I would like to know how to calculate the temperature change of a moving object. For example if I throw a ball that is warmer than the surrounding air, how much would it lose form it's temperature in every second? I searched for two days now, but I have only partial solutions :(. I would need a formula that takes in account the followings:

  • The material of the ball (Iron, heat conductivity?)
  • Area of the ball
  • Speed of the ball (true airspeed)
  • Material of the surrounding material (air, heat conductivity?)
  • And ofc temperature of the ball and the surrounding material.
  • anything else I forgot and neccessary :):)

It dosen't need to take in account friction generated heat and other things, I only need the temperature loss :)


2 Answers 2


If the speed of ball is large most of the time, then speed of air flow across the ball (as seen from reference frame attached to the ball) is large most of the time, which means that heat transfer from ball to air is predominantly due to forced convection rather than free convection. With this assumption, you may use forced convection relations for heat transfer, which depends on air-speed across the ball, surface temperature of the ball, and thermodynamic properties of air. However these relations are empirical and are usually for constant air-speed, while in your case air-speed is changing with time. You may assume some average value of heat transfer coefficient to get an estimate. If thermal conductivity of the ball is high enough that entire ball is nearly at uniform temperature at all times, then you won't have to solve for temperature field inside the ball (to find its surface temperature, which is what is required ultimately). Regarding this last point read up lumped-system analysis and Biot number.


If you can take that object's temperature loss in terms of radiation just as a black-body, you can have your answer in wikipedia easily.

In equilibrium, for each frequency the total intensity of radiation that is emitted and reflected from a body (that is, the net amount of radiation leaving its surface, called the spectral radiance) is determined solely by the equilibrium temperature, and does not depend upon the shape, material or structure of the body.[17] For a black body (a perfect absorber) there is no reflected radiation, and so the spectral radiance is due entirely to emission. Here, you take total output by ball minus total input by surrounding.

(so the temperatures of ball and environment are important with the surface area of ball)


Ofcourse friction is important that how fast that object is relevant. That was already asked and answered below link.

(area of ball, material of ball, material of surrounding, speed of ball, structure of ball(flat surface or noisy surface))

After what speed air friction starts to heat up an object?

I want to add some more parameters, electric charge of object and magnetic field of the surrounding. When you move a charged object in a magnetic field that is not parallel to velocity of object, object is under a force. If it is fast enough and is in a constrained orbit, it will get hotter because electric charge on it will get affected and move to one side of object thus making the object to have a voltage-potential between two poles. When charges move to these poles, it has conduct a curent that heated it. If you change direction of flight of obejct, opposite polarisation happens and heats more. So even discontinuity of velocity is important if there are parameters such as charge and magnetic field.

Lets take bigger objects like planets. When two objects move close, they strain each other with gravity and get hotter. Especially the closermost parts.

Lets take smaller object, they are so small that even time is a parameter. You dont even need to move that. There is always a possibility of a molecule to change its state, angle of bond, direction of bond, polarisation (like inversion of NH3) which makes them resonate with a power source which could be even the infrared-band . If you take a small group of these, their natural-state-changing becomes more important thanks as Quantum-Physics shows.

Again for small objects, if those are fast enough(coming near speed of light), their mass increase and make the time go slower so the expected temperature would be smaller or I am wrong.

As Nathaniel reminds, heat change with conduction become more important as the heat transfer constant of surfece between ball and surrounding material increases(fluid density can be important too), surface area of ball is also important. When fluid passes faster, it takes heat faster. Pressure of surrounding fluid on the surface can be important too(maybe multiplies the transfer constant)

After speed of sound, some phasechanging can occur near surface and that could affect heat conduction too.

  • 4
    $\begingroup$ Unless you're throwing the ball in a vacuum, all of these effects will be tiny compared to the conductive loss of heat to the surrounding air. $\endgroup$
    – N. Virgo
    Jun 28, 2013 at 9:51
  • $\begingroup$ :D yes I forgot that. Adding. $\endgroup$ Jun 28, 2013 at 9:53
  • 4
    $\begingroup$ @Nathaniel - Technically, that's "convective". $\endgroup$ Nov 30, 2015 at 2:03
  • 2
    $\begingroup$ @WhatRoughBeast it's both - first the heat conducts into the air, and then the air convects away. But you're right, "convective" is a better term here. $\endgroup$
    – N. Virgo
    Nov 30, 2015 at 2:24

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