The Basic Soltion he demerara es Problems OTOT a-on cos(n, x) dx OTOT av Ar cos(n, y) OTOT cos(n, 2) az an Define no to be the unit vector in normal direction of the isothermal surface, pointing to the temperature increasing direction △TT (1) 4.Thermal flux speed: The quantity of heat flowing through the area S on the isothermal surface in unit time, denoted by dg d 11
11 Define n0 to be the unit vector in normal direction of the isothermal surface, pointing to the temperature increasing direction. n T n △T = 0 （1） 4.Thermal flux speed: The quantity of heat flowing through the area S on the isothermal surface in unit time, denoted by . dt dQ cos( ) cos( ) cos( ) n z n T z T n y n T y T n x n T x T ， ， ， = = =
温动向边签解法 OTOT cos(n, x) ax an OTOT av Ar cos(n, y) OTOT cos(n, 2) dn 取n为等温面法线方向且指向增温方向的单位矢量,则有 一T △T=no (1 4热流速度:在单位时间内通过等温面面积S的热量。用表示。 12
12 0 取 n 为等温面法线方向且指向增温方向的单位矢量，则有 n T n △T = 0 （1） 4.热流速度：在单位时间内通过等温面面积S 的热量。用 dt 表示。 dQ cos( ) cos( ) cos( ) n z n T z T n y n T y T n x n T x T ， ， ， = = =
Thermal flux density: The thermal flux speed flowing through unit area q= no do yq. Then we have on the isothermal surface, denoted by /S dt (2) Its value is / 5. The basic theorem of heat transfer: The thermal flux density is in direct proportion to the temperature gradient and in the reverse direction of it. i. e n is called the coefficient of the heat transfer. Equations (1),( 2)and(3) ead to do ot S dt a 13
13 Its value is: S dt dQ q = / S dt dQ q n / = − 0 (2) Thermal flux density: The thermal flux speed flowing through unit area on the isothermal surface, denoted by q . Then we have 5.The basic theorem of heat transfer: The thermal flux density is in direct proportion to the temperature gradient and in the reverse direction of it. i.e. q = − (3) S n T dt dQ = / is called the coefficient of the heat transfer. Equations (1), (2) and (3) lead to
温动向边签解法 热流密度:通过等温面单位面积的热流速度。用q表示, 则有 →dO AS (2) 其大小为 /S 5.热传导基本定理:热流密度与温度梯度成正比而方向相反。 即 q=一AT (3) 称为导热系数。由(1)、(2)、(3)式得 do oT 兄 7-S dt on 14
14 热流密度：通过等温面单位面积的热流速度。用 表示， 则有 q S dt dQ q = / 其大小为 S dt dQ q n / = − 0 (2) S n T dt dQ = / 称为导热系数。由（1）、（2）、（3）式得 5.热传导基本定理：热流密度与温度梯度成正比而方向相反。 即 q = − △T (3)
The Basic oltion of he tanerauire Stress rol We can see that the coefficient of the heat transfer means the thermal flux speed through unit area of the isothermal surface per unit temperature gradient From equations(1)and 3), we can see that the value of the thermal flux density The projections of the thermal flux density on axes 一况 4y=一兄 4==—兄 7 It is obvious that the component of thermal flux density in any direction is equal to the coefficient of heat transfer multiplied by the descending rate of the temperature in this direction
15 We can see that the coefficient of the heat transfer means “the thermal flux speed through unit area of the isothermal surface per unit temperature gradient”. n T q = From equations (1) and (3), we can see that the value of the thermal flux density The projections of the thermal flux density on axes: x T qx = − y T qy = − z T qz = − It is obvious that the component of thermal flux density in any direction is equal to the coefficient of heat transfer multiplied by the descending rate of the temperature in this direction