperatures here are a kind of combination of the adiabatic stagnation temperature, the material surface temperature and the actual free-stream temperature. I can't remember exactly how to calculate it, but any introductory heat transfer text could tell you.

In this case, q is the rate of heat exchange (energy per time), but h is the coefficient of convection heat transfer and A is the surface area that the fluid (air) is in contact with, usually the surface area of the object. The deltaT is temperature, but if I remember my supersonic flow equations, the temperatures here are a kind of combination of the adiabatic stagnation temperature, the material surface temperature and the actual free-stream temperature. I can't remember exactly how to calculate it, but any introductory heat transfer text could tell you.
So, how these q and h can be calculated? Imagine that we have got long rod with following parameters-1000 m length, 1 m radius. The surface area of such cylinder would b:
A = 2πr2 + 2πrh = 2πr(r + h).
A = 2*3.14*r2 + 2*3.14*r*1000 =6.28+6280= 6286.28 square meters
As for temperature, let’s rod’s speed be 3000 m/sec and altitude 0 meters (sea level), as we these at this site http://www.grc.nasa.gov/WWW/BGH/stagtmp.html the Total temperature of calorically imperfect gas (this should be takes, right?) is 4008 K, then what?

I have attached an excerpt from the 10th edition "Heat Transfer" textbook by J.P. Holman. This is what I would use to estimate the heat generated by supersonic flow. The calculator will save you some time in determining the temperatures you will need to use. See if this helps.

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I have attached an excerpt from the 10th edition "Heat Transfer" textbook by J.P. Holman. This is what I would use to estimate the heat generated by supersonic flow. The calculator will save you some time in determining the temperatures you will need to use. See if this helps.
Thanks I will take a look at it