Asymmetric Graetz Problem: The Analytical Solution Revisited

Resistor-Network Formulation of Multitemperature Forced-Convection Problems

“…Comparing Equations 16 and 17, obtained by dQdT, with the expressions reported in [1], found by solving equating R 10 and R 20 and solving the nodal energy balances, it can be seen that they are identical. The dQdT technique for calculating the paired resistances is thus verified.…”

“…The resistor-network approach is computationally advantageous in time-step simulations since it provides the opportunity to model heat transfer a high level of detail and at a very low computational expense [2,3]. The utility of this approach has also been demonstrated [1] for the classical multi-temperature convection problem of fully-developed laminar flow in an asymmetrically-heated channel, the asymmetric Graetz problem. The resistor-network formulation has been shown to lead to a simpler representation of the solution, while revealing new details about the heat transfer phenomenon.…”

“…The results obtained in [1] by equating the two wall-to-fluid resistances, R 10 =R 20 , and solving the nodal energy balances are used here to validate the dQdT results. …”

“…The number of the unknowns is therefore reduced to two and the system of energy-balance equations can be solved for {R ij }. In a recent paper [1], the analytical solution by Hatton and Turton [4] was used to derive expressions for {R ij }. For the purpose of verification, the dQdT technique is applied here to obtain {R ij } of the same problem.…”

“…The resulting heat transfer coefficient will depend on this temperature ratio. Shortcomings of this approach are discussed in detail in reference [1]. A major shortcoming is that it does not give the "split" of heat (transfer) between different sources.…”