Question

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Define thermal diffusivity (α) and give its mathematical expression.

Answer 1

Answer:

• Explaination:

In the heat transfer analysis, thermal diffusivity can be defined as the ratio of themal conductivity to the density and specific heat at the constant pressure.

It generally defines the rate at which the heat transfer takes place from hot end of any material to the cold end. Thermal diffusivity describes the ability of the materail of conducting the thermal energy with respect to the ability of thermal energy storage.

If any material is having high diffusivity it means heat transfer will be very quick and it is also found by experiments and general relation that thermal diffusivity decreases as the temperature increases.

• Unit: SI unit of thermal diffusivity is

• Mathematical expression:  Thermal diffucivity is denoted by  apart from this it is alos denoted by D , a,h,k are also used sometimes

Formula of thermal diffusivity

where,

• K is thermal counductivity (W/m.K)
• is specific heat at constant pressure (J/Kg.K)
• is density (Kg/m^3)
• is known as volumetric heat capacity is taken together (J/m^3K)

Thermal diffusivity in Heat equation :

From this equation we can see that, thermal diffusivity is the ratio of derivative of time of trmperature with the curvature. It is generally measuremnet of thermal interial present in the specimen or metarial.

In a specimen or substance, if the thermal diffusivity is high, heat will move rapidly as the conduction of the heat will be high relative to heat capacity which is also known as thermal bulk.

Assumptons made in heat conduction equation:

• Specimen of the known material with infinite, homogenous, isotropic and plate of constant thickness is considered.
• Surface of the plate or speciment should be heated uniformely
• Surface of the plate is isothermal
• Radiation and convection heat transfer is negligible in comparison with heat conduction.

Experimental method to find thermal diffusivity:

If the density is known than thermal diffusivity can also be known along with the thermal conductivity. The method of calculating thermal diffusivity experimentally is by searle's bar experiment. Which given the equation for thermal conducticity and with the help of that equation thermal diffusivity is also calculated.

Thermal diffusivity is also measured with the flash method. In the process, heating of the strip is carried out with a short energy pulse.