## Hybrid formulation and solution for transient conjugated conduction-external convection.(English)Zbl 1156.80357

Summary: This work presents a hybrid numerical-analytical solution for transient laminar forced convection over flat plates of non-negligible thickness, subjected to arbitrary time variations of applied wall heat flux at the fluid-solid interface. This conjugated conduction-convection problem is first reformulated through the employment of the coupled integral equations approach (CIEA) to simplify the heat conduction problem on the plate by averaging the related energy equation in the transversal direction. As a result, an improved lumped partial differential formulation for the transversally averaged wall temperature is obtained, while a third kind boundary condition is achieved for the fluid from the heat balance at the solid-fluid interface. From the available steady velocity distributions, a hybrid numerical-analytical solution based on the generalized integral transform technique (GITT), under its partial transformation mode, is then proposed, combined with the method of lines implemented in the Mathematica 5.2 routine NDSolve. The interface heat flux partitions and heat transfer coefficients are readily determined from the wall temperature distributions, as well as the temperature values at any desired point within the fluid. A few test cases for different materials and wall thicknesses are defined to allow for a physical interpretation of the wall participation effect in contrast with the simplified model without conjugation.

### MSC:

 80A20 Heat and mass transfer, heat flow (MSC2010) 76D05 Navier-Stokes equations for incompressible viscous fluids

Mathematica
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### References:

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