Two solid blocks with different properties and with the same intiial temperature

Question

Two solid blocks with different properties and with the same intiial temperature are suddenly placed in contact and rubbed against each other. The friction between the two blocks generates the heat flux q" in the interface. A fraction of this flux, q1", is absorbed by the upper block, while the remainder, q2", flows into the lower block. Determine the manner in which the properties of the two materials affect the ratio q2"/q1". Derive the formulas needed for calculating q1", q2", and the interface temperature To.

Explanation / Answer

intital uniform temperature as T

we will consoder axial conduction .. say in x direction

A1 is area of surface where rubbing is taking place.. l1 is axial length

q1 "=k1 (T0-T)/l1 = k1 (del T)/l1

similarly

q2 "=k1 (T0-T)/l1 =k2 (del T) l2

............

here rubbing surfaces will have same temperature To

and as the box was first at initial temp T for rubbing time end of the box will stil be at T hence del T for both boxes will be same

hence

q1" /q2" = [k1 (del T)/l1 ] /[k2 (del T)/l2 ]

=(k1*l2)/(k2*l1)

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