Heat Transfer Handbook part 22. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | EXTENDED SURFACES 201 Radiative-Convective Cooling of Solids with Uniform Energy Generation The solutions obtained in Section for a plane wall the thermal symmetry case a solid cylinder and a solid sphere are now extended to accommodate surface cooling by simultaneous convection and radiation. The surface energy balance for each geometry gives 7 i T T A I i T 4 T 4 i 7 C h Ts Tœ ea Ts Tœ le 0 plane wall h Ts Tm ea Ts4 Tæ k 0 solid cylinder and sphere r ro where e is the surface emissivity a the Stefan-Boltzmann constant and . represents the surrounding or ambient temperature for both convection and radiation. In eqs. and the last terms can be evaluated using eqs. and respectively. Because eqs. and require a numerical approach for their solutions it is convenient to recast them in dimensionless form as N1 Qs 1 N2 04 1 0 plane wall dX X 1 . . d. 0 N1 0s 1 N2 04 1 ------- 0 cylinder and sphere dR r 1 where 0 Ts T N1 hL k for the plane wall N hr0 k for the cylinder and sphere N2 eaT3L k for the plane wall and N2 eoT r0 k for the cylinder and sphere X x L R r r0 and 0 T T . The numerical values for 0s are given in Table for a range of values of N1 and N2 and qlx kT 1 for the plane wall and r kT 1 for the cylinder and sphere. EXTENDED SURFACES The term extended surface is used to describe a system in which the area of a suffcce is increased by the attachment offins. A fin accommodates energy transfer by conduction within its boundaries while its exposed surfaces transfer energy to the surroundings by convection or radiation or both. Fins are commonly used to augment heat transfer from electronic components automobile radiators engine and compressor cylinders control devices and a host ofother applications. A comprehensive treatment of exeended surfaee technology is provided by Kaaus ea al. 200 . In this section we provide the performance characteristics temperature distribution rate of
