Heat flux density conduction/convection

For spherical symmetry, can vary only in the radial direction and not with any angle. The heat flux density at a sphere s surface for heat conduction across the air boundary layer followed by heat convection in the surrounding turbulent air then is... 

The moisture flux g (kg/(m, s)) in the bentonite has a liquid and a vapor component. The liquid flux g, is proportional to the gradient of the pore water pressure P with a hydraulic conductivity k(S) that is a function of the degree of water saturation S. The flux is inversely proportional to the viscosity rj(T). The water vapor flux g, is proportional to the gradient of the water vapor density in the gas phases in the pores with a vapor conductivity factor D,(5) that is a decreasing function of S. The heat flux q (W/m ) has a conductive part with a thermal conductivity. /i(S). There is also a negligible convective part. We have... 

K = thermal flux density from the interior of the body to its surface // = flux density of the sensible heat from the atmosphere to the surface as a result of molecular and convective heat conduction V = flux density of latent heat as a result of condensation and evaporation P = flux density of the heat carried to the surface by precipitation... 

Cooling fluid Approximate Range of Operation Min/Max °C Temp for Ref. Data, C Density, kg/m Heat Capacity, J/kgK Thermal Conductivity, W/m K Viscosity, mPa-s Prandtl Number Reynolds Number at Nusselt Number 25 mm Tube Forced Convection Heat Transfer Coefficient, W/m -K Cooling Channel Surface Temperature, C for 424 kW/m heat flux Approximate Copper Hot Face Temperature, C... 

In order to identify EPHs of the cell or electrode reactions from the experimental information, there had been two principal approaches of treatments. One was based on the heat balance under the steady state or quasi-stationary conditions [6,11, 31]. This treatment considered all heat effects including the characteristic Peltier heat and the heat dissipation due to polarization or irreversibility of electrode processes such as the so-call heats of transfer of ions and electron, the Joule heat, the heat conductivity and the convection. Another was to apply the irreversible thermodynamics and the Onsager s reciprocal relations [8, 32, 33], on which the heat flux due to temperature gradient, the component fluxes due to concentration gradient and the electric current density due to potential gradient and some active components transfer are simply assumed to be directly proportional to these driving forces. Of course, there also were other methods, for instance, the numerical simulation with a finite element program for the complex heat and mass flow at the heated electrode was also used [34]. 

The shell side heat transfer coefficient (ho) is calculated as the sum of the convective and nucleate boiling heat transfer coefficients he and hn respectively). Both hi (the inside tube coefficient) and he are given in terms of tube diameters, thermal conductivities, vapour and liquid densities and Reynolds and Prandtl numbers in the appropriate streams by standard correlations [25]. hn is given as a function of heat flux, pressure and solvent critical pressure by the Mostinski equation [26]. 

Similarity criteria are ratios of the various forces or fluxes controlling the rate of the process involved. These are the momentum, viscous, gravity, and surface-tension forces and the conduction and convection terms, determined by the geometry of the system and the physical properties of the fluids. Density, viscosity, surface tension, heat capacity, and thermal conductivity are the physical properties to be considered. 

The model discussed here uses the effective transport concept, this time to formulate the fiux of heat or mass in the radial direction. This flux is superposed on the transport by overall convection, which is of the plug flow type. Since the effective diffusivity is mainly determined by the flow characteristics, packed beds are not isotropic for effective diffusion, so that the radial component is different from the axial mentioned in Sec. 11.6.b. Experimental results concerning D are shown in Fig. 11.7.a-l [61, 62,63]. For practical purposes Pe may be considered to lie between 8 and 10. When the effective conductivity, X , is determined from heat transfer experiments in packed beds, it is observed that X decreases strongly in the vicinity of the wall. It is as if a supplementary resistance is experienced near the wall, which is probably due to variations in the packing density and flow velocity. Two alternatives are possible either use a mean X or consider X to be constant in the central core and introduce a new coefficient accounting for the heat transfer near the wall, a , defined by ... 

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