Consider the boilers made up of different layers of conducting materials. How the heat conduction takes place in such an arrangement when they are connected in series and parallel?
Answers
Consider the boilers made up of different layers of conducting materials.
We have to explain how the heat conduction takes place in such an arrangement when they are connected in series and parallel.
Let k₁ , k₂ and k₃ are three different layers of conducting materials used to make up boiler, change in the temperature is ∆T and cross sectional area is A and separation between two ends from which heat flows is ∆x.
Series combination : for series combination,
R = R₁ + R₂ + R₃
we know, R = ∆x/kA
∴ ∆x/(keq A) = ∆x/k₁A + ∆x/k₂A + ∆x/k₃A
⇒1/keq = 1/k₁ + 1/k₂ + 1/k₃
⇒keq = (k₁k₂ + k₂k₃ + k₃k₁)/k₁k₂k₃
hence, heat conduction taken place in series combination is given by, Q = keq ∆T/∆x
= (k₁k₂ + k₂k₃ + k₃k₁)/k₁k₂k₃ ∆T/∆x
Parallel combination : for series combination,
1/R = 1/R₁ + 1/R₂ + 1/R₃
⇒keq A/∆x = k₁A/∆x + k₂A/∆x + k₃A/∆x
⇒keq = k₁ + k₂ + k₃
hence, heat conduction taken place in parallel combination is given by, Q = keq ∆T/∆x
= (k₁ + k₂ + k₃) ∆T/∆x