where Q is the heat transferred per unit across a surface A, dT/dL the temperature gradient with respect to thickness L at the surface A, and k the thermal conductivity expressed as the amount of heat transferred per unit time through a unit area of surface for 1° temperature difference over a unit wall thickness. The negative sign indicates that temperature decreases as thickness increases.
The steady-state heat transfer through the chamber wall of a liqud-cooled rocket chamber can be treated as a series type, steady-state heat transfer problem with a large temperature gradient across the gaseous film on the inside of the chamber wall, a temperature drop across the wall, and, in cases of cooled chambers, a third temperature drop across the film of the moving cooling fluid. It is a combination of convection at the boundaries of the flowing fluids and conduction through the chamber walls. The problem is basically one of heat and mass transport associated with conduction through a wall. It is shown schematically in Fig. 8-20.
The general steady-state heat transfer equations for regeneratively cooled thrust chambers can be expressed as follows:
where q is heat transferred per unit area per unit time, Tg the absolute chamber gas temperature, 7} the absolute coolant liquid temperature, Tw/ the absolute wall temperature on the liquid side of the wall, Twg the absolute wall temperature on the gas side of the wall, h the overall film coefficient, hg the gas film coefficient, hi the coolant liquid film coefficient, tn. the thickness of the chamber wall, and k the conductivity of the wall material. The strength and thermal properties of materials are functions of temperature. Any consistent set of units
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