How can i analyse the heat transfer through a composite system having conduction heat transfer by using Biot number and Fourier number. Will these number play any significant role for transient conduction through the composite system.
Biot number shows how convection and conduction heat tranfer phenomena are related. Small values of thsi numer shows that the conduction is the main heat tranfer method, while high values of this number indicates that the convection is the main heat tranfer mechanism.
Fourier number is able to determine the characteristic "time" of the problem. This time is important in studies because it indicates if the phenomenon is quick or slow. Practically, in a transient analysis, the simulation time is in the same order of magnitude with the respective chareacteristic time calculated by the fourier number.
Example. You solve a problem with caharcteristic time 2sec. In order to find the steady state solution, simulate for a time about 3-4 times the characteristic; so use 6-8 sec as the minimum simulation time.
Read Heat Transfer by Kern or McCabe Smith's Unit Operation book to find the answer.
Fourier number and Biot number are dimensionless quantities arising in heat conduction problem. Fourier number is also known as dimensionless time and have effect on temperature before the steady state achieved. Biot number arises when we use third kind of boundary condition (i.e convective heat transfer in presence of external fluid surface). Both have significant effect on temperature distribution. For further details go through our following papers.
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Biot number shows how convection and conduction heat tranfer phenomena are related. Small values of thsi numer shows that the conduction is the main heat tranfer method, while high values of this number indicates that the convection is the main heat tranfer mechanism.
Fourier number is able to determine the characteristic "time" of the problem. This time is important in studies because it indicates if the phenomenon is quick or slow. Practically, in a transient analysis, the simulation time is in the same order of magnitude with the respective chareacteristic time calculated by the fourier number.
Example. You solve a problem with caharcteristic time 2sec. In order to find the steady state solution, simulate for a time about 3-4 times the characteristic; so use 6-8 sec as the minimum simulation time.
Fourier Number: Let alpha = thermal diffusivity and L = characteristic scale for heat transfer. Then L^2/alpha = tau is characteristic time scale for diffusive heat transfer. Now define a 2nd timescale tauOB which is some characteristic time scale for an observed process. Then Fo = Fourier Number = alpha * tauOB / L^2 is dimensionless. One can rewrite it as Fo = tauOB/tau. Thus Fo is the ratio of the the observed timescale to the conduction time scale. If Fo > 1 then the reverse is true.
Biot Number: Let h = convection heat transfer coeffcient, k = thermal conductivity and L a characteristic length scale as above. Then Bi = Biot Number = h L / k = (L/k) / (1/h) is a dimensionless number that can be thought of a ratio of conduction to convection thermal resistances. For a given rate of HT through some solid/fluid interface, the HT rate (flux) must match on both sides of the interface. If Bi
Look at this may be helpful. Good luck.
https://www.quora.com/What-is-the-significance-of-Fourier-number-and-biot-number-in-Heat-transfer
The Fo number refers to the rate of heat conduction in relation to the rate of accumulation of thermal energy in the body. In turn, the Bi number determines the relationship between the resistance due to thermal conductivity in body and the resistance due to convective heat transport. These are not comparable behaviors. The Bi number is also used in the description of catalytic processes, especially for the description of interparticle heat transfer. Regards,
Biot and Fourier Number simultaneously are applied when the transient heat transfer of an immersed solid body is going to be investigated.
It means you should to find out the significance of solid body and environment over heat propagation during the time.
Biot Number expresses the ratio of Heat Conduction Resistance through the solid mass to Heat Convection Resistance between the body and environment showing how the temperature varies from the mass interior to the atmosphere. While, the Fourier Number represents how during the time the heat is transporting in the solid body from hot to cold spots and is the ratio of thermal diffusivity per rate of storage.
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