Heat transfer thin bodies

Our bodies are always surrounded by a thin layer or film of stagnant air. This film is like a layer of insulation. It retards heat transfer between our skin and any surrounding fluid. Movement of the fluid causes turbulence. The turbulence disturbs the film and reduces the film s resistance to heat transfer. 

When the heat transfer resistance is concentrated at the surface of a body of area A, the thermally thin body approximation can be applied, and the temperature throughout the solid, T, is assumed to be independent of position. In this case, the heat balance becomes... 

To determine whether the thin body approximation may be used, one should compare the surface heat transfer coefficient, and the thermal conductance of the solid, ksom/8. Their ratio is the Biot number,... 

This temperature drop creates temperature differences within the water at the top as well as between the water and the surrounding air. These temperature differences drive heat transfer toward the water surface from both the air and the deeper paits of the water, as shown in Figure 14-52, If the evaporation rate is high and thus the demand for the heat of vaporization is liigher than the amount of heat that can be supplied from the lower parts of the water body and the surroundings, the deficit is made up from the sensible heat of the water at the surface, and thus the temperature of water at the surface drops further. The process continues until the latent heat of vaporization equals the heat tran.sfer to the water at the surface. Once the steady operation conditions are reached and the interface temperature stabilizes, the energy balance on a thin layer of liquid at the surface can be expressed as... 

Boundary Layer Concept. The transfer of heat between a solid body and a liquid or gas flow is a problem whose consideration involves the science of fluid motion. On the physical motion of the fluid there is superimposed a flow of heat, and the two fields interact. In order to determine the temperature distribution and then the heat transfer coefficient (Eq. 1.14) it is necessary to combine the equations of motion with the energy conservation equation. However, a complete solution for the flow of a viscous fluid about a body poses considerable mathematical difficulty for all but the most simple flow geometries. A great practical breakthrough was made when Prandtl discovered that for most applications the influence of viscosity is confined to an extremely thin region very close to the body and that the remainder of the flow field could to a good approximation be treated as inviscid, i.e., could be calculated by the method of potential flow theory. 

Fully Laminar Nusselt Number Nu,. As the next step in the correlation method, the thin-layer solution is corrected to account for thick-layej" effects [175,223]. The body is surrounded by a uniform layer of stationary fluid of thickness A, and outside that thickness the fluid temperature is taken to be T . The heat transfer that would occur across this layer is determined by a conduction analysis and converted to a Nusselt number, and this Nusselt number is Nu,. 

Laminar Free Convection. When a stagnant vapor condenses on a vertical plate, the motion of the condensate will be governed by body forces, and it will be laminar over the upper part of the plate where the condensate film is very thin. In this region, the heat transfer coefficient can be readily derived following the classical approximate method of Nusselt [12], Consider the situation depicted in Fig. 14.4 where the vapor is at a saturation temperature Ts and the plate surface temperature is T . Neglecting momentum effects in the condensate film, a force balance in the z-direction on a differential element in the film yields... 

Heat transfer in the material is not considered. The temperature is then treated as uniform over the entire body. Obviously, this assumption requires that the test specimen should be thin in order to neglect the heat transfer effect. 

Instabilities in beds of porous catalysts, for strongly exothermic processes, occur when heat transfer rates from the bed are not adequate, so the temperature rises, increasing reaction rates, and thus producing heat energy. This instability produces hot spots inside the bed and melts or inactivates the catalyst. Besides other solutions, our microcapillary catalytic reactor elements, using very thin porous layers of a catalyst (6-10 pm), attached to the heat-transferring body (glassy carbon), ensure stable exothermal processes, as the ammonia synthesis, or CO oxidation to CO2. 

By the effect of centrifugal forces the solution is spread as a thin film (mean ca. 0.1 mm) over a conical frustum, rotating with 1600 revolutions/min. Short residence time of ca. 1-2 seconds, relatively low wall temperature on the product side, treatment of higher viscosity, temperature-sensitive products, high heat transfer coefficient of 500-1000 W/ (m k) depending on evaporator body revolutions, product and operating conditions [7.21]. 

The iirteraction of a fluid flow with the surface of a solid body is a subject of great interest. Matty technical measurements are aimed to determine the shear forces, pressure forces, or heating loads apphed by the flow to the body. A possible means of estimating the rates of momentum, mass, and heat transfer is to visualize the flow pattern very close to the body surface. For this purpose, the body surface can be coated with a thin layer of a substance that, upon the interaction with the fluid flow, develops a certain visible pattern. This pattern can be interpreted qualitatively, and in some cases, it is possible to measure certain properties of the flow close to the surface. Three different interaction processes can be used for generating different kinds of information. 

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