ANS:B - sum of all resistances.

1. Series Configuration: When heat transfer occurs through a series of resistances, it means that the heat must pass through each resistance in succession. This setup is akin to a chain where each link represents a resistance to heat flow.
2. Additivity of Resistances: In series configuration, the resistances to heat transfer add up. This is due to the nature of heat flow, where the resistance offered by each material or interface impedes the flow of heat. Think of it like adding up the resistance values in an electrical circuit; the total resistance is the sum of individual resistances.
3. Analogy with Electrical Circuits: Just like how the total resistance in an electrical circuit is the sum of individual resistances in series, the same principle applies to thermal resistance in a heat transfer system. In an electrical circuit, current encounters resistance as it flows through resistors in series; similarly, heat encounters resistance as it flows through materials or interfaces in a series of thermal resistances.
4. Mathematical Representation: Mathematically, if R1​,R2​,R3​,…,Rn​ represent the individual thermal resistances in the series, then the total thermal resistance totalRtotal​ is given by:

Rtotal​=R1​+R2​+R3​+…+Rn​

5. Conservation of Energy: The principle behind this summation is based on the conservation of energy. Each resistance component absorbs or impedes a portion of the heat energy, and these effects accumulate along the series path. The total resistance represents the total opposition encountered by the heat flow as it traverses the series of resistances.

In summary, in a series configuration of flat resistances for conductive heat transfer, the overall thermal resistance is the sum of all individual resistances because each resistance hinders the flow of heat, and these hindrances add up along the heat flow path.