Downloaded from https://www.everyspec.com 4" STRUCTURES p tures respectively. In practice, a linearized to higher thermal stresses than those basd approximation can usually be taken and tie on a consideration of all three modes. In a analytical expression for the convective cool- solid structure the oniy mode f heat transfer ing of a surface can be written as is conduction; in hollow structure, however, conv ion and radiation can significantly Tmoify the temperature distribution calcu- where lated on the basis of conduction alone.
q = rate of cooling, Btu/hr It might be mentioned that a relativly h = heat transfer coefficiet, complete analysis of simultaneous effects of Btu/(br)(ft )(F) conduction, convection, and radiation is pos- Strictly speaking, the convective cooling of a sible through the use of computers. surface is a combination of heat transfer The basic law of heat conduction has ts br th by coivectic n and conduction within the origin in the fundamental work of the F.ench fluid. The 'eader will note that- the above mathematician Jean Fourier. Fourier's Law equation is similar to Fourier's basic heat states that the instant-neous rate of heat conduction Equation (?-5).
The reason for flow in a one-dimen:lienuO booy is given by its appearance here lies n a concept which the prduct of the area perpendicular to the essentially converts the convective cooling flow, the rate of change of temperature in problem to a conduction problem. This con- the direction of f!c'- .nd the thermal cept considers that there is a film adjacent to conductivity. the surface throtigh which there is a linear dQ aT ( temperature drop from TW to T,. The effec- t q - kA (25) tive film thickness is difficult to measure and In t above expresio, is incorporated in the heat transfer coefficient Q =.
uqntity of heat, Btu h which also is a function of the physical t =time, hr and dys'amical properties of the media q =rate of heat flow, Btu/hr invoived. k =therm co.iductivily, the a.nount of heat 4 2-3.3. Conduction. Of greatest interest to per unit time flowing through a unit the missile structural designer is the tkans- area under a unit temperature gradient, mission ;f heat by conduction. This process Btu-in.ift 2 hr F is generally interpreted as a simple molea- A =area normal to heat flow, ft 2 lar interchange of kinetic energy from one T temperature, F molecule to an adjacent molecule by virtue of x =space zoordinate in 'tow direction, ft elac-tic impacts.
The heat flow is observed to The units uised are British Gravitational pass frurn the molecules at high temperature units, and the minus sign is arbitrarily to those at a relatively low:er temperature. chosen to make Q a positive- quantity. In the it has been custo ary ;n Lh azialysis of formi 2itown, the temperature T is.assumed the temperature distribution in a structure to to bc a function of space and time (transient consider convective and radiant heat transfer conduction), although it may be a function of as the mneans by which the external air flow space alone isteady conduction).
Taking the heats the structure, and to disregard these case of steady conduction in one dimension modes of beat transfer when the flow of heat and one for which A is not a function of x, in the interior of the structure is sought. Fourier's Equation is Two reasons can be mentioned in defense of A this iimplified approach; first, the equations q k -, ("r, T of conduction have been solved rigorously for (2 6) many more cases than those governing the where o'her t wo modes of heat transfer; and sec- L = total path length (x 2 - xi) ond, the resuits obtained from an analysis T7 = temperature at x 2 based on conduction alone always correspond T, = temperature at x, / 14