Transient heat conduction or mass transfer

Transient heat conduction or mass transfer in solids with constant physical properties (diffusion coefficient, thermal diffusivity, thermal conductivity, etc.) is usually represented by a parabolic partial differential equation. For steady state heat or mass transfer in solids, potential distribution in electrochemical cells is usually represented by elliptic partial differential equations. In this chapter, we describe how one can arrive at the analytical solutions for linear parabolic partial differential equations and elliptic partial differential equations in semi-infinite domains using the Laplace transform technique, a similarity solution technique and Maple. In addition, we describe how numerical similarity solutions can be obtained for nonlinear partial differential equations in semi-infinite domains. 

Of a more complete approach are the zone models [3], which consider two (or more) distinct horizontal layers filling the compartment, each of which is assumed to be spatially uniform in temperature, pressure, and species concentrations, as determined by simplified transient conservation equations for mass, species, and energy. The hot gases tend to form an upper layer and the ambient air stays in the lower layers. A fire in the enclosure is treated as a pump of mass and energy from the lower layer to the upper layer. As energy and mass are pumped into the upper layer, its volume increases, causing the interface between the layers to move toward the floor. Mass transfer between the compartments can also occur by means of vents such as doorways and windows. Heat transfer in the model occurs due to conduction to the various surfaces in the room. In addition, heat transfer can be included by radiative exchange between the upper and lower layers, and between the layers and the surfaces of the room. 

You saw how the equations governing energy transfer, mass transfer, and fluid flow were similar, and examples were given for one-drmensional problems. Examples included heat conduction, both steady and transient, reaction and diffusion in a catalyst pellet, flow in pipes and between flat plates of Newtonian or non-Newtonian fluids. The last two examples illustrated an adsorption column, in one case with a linear isotherm and slow mass transfer and in the other case with a nonlinear isotherm and fast mass transfer. Specific techniques you demonstrated included parametric solutions when the solution was desired for several values of one parameter, and the use of artificial diffusion to smooth time-dependent solutions which had steep fronts and large gradients. 

ABSTRACT. Most important elementary processes governing the behaviour of the converter (chemical reactions, heat and mass transfer processes to the catalyst surface, hydrodynamic, heat conduction and heat loss) are first described. Next, published models are reviewed and main modeling problems are considered. Then, the structure of a fairly general model is proposed. The behaviour of the converter at steady state and in the transient state is reported and the sensitivity of the model to various parameters is discussed. It is concluded that the lack of accurate data (especially kinetic data) makes the predictions with available models only qualitative assessments. However, many design or operating improvements can be deduced from these models. 

Improvements to the model have been made by Lawson et al. [44-46]. The improvements use estimates of thermal conductivity, specific heat and thermo-optical properties (transmittance, reflectance and absorptance) obtained from the thermal data collected from the testing of a variety of fabrics typically used in fire fighters protective clothing. A detailed mathematic model is developed to study transient heat and moisture transfer through multilayered fabric assemblies with or without air gaps. First principles are used to derive the governing equations for transient heat and moisture transfer. The equations also account for the effect of moisture on thermodynamic and transport properties. Numerical simulations are used to study heat and mass transfer. A software tool (Protective Clothing Performanee... 

Slime masses or any biofilm may substantially reduce heat transfer and increase flow resistance. The thermal conductivity of a biofilm and water are identical (Table 6.1). For a 0.004-in. (lOO-pm)-thick biofilm, the thermal conductivity is only about one-fourth as great as for calcium carbonate and only about half that of analcite. In critical cooling applications such as continuous caster molds and blast furnace tuyeres, decreased thermal conductivity may lead to large transient thermal stresses. Such stresses can produce corrosion-fatigue cracking. Increased scaling and disastrous process failures may also occur if heat transfer is materially reduced. 

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