Question

Why are the convection and the radiation resistances at a surface in parallel instead of being in series?

Short answer

Answer: Convection and radiation resistances are considered to be in parallel at a surface because heat can transfer simultaneously through both modes of heat transfer, allowing for more efficient and simultaneous heat flow. In contrast, series resistances would require heat to transfer sequentially through each resistance, creating a more limited and slower heat flow process.

Step-by-step solution

Understanding Convection and Radiation Resistances

Convection and radiation are two different methods of heat transfer. Convection resistance is the resistance to heat transfer between a heat source and a fluid or gas in contact with the heat source (such as air). Radiation resistance is the resistance to heat transfer between a heat source and other surfaces or objects within its surroundings without direct contact (for example, through thermal radiation). These resistances represent the difficulty and efficiency of heat transfer through these different modes.

Interactions of Convection and Radiation Resistances

At a surface, both convection and radiation resistances exist simultaneously since heat is being transferred from the surface to its surroundings through both convection (to the surrounding fluid or gas) and radiation (to the surrounding objects).

Parallel versus Series Resistances

Resistances can be present in either parallel or series, depending on how they affect the flow of heat. In series resistances, heat must pass through one resistance and then the other, meaning the heat transfer is sequential and the sum of the resistances is the total resistance. In parallel resistances, heat transfer can occur simultaneously through both resistances, and the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.

Convection and Radiation Resistances in Parallel

Convection and radiation resistances at a surface are considered to be in parallel because heat can transfer simultaneously through both modes of heat transfer. The surface does not have to release heat exclusively through convection before releasing it through radiation or vice versa. Instead, heat can be transferred through both convection and radiation at the same time.

Calculating Total Resistance

To calculate the total resistance in a system with convection and radiation resistances in parallel, you can use the following formula: \[\frac{1}{R_{total}} = \frac{1}{R_{convection}} + \frac{1}{R_{radiation}}\] R_total is the total resistance, R_convection is the convection resistance, and R_radiation is the radiation resistance. In summary, convection and radiation resistances are considered to be in parallel at a surface because heat can transfer simultaneously through both modes of heat transfer. This is contrary to series resistances, where heat transfer would need to occur sequentially through each resistance.