Thermal Energy Conservation

Neglecting the effect of convection in the ceU, the thermal energy equation can be expressed as  

The heat capacity, pCp, and the effective thermal conductivity, X, can be calculated from the constituent component values, as  

The effect of tortuosity on the effective thermal conductivity is often neglected because of the sufficiently high thermal conductivity of the active particles. 

The first term on the RHS of Equation 25.28 represents the heat generation effect due to electrode reactions the second and third terms correspond to the joule heating in the solid active material and electrolyte phases, respectively. The subscript n refers to the anode and cathode electrodes. 

Thermal and electrochemical coupling emanates from temperature-dependent physicochemical properties. Temperature dependence of physicochemical properties, r, can be described by the Arrhenius expression [33, 51]  

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Combining the thermal energy conservation with Eq. (2.107) yields... 

The mathematical formulation of such a problem begins with the statement of the appropriate equations of change. In Rayleigh s problem, these were the equations of motion, the equation of continuity, and the equation of thermal-energy conservation, together with an appropriate equation of state. In their most general form, these equations are... 

The final state variables are saturation j , temperature T, and vapour fraction f Inertial terms and gravitation are neglected and the total pressure is assumed to be constant. The model consists of the conservation of the mass of the water species, and the thermal energy conservation, i.e.. 

Numerical studies have been carried out in three-dimensional (x, y, z) geometry. The system of equations of the mathematical model includes the continuity equation, a generalization of Darcy law for the case of variable density flow, equation of thermal energy conservation, and closing relationships for the calculation of the pore solution density and viscosity. 

An abuse model requires (i) materials (mass) balance for the exothermic side reactions, (ii) estimation of the reaction parameters (e.g., heat of reaction) from experimental measurements such as differential scanning calorimetry (DSC) and accelerated rate calorimetry (ARC), (iii) devising the kinetic expressions of the reactions, and (iv) incorporation of the thermal behavior due to these reactions in the energy balance equation (e.g., in terms of volumetric source terms). Specifically, the thermal energy conservation equation is duly modified to include the additional heat generation effects to reflect the specific abuse behavior in terms of heat generation due to side reaction kinetics and/or joule heating. The thermal boundary condition may also include radiative heat transfer to the ambient air. 

This equation is the expression of the conservation of thermal energy (first law of themiodynamics) and is written as... 

Insulation provides other functions in addition to energy conservation. A key role for insulation is safety. It protects personnel from bums and minimizes hot surfaces that could ignite inflammables. It also protects equipment, piping, and contents in event of fire. Thus materials such as mineral wool are sometimes used despite relatively poor thermal quaUties. 

A thermal pulse cycle is a means of conserving thermal energy in... 

With these relays, there is no need to use HRC fuses or thermal OCRs. The power circuit is thus devoid of any heat generation in these components and provides energy conservation. 

The objectives are not realized when physical modeling are applied to complex processes. However, consideration of the appropriate differential equations at steady state for the conservation of mass, momentum, and thermal energy has resulted in various dimensionless groups. These groups must be equal for both the model and the prototype for complete similarity to exist on scale-up. 

Thermal plumes above point (Fig. 7.60) and line (Fig. 7.61) sources have been studied for many years. Among the earliest publications are those from Zeldovich and Schmidt. Analytical equations to calculate velocities, temperatures, and airflow rates in thermal plumes over point and line heat sources with given heat loads were derived based on the momentum and energy conservation equations, assuming Gaussian velocity and excessive temperature distribution in... 

Traditional air curtains, which utilize only indoor air heated in the curtain heaters, are not always economical (due to considerable thermal energy consumption). Reduction of heat consumption is achieved by curtains that utilize unheated indoor or outdoor air, and also combined air curtains, which heat, 3only part of the supplied air. Air curtains that use unheated air conserve. 30-70% of thermal energy. 

The quasi-one-dimensional model of flow in a heated micro-channel makes it possible to describe the fundamental features of two-phase capillary flow due to the heating and evaporation of the liquid. The approach developed allows one to estimate the effects of capillary, inertia, frictional and gravity forces on the shape of the interface surface, as well as the on velocity and temperature distributions. The results of the numerical solution of the system of one-dimensional mass, momentum, and energy conservation equations, and a detailed analysis of the hydrodynamic and thermal characteristic of the flow in heated capillary with evaporative interface surface have been carried out. 

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