True or false explain reasoning 14 The oneterm transient hea

True or false explain reasoning

14) The \"one-term\" transient heat conduction analysis will give reasonably accurate predictions if the

Biot number is less than about 0.1 for any Fourier number.

a) True

b) False

Solution

Answer - a) True

Reason: Both Biot & Fourier numbers are dimensionless numbers. Dimensionless numbers are generally used to reduce the no. of independent variables that occur while solving the problems analytically. Thus they are used to simplify the calculations.
Bi=hL/k. If we rearrange this equation, we get Bi=L/k/1/h. This equation represents the ratio of internal resistance of body to heat conduction, to external resistance to heat convection. Thus small biot no. represents small resistance to heat conduction & thus small temperature gradient within the body.
Both nos. are used in lumped system analysis which assumes uniform temperature distribution within body , which is the case when internal resistance to heat conduction of body is zero, i.e. Bi=0. But this is the ideal case & we assume lumped system analysis to be valid when Bi is less than, or equal to 0.1.
Fourier no. represents the dimensionless time in lumped heat analysis.