Calculation procedure for transient heat transfer to a cooled plate in a heated stream whose temperature varies arbitrarily with time

Heat transfer equations have been developed to calculate surface temperature and surface heat flux for cooled flat plate when temperature of fluid passing over leading edge varies arbitrarily

Application of differential similarity to finding nondimensional groups important in tests of cooled engine components

The method of differential similarity is applied to the partial differential equations and boundary conditions which govern the temperature, velocity, and pressure fields in the flowing gases and the solid stationary components in air-cooled engines. This procedure yields the nondimensional groups which must have the same value in both the test rig and the engine to produce similarity between the test results and the engine performance. These results guide the experimentalist in the design and selection of test equipment that properly scales quantities to actual engine conditions. They also provide a firm fundamental foundation for substantiation of previous similarity analyses which employed heuristic, physical reasoning arguments to arrive at the nondimensional groups

Transient Heat Transfer between a Plate and a Fluid whose Temperature Varies Periodically with Time

Using the method of complex temperature in conjunction with the Laplace transformation, an exact analytical solution is found for the transient, conjugate, forced convection problem consisting of a plate, whose base is insulated, interacting with a fluid, moving in a steady slug fashion, whose temperature, at points far from the plate, varies sinusoidally with time. Simple quasi-steady results are derived for comparison. Also presented is a method for determining the qualitative conditions under which one might expect a quasi-steady analysis to be valid in a general problem.</jats:p

Exact Solution for Unsteady Conjugated Heat Transfer in the Thermal Entrance Region of a Duct

By use of the Laplace transformation, an exact analytical solution is developed for the case of transient conjugated heat transfer in the thermal entrance region of a parallel plate duct when the unsteadiness is induced by a sudden change in temperature of the ambient fluid outside the duct walls. The solution is presented for the fastest part of the transient, time domain I, and comparison is made with a finite difference solution and also with the approximate, standard quasi-steady approach which is seen to be appreciably in error for a wide range of conjugation parameter values.</jats:p

Analytical Solution for Unsteady Heat Transfer in a Pipe

Under consideration is transient, convective heat transfer to a fluid flow within a pipe due to a sudden change in the temperature of the ambient medium outside the pipe. A solution is developed by the Laplace transformation, for the fastest portion of the transient, which gives the pipe wall temperature, surface heat flux, and fluid bulk mean temperature. These analytical results are compared with available finite difference results and with quasi-steady solutions. A criterion is developed that indicates when the zero thermal capacity wall solution can be used with adequate accuracy.</jats:p