Nonsteady State Conduction

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. 

The quantity (Mi) is called the Nusselt Number (N), while (m ) is called the Fourier Number (Fq). It is found experimentally that the temperature of the soUd body may be considered constant throughout with time as long as. iV 0.1. It may be shown by more complete analysis that  

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 important variables in this problem with their dimensions in terms of (7, Z, Z, 6) are listed in Table 11.6. 

The thermal quantity k/pc) that appears in this problem is called thermal diffusivity, and is frequently assigned the symbol (a). The dimensions of thermal diffusivity are  

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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. 

The resulting solution is a function of two dimensionless parameters, AT kpcy laH(ty, and xliat). In reality, the nonsteady-state temperature distribution in a cellulosic fuel is not accurately represented by the above solution, since the boundary conditions are not perfectly matched with those of the experiment, and the partial differential does not include the effects of heats of reaction and of phase change. However, Martin and Ramstad, " in their study of ignition, have demonstrated that the actual temperature profiles can be expressed as functions of the same dimensionless parameters derived from the solution of the heat-conduction equation,... 

Electrical measurements of ice are diflBcult to interpret because of polarization effects, surface conductivity, injection of defects and/or impurity atoms from sandwich electrodes, diffusion effects, differential ion incorporation, and concentration gradients due to nonsteady state impurity distribution. Theories formulated for pure ice and for ice doped with HF (KF and CsF) in terms of ion states and valence defects, qualitatively account for experimental data, although the problem of the majority and minority carriers in doped ice, as a function of concentration and temperature, requires further examination. The measurements on ice prepared from ionic solutes other than HF, KF, and CsF are largely unexplained. An alternative approach that treats ice as a protonic semiconductor accounts for results obtained for both the before-named impurities as well as ammonia and ammonium fluoride. 

Details are given of a non-steady-state operation for controlling latex particle size distribution by using a continuous emulsion polymerisation of vinyl acetate. The experiment was conducted in a continuously stirred tank reactor under conditions below the critical micelle concentration of the emulsifier. The mean residence time was switched alternately between two values in the nonsteady-state operation to induce oscillations in monomer conversion in time. The effect of the switching operation on particle size distribution is discussed. 13 refs. 

Thermal conductivity, thermal diffusivity, and specific heat have been measured during nonsteady-state sample heating using the installation and methods described in Ref. 1. Test samples were... 

The potential drop across the electrolyte solution is determined by the product of current intensity and ionic resistance. In a microelectrode, the ionic resistance is independent of the distance to the other electrode, which allows working in solutions with low ionic conductivity. In addition, the ionic resistance is proportional to the inverse of the radius of the electrode. Since the intensity is proportional to the radius for steady-state conditions, the iR drop is not dependent on the size of the microelectrode. However, at nonsteady-state conditions, that is, e.g., in ultrafast cyclic voltammetry, the intensity is proportional to the area, and thus the iR drop is proportional to the radius of the microelectrode. In other words, the iR drop decreases as the size of the microelectrode decreases under nonsteady-state conditions. 

The first mechanistic KDIE correlation of the thermal decomposition process with explosive sensitivity was accomplished with the thermally initiated nonsteady—state thermal explosion event. The HMX thermal explosion event has been discussed and represents an intermediate temperature/pressure regime between the less drastic combustion event and the high order steady—state detonation event. Mechanistic KDIE detonation investigations recently have been conducted and provide the first correlation between the thermochemical decomposition process and shock—induced detonation using an exploding foil driven flyer plate test. i ... 

Semiempirical Model for Fuel Cell Performance in the Presence of Toluene In the presence of toluene in the air stream, the fuel cell performance degraded. Figure 3.15 illustrates two sets of representative results of toluene contamination tests, conducted with various levels of toluene concentration at current densities of 0.75 and 1.0 A cm , respectively. The cell voltage experienced a transient period (nonsteady state) immediately after the introduction of toluene, then reached a plateau (steady state). The duration of the transient period and the magnitude of the cell voltage drop to the plateau were strongly dependent on toluene concentration and current density. 

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 ... 

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. 

Thermal Diffusivity. Much of the literature in the past dealing with the thermal properties and characteristics of polymers, thermal diffusivity was either neglected or treated as an easily derivable quantity or mathematical parameter. However, thermal diffusivity is an important material property, determining temperature distributions in nonsteady-state heat conduction. Like thermal... 

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