What is the correct expression for the total thermal resistance in series for conduction?

What is the correct expression for the total thermal resistance in series for conduction?

• A. R_total = L1/(k1 A1) + L2/(k2 A2)
• B. R_total = (L1+L2)/(k A)
• C. R_total = kA/(L1+L2)
• D. R_total = L1/(k1 A1) * L2/(k2 A2)

Answer: (A)

In conduction through multiple layers in series, the same heat flow passes through each layer, so the temperature drop adds up across the stack. Each layer has its own thermal resistance R = L/(k A), depending on its thickness, conductivity, and cross-sectional area. Therefore the total thermal resistance is the sum of the individual resistances: R_total = L1/(k1 A1) + L2/(k2 A2). If both layers share the same material and cross-sectional area, this simplifies to R_total = (L1 + L2)/(k A). The other forms are not generally correct: multiplying the two resistances would not reflect series behavior, and using a single (L1+L2)/(k A) ignores differences in properties between the layers when k and A are not identical.

In conduction through multiple layers in series, the same heat flow passes through each layer, so the temperature drop adds up across the stack. Each layer has its own thermal resistance R = L/(k A), depending on its thickness, conductivity, and cross-sectional area. Therefore the total thermal resistance is the sum of the individual resistances: R_total = L1/(k1 A1) + L2/(k2 A2).

If both layers share the same material and cross-sectional area, this simplifies to R_total = (L1 + L2)/(k A). The other forms are not generally correct: multiplying the two resistances would not reflect series behavior, and using a single (L1+L2)/(k A) ignores differences in properties between the layers when k and A are not identical.