Heat Transfer Handbook part 20. 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. | STEADY ONE-DIMENSIONAL CONDUCTION 181 Ts 1 k r r2 q Ts 2 Figure Radial conduction through a hollow cylinder. in the radial direction with no internal heat generation and constant thermal conductivity the appropriate form of the general heat conduction equation eq. is d dT _ 0 dr dr with the boundary conditions expressed as T r ri Ts 1 and T r r2 Ts Following the same procedure as that used for the plane wall will give the temperature distribution T Ts 1 ln r s i ln ri r2 ri and the heat flow 2nkL Tx i - Ts 2 q i x ln r2 ri Hollow Sphere The description pertaining to the hollow cylinder also applies to the hollow sphere of fig. except that the length L is no longer relevant. The applicable form of eq. is d dr dT r2 0 182 CONDUCTION HEAT TRANSFER Ts l Figure Radial conduction through a hollow sphere. with the boundary conditions expressed as T r ri Ts i and T r r2 Ts 2 The expressions for the temperature distribution and heat flow are T Ts 1 ------ - 1 1 r2 1 r1 r r 4nkCkt Ts 2 q 1 r 1 r2 Thermal Resistance Thermal resistance is defined as the ratio of the temperature difference to tha associated rate of heat tra eer. This is somptotely analoguus oo dcclicca fesiotnnfe which according to Ohm s law is defined as the ratio of the voltage c efi i e c cti tt the cuerent flow. With this definition the thermal resistance of the plane wall the hollow cylinder and the hollow sphere are respectively Rcond kA _ ln r2 r Rcond T 2nkL _ r r2 Rcond 4nk STEADY ONE-DIMENSIONAL CONDUCTION 183 When convection occurs at the boundaries of a solid it is convenient to define the convection resistance from Newton s law of cooling q hA Ts - Tm where h is the convection heat transfer coefficient and 7 is the convecting fluid temperature. It follows from eq. that Rconv TS - Tœ q hA Composite Systems The idea of thermal resistance is a useful tool for analyzing conduction through .
