Unsteady Heat Transfer

Consider the following heat transfer problem corresponding to heat transfer in a slab, 

The temperature depends on both time, f, and position, x. The coefficient of thermal diffusion is 

The slab is insulated at the left (x = 0) and has a temperature value of zero on the other side (x = L) 

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Elastoviscous behaviour 104 Elbows, friction losses in 91 Electrical analogue for unsteady heat transfer 397... 

To study the effects due to droplet heating, one must determine the temperature distribution T(r, t) within the droplet. In the absence of any internal motion, the unsteady heat transfer process within the droplet is simply described by the heat conduction equation and its boundary conditions... 

Temperature variations during the formation of LDPE foam sheet were investigated. A thermal model was coupled with a viscoelastic growth model, and an iterative finite difference technique was used to solve unsteady heat transfer equations and viscoelastic growth equations. The heat transfer characteristic time became comparable to the expansion time when the sheet thickness decreased to the millimetre range, during which foam thickness and density became sensitive to temperature effects. 12 refs. USA... 

In what follows, the preceding evaluation procedure is employed in a somewhat different mode, the main objective now being to obtain expressions for the heat or mass transfer coefficient in complex situations on the basis of information available for some simpler asymptotic cases. The order-of-magnitude procedure replaces the convective diffusion equation by an algebraic equation whose coefficients are determined from exact solutions available in simpler limiting cases [13,14]. Various cases involving free convection, forced convection, mixed convection, diffusion with reaction, convective diffusion with reaction, turbulent mass transfer with chemical reaction, and unsteady heat transfer are examined to demonstrate the usefulness of this simple approach. There are, of course, cases, such as the one treated earlier, in which the constants cannot be obtained because exact solutions are not available even for simpler limiting cases. In such cases, the procedure is still useful to correlate experimental data if the constants are determined on the basis of those data. 

L. Unsteady Heat Transfer to a Liquid in Steady Laminar Flow along a Plate... 

Furnas (1930a, b, c, 1932) Unsteady heat transfer H, C Air, flue gas Iron ore, limestone, coke, etc. Granules 4-70 -... 

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. To take into account the unsteady heat transfer behavior and particle convection in fluidized beds, a surface renewal model can be used. The model accounts for the film resistance adjacent to the heat transfer... 

Heat transfer in many systems occurs as a steady-state process, and the temperature at any point in the system does not vary with time. In other important processes, temperatures in the system do vary with time. This situation, which is common among the small-scale, batch-operated processes of the pharmaceutical and fine chemical industry, is known as unsteady heat transfer and, as warming or cooling occurs, the thermal capacity (i.e., the size and specific heat), of the system becomes important. Analysis of unsteady heat transfer is complex. 

The time-averaged heat-transfer coefficientbetween the vertical wall and fluidized beds, using fine particles, is controlled by the unsteady heat transfer due to packet renewal at the heat-transfer surface (M14, M16, Y18). According to this mechanism, is expressed as ... 

Feng, Zhi-Gang and Michaelides, E. E., Unsteady heat transfer from a sphere at small Peclet numbers, Trans. ASME, J. Fluids Eng., Vol. 118, No. 1, pp. 96-102,... 

In unsteady-state diffusion processes, the concentration distribution (or concentration gradient) changes with time and position. Fiek s seeond law for unsteady-state diffusion is analogous to the Fourier equation for unsteady heat transfer... 

Fourier number n (Np). A dimensionless group important in analysis of unsteady heat transfer in solids, such as sheets being heated or cooled in thermoforming, or cooling of extrudates and moldings, ATp = a f/x , where a is the material s thermal diffiisivity, t the heating or cooling time, and x is the a thickness or half-thickness in the direction of heat flow. 

Kunsch, J. P., and T. K. Fannel0p. 1995. Unsteady Heat-Transfer Effects on the Spreading and Dilution of Dense Cold Clouds, Journal of Hazardous Materials, vol. 43, pp. 169-193. 

Another thermal parameter that emerges from unsteady heat transfer analyses is the thermal diflfusivity a = Kipc, which, according to equations 26-28, should be relatively independent of temperature... 

Typical values of thermal conductivities and thermal diffusivities in gases, liquids, and solids are given in Table 20.4-2. Some of the values are expected from experience for example, the thermal conductivities of metals are much higher than those of liquids or gases. Less obviously, the thermal diffusivities of nonmetallic solids and liquids are more nearly the same, indicating that unsteady heat transfer proceeds at more similar rates in these materials. 

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