Question: In a heat transfer analysis, which material will
heat faster if the thermal conductivity and density properties are almost
equal, a material with a higher or lower specific heat?
Answer: A material with the lowest specific heat will heat
faster than a material with a higher specific heat, if the conductivity and
density are the same.
The important property that decides how quickly a material
will respond to changes in a thermal environment is called thermal diffusivity,
α, which is the ratio of thermal conductivity to heat capacity and has units of
length2 / time.
Where: k = thermal conductivity, ρ = density and Cp =
specific heat
This quantity "α" relates the capacity of the
material to transport thermal analysis energy through conduction (k) in relation to its
capacity to store it (ρ * Cp). Which means that materials with a high α will
respond quickly to changes in the thermal environment (i.e., the material is
better for conducting thermal energy than storing it) and materials with a low
α will respond slowly and take longer to reach a new Balance. As an example,
metals generally have a higher α than nonmetallic materials.
The problem shown below demonstrates this behavior for
various materials.
Figure 1 shows a metal handle surrounded by insulation at
all ends except one. The metal body is initially at a uniform temperature (300
° K) until the exposed end (x = 0) undergoes convection heating, which causes
the body to rise to a new equilibrium temperature (350 ° K). The problem is
treated as one-dimensional in x, and the temperature variation in the metal at
the isolated end of the body (x = L) over time is shown in Figure 2 for various
materials. The materials are also listed in the legend in descending order α
(in units of 1e-6m2 / s).
The response of various materials to an environmental change
is shown in Figure 2, which illustrates the influence of the thermal
diffusivity property. However, for conduction problems involving surface
convection, the profile of the temperature distribution along the length at any
point in time and, ultimately, the temperature at the isolated end (x = L) is
also a function of the number of Biot, Bi.
Where: h = convection heat transfer coefficient, L =
characteristic length, and k = thermal conductivity.
The number of Biot influences the problems that involve
surface convection, since it relates the relationship of the temperature drop
across the material to the difference between the temperature of the convection
surface and the environment. For small Bi numbers, thermal energy will pass
through the conduction much easier than it can travel through the fluid
boundary layer through convection. As a result, the temperature distribution along
the handle at any time will be approximately uniform
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