Heat Transfer Handbook part 47. 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. | 452 FORCED CONVECTION EXTERNAL FLOWS dT 8 dT 9x 8t dyT 1 f 8 Y Pr 87 d 2t dyT2 2Ec O 2ßT Ec u dx q L pcpU AT The corresponding dimensional form of eq. is dT dT _ d2T ßT dp du y q dx dy dy2 pcp dx pcp dy pcp Equation can be used to demonstrate that when Pr 1 8T o 8 O I Pr1 2 and when Pr 1 o 8 O Pr1 3 Similarity Transformation Technique for Laminar Boundary Layer Flow Following the simplifications of eqs. - the two-dimensional steady-state boundary layer equations are du dv dx dy du du 1 dp d 2u d2 u dx dy p dx dy2 x dy2 dT dT dT2 dp du Ÿ q . . . Tu x pp jy pcp The boundary conditions for an impermeable surface are u x 0 v x 0 0 T x 0 To x u x œ U x T x œ Tœ x Equations - constitute a set of nonlinear partial differential equations. Under certain conditions similarity solutions can be found that allow conversion of this set into ordinary differential equations. The concept of similarity means that HEAT TRANSFER FROM SINGLE OBJECTS IN UNIFORM FLOW 453 certain features . velocity profiles are geometrically similar. Analytically this amounts to combining the x and y spatial dependence on a single independent variable n. The velocity components u x y and v x y are expressed by a single nondimensional stram function f n and the temperature T x y into a nondimensional temperature n . Similarity for boundary layer flow follows from the observation that while the boundary layer thickness at each downstream location x is different a scaled normal distance n can be employed as a universal length scale. Presence of natural length scales such as a finite-length plate cylinder or sphere generally precludes the finding of similarity solutions. Using the scaled distance the similarity procedure finds the appropriate normalized stream and temperature functions that are also valid at all locations. Following Gebhart 1980 the similarity variables are defined as n x y yb x x y f n vc x . .
