Heat Transfer Handbook part 5. 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. | 30 BASIC CONCEPTS in the cylindrical coordinate system as o 2 . 2 dVr dr I 1 dV 2 - 2 l ri 7J dr r d e 1 dV 2 dr Ve r 1 dVr V 1 1 d Vz m 2 71e _ - 2 dz 2 aiVr dVz dz dr I 1 3 2 and in the spherical coordinate system as o 2 9Vr V 1dve Vr V 1 dve V it Im T l TSinĩ M 2 V cot Ộ r 1 2 2 V 1 dVr 1 r I r d Ộ 3 2 sin Ộ d r d Ộ Ve 1 dV6 r sin I r sin Ộ d e 1 2 1 dvr d Ve r sin Ộ de dr r 2 - 3 V- V 2 DIMENSIONAL ANALYSIS Bejan 1995 provides a discussion of the rules and promise of scale analysis. Dimensional analysis provides an accounting of the dimensions of the variables involved in a physical process. The relationship between the variables having a bearing on friction loss may be obtained by resorting to such a dimensional analysis whose foundation lies in the fact that all equations that describe the behavior of a physical system must be dimensionally consistent. When a mathematical relationship cannot be found or when such a relationship is too complex for ready solution dimensional analysis may be used to indicate in a semiempirical manner the form of solution. Indeed in considering the friction loss for a fluid flowing within a pipe or tube dimensional analysis may be employed to reduce the number of variables that require investigation suggest logical groupings for the presentation of results and pave the way for a proper experimental program. One method for conducting a dimensional analysis is by way of the Buckingham-n theorem Buckingham 1914 If r physical quantities having v fundamental dimensions are considered there exists a maximum number q of the r quantities which in themselves cannot form a dimensionless group. This maximum number of quantities q may never exceed the number of 5 fundamental dimensions . q s . By combining each of the remaining quantities one at a time with the q quantities n DIMENSIONAL ANALYSIS 31 dimensionless groups can be formed where n r q. The dimensionless groups are called n terms and are represented by n n2 n3
