Transient heat conduction defined

In the emulsion phase/packet model, it is perceived that the resistance to heat transfer lies in a relatively thick emulsion layer adjacent to the heating surface. This approach employs an analogy between a fluidized bed and a liquid medium, which considers the emulsion phase/packets to be the continuous phase. Differences in the various emulsion phase models primarily depend on the way the packet is defined. The presence of the maxima in the h-U curve is attributed to the simultaneous effect of an increase in the frequency of packet replacement and an increase in the fraction of time for which the heat transfer surface is covered by bubbles/voids. This unsteady-state model reaches its limit when the particle thermal time constant is smaller than the particle contact time determined by the replacement rate for small particles. In this case, the heat transfer process can be approximated by a steady-state process. Mickley and Fairbanks (1955) treated the packet as a continuum phase and first recognized the significant role of particle heat transfer since the volumetric heat capacity of the particle is 1,000-fold that of the gas at atmospheric conditions. The transient heat conduction equations are solved for a packet of emulsion swept up to the wall by bubble-induced circulation. The model of Mickley and Fairbanks (1955) is introduced in the following discussion. 

Another material property that appears in the transient heat conduction analysis is the thermal diffusivity, which represents how fast heat diffuses through a material and is defined as... 

Therefore, the proper form of the dimensionless time is t atlL, which is called the Fonrier number Fo, and we recognize Bi = kJliL as the Biot number defined in Section 4—1. Then the formulation of the one-diniensional transient heat conduction problem in a plane wall can be expressed in nondimensional form as... 

As a final example, consider line D of Table 9.1. We represent this problem as a body of density p, and heat capacity cp and whose surface is in contact with another medium of temperature Ts. Assume the initial body temperature is the same as the temperature of the other medium at I m = Ts. From the fundamental equation we can write, pcpLdTb/dt = X(TS — Tb)/L, where L is the characteristic conductive length, and X is the thermal conductivity. We now scale this problem over the entire time of the thermal transient. Once the entire time of the transient passes fe - t ), the body will have reached the new temperature of 7, 2. For the overall transient, the temperature rate of change is (Tb2 - Tb )/Gi -t ). and the average driving potential for the thermal conduction will be TS2 - T, )/2 = ( 7),2 - Tj, )/2. We now define the first-order relationship between the parameter as... 

The thermal conductivity of a material is defined in terms of the transport of heat under steady-state conditions. On the other hand, one is often interested in the transport of heat when a specimen is not at equilibrium so that the flow of heat is transient. The thermal diffusivity a , which is defined by Equation 14.2, describes these time-dependent, non-steady-state aspects of heat flow. The thermal diffusivity is used to calculate the temperature (T) as a function of the position within the specimen (z) and the time (t) under non-steady-state conditions. It is related by Equation 14.3 to the thermal conductivity, the density, and the specific heat capacity. The values of X and a can be measured independently. However, often one of them (usually a) is estimated from the measured value of the other one (usually X) by using Equation 14.3. If X is in J/(K m sec), cp is in J/(g K) and p is in g/cc, then the a value calculated by using Equation 14.3 must be multiplied by 100 to convert it into our preferred diffusion units of cm2/sec. 

The analytical solutions for transient conduction in plates, cylinders, and spheres have been obtained by Heisler [9] and the solutions represented graphically for more convenient use. These solutions are for the case of a solid of initially uniform temperature Tg exposed at time zero to a surrounding fluid medium at a constant temperature T. The surface of the solid is cooled or heated by the fluid with a constant convective heat-transfer coefficient h. The sohd is assumed to have a constant thermal conductivity and a constant thermal diffusivity a, defined as... 

The computer display then shows the steady-state values for characteristics such as the thermal conductivity k [W/(mK)], thermal resistance R [m K/W] and thickness of the sample s [mm], but also the transient (non-stationary) parameters like thermal diffusivity and so called thermal absorptivity b [Ws1/2/(jti2K)], Thus it characterizes the warm-cool feeling of textile fabrics during the first short contact of human skin with a fabric. It is defined by the equation b = (Xpc)l, however, this parameter is depicted under some simplifying conditions of the level of heat flow q [ W/m2] which passes between the human skin of infinite thermal capacity and temperature T The textile fabric contact is idealized to a semi-infinite body of the finite thermal capacity and initial temperature, T, using the equation, = b (Tj - To)/(n, ... 

For a flat slab specimen of thickness h (m), the thermal conductivity X (W m K ) is the heat flux per unit of temperature gradient in the direction perpendicular to an isothermal surface and is a material constant defined by the one-dimensional Fourier equation X = Qh/A(Ti — Tq) where Q is the time rate of the heat flow (W), A the area (m ) on a selected isothermal surface, and T and T2 the temperatures of the hot and cold surfaces, respectively, and h the sample thickness (m). Several steady-state or transient methods are available to measure the thermal conductivity of organic and inorganic materials." The guarded-hotplate (ASTM F433), heat-flow (ASTM C518), and Colora ther-moconductometer methods are accurate for thick plastic samples with thermal conductivity of 0.1—10 W m K . In electronics, steady-state techniques... 

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