Question  set 169

Biot Number

1.     A gold ring (k = 65 W/m K) measuring 15 * 10 * 60 cm is exposed to a surface where h = 11.5 W/m² K. Find the value of biot number
a) 0.68
b) 0.58
c) 0.48
d) 0.38
Answer: c
Explanation: Biot number = h l/k = 0.48.

2.     In the lumped system parameter model, the variation of temperature with time is
a) Linear
b) Exponential
c) Sinusoidal
d) Cube
Answer: b
Explanation: t – t _a/t _I – t _a = exponential [-h A T/p V c].

3.     Which of the following dimensionless number gives an indication of the ratio of internal (conduction) resistance to the surface (convective) resistance?
a) Biot number
b) Fourier number
c) Stanton number
d) Nusselt number
Answer: a
Explanation: It is the ratio of conduction resistance to that of convective resistance.

4.     Lumped parameter analysis for transient heat conduction is essentially valid for
a) B _I < 0.1
b) 1 < B _I < 10
c) 0.1 < B _I < 0.5
d) It tends to infinity
Answer: a
Explanation: It is generally accepted that lump system analysis is applicable if Biot number is less than 0.1.

5.     In the non-dimensional Biot number, the characteristics length is the ratio of
a) Perimeter to surface area of solid
b) Surface area to perimeter of solid
c) Surface area to volume of solid
d) Volume of solid to its surface area
Answer: d
Explanation: We introduced characteristics length for lump system analysis.

6.     During heat treatment, cylindrical pieces of 25 mm diameter, 30 mm height and at 30 degree Celsius are placed in a furnace at 750 degree Celsius with convective coefficient 80 W/m² degree. Calculate the time required to heat the pieces to 600 degree Celsius. Assume the following property values
Density = 7850 kg /m³
Specific heat = 480 J/kg K
Conductivity = 40 W/m degree
a) 226 sec
b) 326 sec
c) 426 sec
d) 526 sec
Answer: b
Explanation: t – t _a/t _I – t _a = exponential (- h A T/p V c).

7.     The quantity h L _C/k is known as
a) Biot number
b) Fourier number
c) Stanton number
d) Nusselt number
Answer: a
Explanation: Biot number = conduction resistance/convection resistance.

8.     For a plat plate (thickness δ, breadth b and height h) the heat exchange occurs from both the sides. The characteristics length is equal to
a) δ/4
b) δ/3
c) δ/2
d) δ
Answer: c
Explanation: l = δ b h/2 b h = δ/2.

9.     Fourier number is given by
a) α T/L_C²
b) 2 α T/L_C²
c) 3 α T/L_C²
d) 4 α T/L_C²
Answer: a
Explanation: It signifies the degree of penetration of heating or cooling effect through a solid. Where, α is thermal diffusivity, T is time constant and L _C is characteristics length

10. Identify the correct relation between Biot number and Fourier number
a) 4 b T = B _I F ₀
b) 2 b T = B _I F ₀
c) 3 b T = B _I F ₀
d) b T = B _I F ₀
Answer: d
Explanation: B _I = h L _C/k and F ₀ = α T/L_C².