Heat transfer nonsteady-state

Figure 5 shows conduction heat transfer as a function of the projected radius of a 6-mm diameter sphere. Assuming an accommodation coefficient of 0.8, h 0) = 3370 W/(m -K) the average coefficient for the entire sphere is 72 W/(m -K). This variation in heat transfer over the spherical surface causes extreme non-uniformities in local vaporization rates and if contact time is too long, wet spherical surface near the contact point dries. The temperature profile penetrates the sphere and it becomes a continuum to which Fourier s law of nonsteady-state conduction appfies. 

Since the adsorbent bed must be heated in a relatively short time to reactivation temperature, it is necessary that the reactivation steam rate calculation is increased by some factor that will correct for the nonsteady-state heat transfer. During the steaming period, condensation and adsorption will take place in the adsorbent bed, increasing the moisture content of the adsorbent. A certain portion of the adsorbate... 

If heat and mass transfer processes inside the treated solid are not sufficiently rapid, in comparison with the rates of heating and pore formation, and the temperature changes significantly with time, one obtains a nonsteady-state situation, whereas enough rapid heat/mass transfer and pore formation assure steady-state in systems with regular fluxes... 

The material presented earlier was confined to steady-state flows over simply shaped bodies such as flat plates, with and without pressure gradients in the streamwise direction, or stagnation regions on blunt bodies. The simplicity of these flow configurations allows reduction of the problems to the solution of steady-state ordinary differential equations. The evaluation of convective heat transfer to more complex three-dimensional configurations, characteristic of real aerodynamic vehicles, involves the solution of partial differential equations. Even when the latter are confined to steady-state problems, they require extensive use of computers in the solution of finite difference or finite element formulations Nonsteady flows further complicate the problems by introducing another dimension, namely, time. 

In the case of nonsteady-state heat transfer, the equation is analogous to the diffusion equation ... 

There are various different methods used in the determination of thermal properties of textile fabrics, including both steady state heat transfer method and nonsteady state (or transient) heat transfer methods. The typical steady state heat transfer methods include guarded hotplate method, Togmeter, and SGHP the typical... 

It should be noted that any analysis or evaluation of the cyclic pressure freeze drying process should involve nonsteady-state heat and mass transfer equations like those presented in Seetion 11.6.1.1 and Section 11.6.1.2. The effectiveness of cyclic pressure freeze drying and the effect of cycle period and shape on drying times have been the subject of a number of investigations [1,60,61]. Litchfield and Liapis [12]... 

Derive steady-state and nonsteady-state mass and energy balances for a catalyst monolith channel in which several chemical reactions take place simultaneously. External and internal mass transfer limitations are assumed to prevail. The flow in the chaimel is laminar, but radial diffusion might play a role. Axial heat conduction in the solid material must be accounted for. For the sake of simplicity, use cylindrical geometry. Which numerical methods do you recommend for the solution of the model ... 

An important nonsteady state heat transfer problem is to determine the temperature (T) of a small body initially at a temperature (Tq), a time (/) after it is plunged into a liquid whose temperature is (Fig. 11.9). In solving this problem, it is assumed that the body is small enough so that its temperature is always uniformly equal to T). This is equivalent to assuming that the conductivity of the solid body is infinite, or that the controlling heat transfer process is convective and not conductive. It is further assumed that the volume of fluid and degree of agitation are sufficient for Tfio remain constant. 

Another nonsteady state conductive heat transfer problem involves a semi-infinite body (Fig. 11.10) where not enough time has elapsed for thermal equilibrium to be established. A typical problem of this sort is where the top surface of the semi-infinite body is heated to a constant temperature (7 ), and the problem is to find the temperature at an interior point (A) a distance (y) beneath the surface (Fig. 11.10), after a certain elapsed time (t). Before the temperature of the surface is brought to temperature (Tg) at (0 equals 0, the body is at uniform temperature (T ). This is similar to the problem of heating one end of a long rod whose sides are perfectly insulated so that heat can flow only along the axis of the rod. 

The following problem is a very important example of nonsteady state heat transfer having a boundary condition of the second kind. Figure 11.12 shows a perfect insulator sliding across a stationary surface having thermal properties A =thermal conductivity andpc = volume specific heat. Thermal energy (q) per unit area per unit time is being dissipated at the surface. The problem is to estimate the mean surface temperature (0), Since this is a problem with a boundary condition of the second kind (constant q), the surface temperature will be a fimction of p= kpcf only. 

In terms of temperature, T, the equation governing nonsteady-state heat transfer in one dimension may be written... 

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