s with temperature, k is replaced by a median k, or km, such as
in which ko is k at T = T0 and koa is the slope of the k-T relationship.
Radial System Conduction. Bejan has shown that the conductivity relationships for curved surfaces are very analogous to those for plane walls, the differences lying wholly in the definition of A, to wit:
qcyl = 2pkl(T1 - T2) / [ln(ro/ri)] (5)
is the heat current for a cylinder of height, l, inside radius, ri, and outside radius, ro -- the thermal resistance being
In exactly analogous fashion, Bejan has derived the heat current through a spherical shell as
qshl = 4pk ri ro(T1 - T2) / (ro - ri) (7)
Rts = (1/ri - 1/ro) / (4pk) (8)
Heat Transfer by Fins. Fins are used as heat transfer devices to combine conduction into the fins (say through a wall of a motor into the base ends of a set of fins) and convection to carry excess heat away from the outside wall (say by air or cooling water passing by the motor and over the fins). They are efficient to the extent that they are made of highly conductive material (i.e., they have a high k) and can transfer heat well to the passing fluid (i.e., the wall-fluid combination has a high convective heat transfer coefficient, h).
Heat Generation Systems. Four authors who have treated internal heat generation present unique analytical descriptions of it, differing among themselves on the geometry and boundary conditions for the phenomenon. The least confusing explanation is given by
Thomas, who describes the case of a plate with volume = V = Ax, conducting heat and also having internally generated energy, with T1 > T2 :
qx = kA(T1 - T2) / L + 0V(x/L - () (9)
in which 0 is the internal energy per unit volume (e.g, W/m3) and L is the plate thickness, as in (2) above. From this, Thomas asserts: "It follows that . . ."
qo = kA(T1 - T2) / L - 0V/2 and qL= kA(T1 - T2) / L + 0V/2 (10)
and: "...