Downloaded from https://www.everyspec.com PROPERTIES OF MATERIALS Cniefor example, a r~rd of unfo01rm assuming k, c. and w eomstant. Utder these crm-settional area A and length L~. F r a conditions, the most genefal heat conduction zontstt vlueof the heat flow q, the tern- equation reda-es to perature diffarence (Tz - TI) is inversely 13T Of e T q proportional to the Ithermal conductivity k. + . a +' 0 Thus -a material of high thermal conduCtIvity 29 will allowi s given heat flow at a lower tern- where(29 perature difference than a material of lower k_ thermal conductivity.
The missile designer a= - .-- rmal diffusivity ftl/hr inteestd ineonfrcing he eatinpu onthe For systems that do not contain heat sources snurface of a ntructur3 to the intrirwt a or sinks, q =0, and Equation (2-9) becomes minium tmpeatur els atthe urfae, he Foarier Equation. If sources and sinks areI will choose a mnatearial hazvin~g high thermal isa T conductivity (assuing all other maicerial present 4at Lkeg temperature iied,-t=0 properties are the samt-).a In the transient state of heat conduction, an Eqain(-)rdcstPiso' the quantity of heat entering and leaving a Equation. Finally, for steady conduction in volurne element at any instant is not equal.
systems free of sources and sinks, the well- The increase in internal energy, dE is known Laplace Equation is obtained. This linear partial-differential equation appears dE = c wVa dt (2?7) frequently in many branches of science. at Solutions are discussed in the literature. The thermal diffu-iivity is a derived, rate- where rial property important to the missile de- c thermal capacity of the rnaternal, th;_% signer as a measure of the ability of a )amount of heat energy the naterial iraterial to absorb or diffuse heat.
As defined can absorb per unit weight for a unit by Equation (2-9) thermal diffusivity is temperature rise Btu/ib./*F essentially the ratio of th.- thermal conduc- w = specific weight of the material, lbs,/ft2 tivity to the specific heat. Thue tirse required V = volume, 11,3 to bring a material to a specified temperature A missile designer interested in using the level varies inversely with the thermal dif- structaral material as a heat sink, would fusivity and directly with the square of the I choose~ a material of high thermal capacity, conducting path length. again assuming that other material proper- 2-3.4, Thermal Expansion. When an engi- tes were equal.
The equation of continuity neering material is heated, it expands in all fr the heat flow thrcugh a volume element directions in a manner that is dependent in three dimensions c~n be written upon the material and the temperature rise. O T 0 aTl a OT For the single dimension case the ratio of the ax (k ax)+ -a.(ka oz (I+ (I unit elongation per unit temperature rise is + e w + q (2 8) called the coefficient of thermnal expansion. where the effect of the heat input q, Btu/ft- d ( 0 hr, has been added. In the most general case, where rk, c, w and q are functions of x, y, z and T; acoefficient of thermal expansiop I F q may also be time dependent.
As written, ~ -elongation per unit length Equation (2-8) is valid for an inhomogene- Engineers find it more convenient to define a ous, but isotropic solid. Moreover, the equa- mean coefficient of thermal expansion as tion is non-linear if k, c, or w depend on T. follows: j by taking q as a function of T only, and a L Man caes f pactcalintres ar coere - ~dT(2 iI'l.