Heat conduction across a thin film

The generalized form for steady-state heat conduction across a thin film (where we allow the insulating material a thickness 8) is given by... 

Fig. 20.1-1. Steady heat conduction across a thin film. Heat conduction across a thin film is like diffusion across a membrane (see Section 2.2). The resulting temperature profile is linear, and the flux is constant and inversely proportional to the film thickness /.

To calculate heat fluxes or temperature profiles, we make energy balances and then combine these with Fourier s law. The ways in which this is done are best seen in terms of two examples heat conduction across a thin film and into a semi-infinite slab. The choice of these two examples is not casual. As for diffusion, they bracket most of the other problems, and so provide limits for conduction. 

Steady Heat Conduction Across a Thin Film... 

The limits of heat conduction across a thin film and into a thick slab are the two most important cases of a rich variety of examples. This variety largely consists of solutions of Eq. 20.1-16 for different geometries and boundary conditions. The geometries include slabs, spheres, and cylinders, as well as more exotic shapes like cones. The boundary conditions are diverse. For example, they include boundary temperatures that vary periodically because this is important for diurnal temperature variations of the earth. They include boundary conditions in which the heat flux at the surface is related to the temperature of the surroundings, Tsurrl for example. 

How does the flux vary with physical properties for the thick slab as compared with the thin fibril Doubling the temperature difference doubles the heat flux in both cases. Doubling the thermal conductivity increases the flux by /2 for the thick slab and by 2 for the thin film. Doubling the heat capacity increases the flux by >/2 for the thick slab, but has no effect for the steady-state conduction across a thin film... 

If you double the thermal conductivity, how much will the heat flux across a thin film change ... 

Heal flux meters use a very sensitive device known as a thermopile lo measure the temperature difference across a thin, heat conducting film made of kapton (k = 0.345 W/m K). If the thermopile can delect temperature differences of 0.1 °C or more and the film thickness is 2 mm, what is the minimum heal flux this meter can detect Ansv/en 17.3 W/rrf... 

Molecular dynamics simulations entail integrating Newton s second law of motion for an ensemble of atoms in order to derive the thermodynamic and transport properties of the ensemble. The two most common approaches to predict thermal conductivities by means of molecular dynamics include the direct and the Green-Kubo methods. The direct method is a non-equilibrium molecular dynamics approach that simulates the experimental setup by imposing a temperature gradient across the simulation cell. The Green-Kubo method is an equilibrium molecular dynamics approach, in which the thermal conductivity is obtained from the heat current fluctuations by means of the fluctuation-dissipation theorem. Comparisons of both methods show that results obtained by either method are consistent with each other [55]. Studies have shown that molecular dynamics can predict the thermal conductivity of crystalline materials [24, 55-60], superlattices [10-12], silicon nanowires [7] and amorphous materials [61, 62]. Recently, non-equilibrium molecular dynamics was used to study the thermal conductivity of argon thin films, using a pair-wise Lennard-Jones interatomic potential [56]. 

Heat conduction also occurs, but free convection does not. Only gas 1 and gas 2 are in the film, and the thermal conductivity is constant. Also assume that the thermal conductivity at the boundaries is much greater than in the bulk. Find the heat transfer coefficient across this thin film in three steps (a) Find the concentration profiles in the film, (b) Find the temperature profile corrected for mass transfer, (c) Find the heat flux at the boundary z = 0. 

On the other hand, it has been argued that the resistance to heat transfer is effectively within a thin gas film enveloping the catalyst particle [10]. Thus, for the whole practical range of heat transfer coefficients and thermal conductivities, the catalyst particle may be considered to be at a uniform temperature. Any temperature increases arising from the exothermic nature of a reaction would therefore be across the fluid film rather than in the pellet interior. 

Diffusion of Heat. In dynamic equilibrium, a transfer of vapor from liquid through a vapor phase to a second liquid (the two liquids being thermally connected only across the thin gap) will require reverse transfer of the heat of vaporization. This will accompany a temperature difference determined by the ratio of heat flow to the thermal conductance of the two heat paths. These two are the diffusion vapor gap and the series of salt water and plastic films. For the diffusion gap the c.g.s. air value 5.7 x 1(H is chosen for the thermal conductivity (neglecting the separating powder), while for the series polyethylene (50 X 10-4 cm. thick), wet cellophane (50 X 10"4 cm. thick), and water (200 X 10-4 cm. thick) the respective thermal conductivities are 3.5 X 10"4, 4 X 10-4, and 14 X 10 4. 

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