Question

The Biot number can be thought of as the ratio of (a) the conduction thermal resistance to the convective thermal resistance (b) the convective thermal resistance to the conduction thermal resistance (c) the thermal energy storage capacity to the conduction thermal resistance (d) the thermal energy storage capacity to the convection thermal resistance (e) none of the above

Short answer

Answer: The correct representation of the Biot number is the conduction thermal resistance to the convective thermal resistance.

Step-by-step solution

Definition of Biot Number

Biot number (Bi) is a dimensionless number that represents the relative importance of convective heat transfer to conductive heat transfer within a solid. It is given by the formula: Bi = h * Lc / k Where: - Bi: Biot number - h: convective heat transfer coefficient (W/m^2.K) - Lc: characteristic length (m) (usually taken as the smallest dimension) - k: thermal conductivity of the solid (W/m.K)

Option (a) Analysis

In option (a), the Biot number is presented as the ratio of the conduction thermal resistance to the convective thermal resistance. To analyze this option, let's define the conduction and convective thermal resistance: - Thermal resistance due to conduction (Rc) is given by: Rc = Lc / k; - Thermal resistance due to convection (Rcv) is given by: Rcv = 1 / (h * A); The Biot number (Bi) can also be expressed as: Bi = (Rc / Rcv) = (Rc * h * A) / (1); Since option (a) presents the Biot number in this form, option (a) is a correct representation of the Biot number.

Option (b) Analysis

In option (b), the Biot number is presented as the ratio of the convective thermal resistance to the conduction thermal resistance. This option is the inverse of option (a). Thus, Option (b) is incorrect.

Option (c) Analysis

In option (c), the Biot number is presented as the ratio of the thermal energy storage capacity to the conduction thermal resistance. This option does not correspond to the definition and formula of the Biot number. Thus, Option (c) is incorrect.

Option (d) Analysis

In option (d), the Biot number is presented as the ratio of the thermal energy storage capacity to the convection thermal resistance. This option also does not correspond to the definition and formula of the Biot number. Thus, Option (d) is incorrect.

Option (e) Analysis

Option (e) states that none of the above options are correct. Since we have already identified option (a) as the correct representation of the Biot number, option (e) is incorrect.

Answer

The correct option that represents the Biot number is: (a) the conduction thermal resistance to the convective thermal resistance.