Heat Transfer Handbook part 48. 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. | 462 FORCED CONVECTION EXTERNAL FLOWS 2cp T0 - TAW C2 -C1 -------U2------ The solution for 9AW qB is obtained numerically by solving eq. . From this 9AW 0 rc Pr Pr1 2 for gases where rc is called the recovery factor. Using this the adiabatic wall temperature is calculated as U1 taw T rc 2cp For low velocities his can be approximated as Taw T The temperature profile for various choices of T0 is shown in Fig. from Gebhart 1971 . The heat fluo can be written as a -k q dy U2 y 0 -k 2cP 6Aw 0 C11 0 k T0 - Taw U Pr1 3 vx 1971. HEAT TRANSFER FROM SINGLE OBJECTS IN UNIFORM FLOW 463 and with the definition q00 hx To - Taw the Nusselt number becomes the well-known Pohlhausen 1921 solution Nu 2 Pr1 3 where the properties can be evaluated at the reference temperature recommended by Eckert T Tw - 7 Taw - T Integral Solutions for a Flat Plate Boundary Layer with Unheated Starting Length Consider the configuration illustrated in Fig. . The solution for this configuration can be used as a building block for an arbitrarily varying surface temperature where a similarity solution does not exist. Assuming steady flow at constant properties and no viscous dissipation the boundary layer momentum and energy equations can be integrated across the respective boundary layers to yield d dx A zV dU u dy v 3y y o d dx tL T dy adT o dy y 0 To integrate eqs. and approximate profiles for tangential velocity and temperature across the boundary layer must be defined. For example a cubic parabola profile of the type T a by cy2 dy3 can be employed with the conditions Figure Hydrodynamic and thermal boundary layer development along a flat plate with an unheated starting length in a uniform stream. 464 FORCED CONVECTION EXTERNAL FLOWS y T T0 0 y T Tœ St dT 0 dy T Tœ By evaluating the energy equation at the surface an additional condition can be developed d 2T dy2 0 y 0 Using these boundary conditions the temperature .
