Unsteady Conjugate Heat Transfer in a Circular Duct With Convection From the Ambient and Periodically Varying Inlet Temperature

Application of integral transform technique to the transient laminar flow heat transfer in the ducts

“…Kim and Ozisik [9] treated the same problem with parabolic velocity profile, the resulting complex eigenvalues problem is solved by using a RungeKutta method. Travelho and Santos [10,11] solved the same problem that had been developed before in ref. [7,8] with the same physical conditions by applying the Laplace transform, avoiding the computation of the complex eigenvalues and numerically calculating the inverse of the Laplace transform.…”

“…The system of equations (5) may be reduced to those analyzed in literature [7][8][9][10][11][12][13] which neglecting the thermal diffusion in the duct walls, if the coupling parameterH is replaced by:…”

“…The investigations on forced convection with periodic inlet temperature have been performed by numerous researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The solution of heat transfer problems of this type usually leads to a non classical Sturm-Liouville complex system which no known solutions are available.…”

“…In references [7][8][9][10][11][12][13][14][15][16], the methodologies used in the previous works are advanced further by considering the effects of heat capacity of a duct wall. Sparrow and Farias [7] seem to be the first investigators who included the effect of wall conjugation.…”

“…In the studies [7][8][9][10][11][12][13][14][15][16], the wall effects are included in the thermal boundary condition at the fluid-wall interface. This condition can be justified only for heat transfer in flows bounded by extremely thin walls.…”