Hello Akshay,

The time constant of a solid such as a metal is equal to (pVc)/(hAs), where p is the mass density, V is the volume, c is the heat capacity at constant pressure, h is the heat transfer coefficient at the surface of the volume V, and As is the surface area of the volume V. This is the assuming that there are no thermal gradients inside the solid, i.e., that the thermal conductivity k of the solid is effectively infinite (compared to h/L, where L is the length scale of the system, see the discussion in the book by Incropera and DeWitt) - the so called lump capacitance model. The heat transfer coefficient h, in turn, depends on the mechanism (conduction, convection, or radiation) by which heat enters or leaves the surface of the solid. For further discussion, see the following book:

Frank P. Incropera, Davd P. DeWitt; Fundamentals of Heat and Mass Transfer; John Wiley & Sons, Inc.; 1985; pp. 174-177.

If the lumped capacitance model is not applicable to your system, i.e., if there are significant thermal gradients in the solid, then you will have to solve the full, time dependent heat equation for the geometry of your solid, which depends on knowing the thermal diffusivity of the solid, D=k/(pc), where k is the thermal conductivity, p is the mass density, and c is the heat capacity at constant pressure. For tables of thermal diffusivity, see the following reference.

Y. S. Touloukian, R. W. Powell, C. Y. Ho, M. C. Nicolaou; Thermophysical Properties of Matter, Volume 10, Thermal Diffusivity; Plenum Publishing Company; 1973; 757 pp.

From pp. 1-222 you will find, for example, the thermal diffusivity data for the elements. The data is many times plotted as a function of temperature up to and sometimes past the melting point of the element; pp.1a - 64a explain the methods used to gather the data, measurement methodology etc. There are also pages of data devoted to alloys, intermetallic compounds, ferrous alloys, etc This volume can be downloaded from the following URL: https://apps.dtic.mil/dtic/tr/fulltext/u2/a129113.pdf

If you are interested in thermal expansion data for different materials, which from your other questions on RG seems to be your main research interest, then see the following volumes of the reference books by Touloukian et al., which can also be downloaded from the Internet:

Y. S. Touloukian et al.; Thermophysical Properties of Matter, Volume 12, Thermal Expansion - Metallic Elements and Alloys; Plenum Publishing Company; 1975.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a129115.pdf

Y. S. Touloukian, et al; Thermophysical Properties of Matter, Volume 13, Thermal Expansion - Nonmetallic Solids; Plenum Publishing Company; 1977.

https://apps.dtic.mil/dtic/tr/fulltext/u2/a129116.pdf

Note, for other thermophysical properties of solid, such as thermal conductivity and specific heats (heat capacities versus a reference substance), see Volumes 1, 2, and 5 of the reference volumes by Touloukian et al.

NOTE, in general, the best you can do with a thermal system is to reach steady state; equilibrium is usually impossible to achieve.

Regards,

Tom Cuff

Hi Tom,

Thank you :) The publications are very helpful.

Hello Akshay,

You are welcome. By the way, I modified the first paragraph of my answer in order to make it more precise. I hope it helps.

Regards,

Tom

Time to reach stable thermal condition depends on thermal diffusivity, Alpha. Strictly it is not a thermal property. It is the relationship of thermal conductivity K, density Rho, and specific heat capacity cp of material: Alpha=K/(cp. Rho)

I forgot to say: the higher the thermal diffusivity the faster will be reached the thermal steady state

Hi Alberto,

Thank you for your help.

Does that mean Tungsten will take more time to stabilize than Aluminum.?

All depends on thermal diffusivity value. This property is a function of temperature for both metals and depends on composition too. If you have the value of thermal diffusivity for both metals just comparing them you can conclude which of them will take more time to stabilize its temperature after being exposed to a thermal disturb. The lower the thermal diffusivity the slower will be the thermal stabilization process.