What do you understand by lumped system derive the expression?
Lumped system analysis assumes a uniform temperature distribution throughout the body, which implies that the conduction heat resistance is zero. Thus, the lumped system analysis is exact when Bi = 0. Therefore, small bodies with high thermal conductivity are good candidates for lumped system analysis.
What is lumped capacity analysis when is it applicable What is the physical significance of the Biot number?
Heat transfer analysis which utilizes this idealization is known as the lumped system analysis. It is applicable when the Biot number (the ratio of conduction resistance within the body to convection resistance at the surface of the body) is less than or equal to 0.1. Chapter 4, Solution 2C.
What is lumped capacitance method?
A lumped-capacitance model, also called lumped system analysis, reduces a thermal system to a number of discrete “lumps” and assumes that the temperature difference inside each lump is negligible. This approximation is useful to simplify otherwise complex differential heat equations.
What is Biot number for lumped capacitance?
0.1
As a general rule of thumb, a lumped capacitance analysis is considered to be valid if the Biot number of the heat transfer situation is below 0.1.
What is the correct formula for the Biot number *?
The Biot number equals the product of the heat transfer coefficient and the characteristic length divided by thermal conductivity.
What is lumped system analysis when is it used?
The lumped system analysis is the method used for the analysis of transient heat transfer systems. The method is used when there is no temperature gradient present in the object to be analyzed for the complete heat transfer process. It means that the temperature of the body should be uniform throughout the object.
What is meant by a lumped capacity what are the physical assumptions necessary for a lumped capacity unsteady state analysis to apply?
lumped system analysis assumptions: 1) The temperature of the body is uniform at any point. 2) The temperature is the function of time. 3) Internal conductive resistance is minimum. 4) The object has infinite thermal conductivity.
What does Biot number represent?
Bi is the Biot number, which is a dimensionless number that represents the ratio of the resistance to heat transfer from the inside of the body to the surface of the body (52).
How do I find my Biot number?
Lc = V / A . For example for a copper pan of water with characteristic length Lc = 15 cm , the Biot number is Bi = 2.807 .
How is Biot number calculated?
What is Biot and Fourier number?
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.
What is difference between Nusselt number and Biot number?
Biot number uses thermal conductivity of the body (not fluid), whereas Nusselt number uses thermal conductivity of the fluid. The differences between Biot and Nusselt number is in definition of heat transfer coefficient, which is defined as: h=-k (dT/dn)w/(Tw-T0).
Which of the following is true for lumped system analysis?
4. Which is true regarding lumped system analysis? Explanation: Solids have infinite thermal conductivities. It implies that internal conductance resistance is very low.
What are benefits of lumped capacitance method?
The most important advantages of the lumped capacity model are its simplicity and practical usability. By means of the model, the following transient heat transfer problems can be solved: Calculation of time required to cool or to heat the solid from its initial temperature to certain (current) temperature.
What is the physical significance of Biot number?
The numerical value of Biot Number (Bi) is a criterion which gives a direct indication of the relative importance of conduction and convection in determining the temperature history of a body being heated or cooled by convection at its surface.
Can Biot number be greater than 1?
If the Biot number is small (much less than 1) then the temperature on the surface and in the interior will be very similar. On the other hand if the Biot number is large (much larger than 1) then there will be a large temperature gradient inside the body.
What is LC in Biot number?
Biot number formula Lc [m] is the characteristic length of a material, h [W/(m² * K)] is the heat transfer coefficient at the material’s surface, k [W/(m * K)] is the thermal conductivity of the material.