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Case Studies in Fluid Mechanics with Sensitivities to Governing Variables
M. Kemal Atesmen
M. Kemal Atesmen
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ASME Press
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In this chapter we will consider heating a room by natural (free) convection and by radiation using a vertical flat plate water heater which is set up perpendicular to the floor. The water heater is 2 m wide and 1 m high and it is thin. The water heater can also be set at desired uniform surface temperatures from 50 to 90°C. When the air next to the vertical water heater starts to increase in temperature, the heated air’s density and therefore its body force decrease, air starts to rise, and is replaced by the higher-density, colder air in the room. This natural convection phenomenon’s governing equation of motion is identical to the momentum equation for a boundary layer over a flat plate, except for a new body force term. Also, the energy equation for this natural convection phenomenon’s governing equation is exactly the same as the energy equation for a boundary layer over a flat plate term. The new body force term in non-dimensional form represents the ratio of buoyant to viscous forces acting on a fluid element in a natural convection boundary layer, namely the Grashof number, Gry.

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