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θ1= temperature of the inner surface
θ2 = temperature of the outer surface
L = length of the cylinder
K = thermal conductivity
Ρ1 and Ρ2 are inner and outer radii of the cylinder
ΔQ/ΔT = Heat flow per second H
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In case of two cylindrical layers
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Heat conduction through a Spherical Shell
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In case of multiple shells:
Thermal Resistance (R): Eq. (ii) in differential form can be written as
...(ii)
Here, DT = temperature difference (T.D) and,
R = 1/kA= thermal resistance of the rod.
Growth of Ice on the Surface of a Lake
A thick layer of ice of thickness x is created on the surface of a river. The water below the ice layer is at a temperature of 0oC. The air above the ice layer is at a temperature of - θoC. Heat transfers from water to air through ice. As a answer of this heat loss, the surface increase in thickness from below.
Let dx be the gain in thickness in time dt.
=> Heat loss form water to air = (mass) * (latent heat) = (A dx) Ρ L
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Where Ρ : density of ice; L: latent heat of ice;
A: area of cross-section of ice slab
Using ΔQ/Δt = {KA(θ1-θ2)}/d
=> Heat flow per second =AΡL(dx/dt) = KAθ/x
Rate of growth of thickness =dx/dt = Kθ/ΡLx
If the thickness changes from x1 to x2 in t time, then:
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