Доступ предоставлен для: Guest

ISSN Online: 2377-424X

ISBN CD: 1-56700-226-9

ISBN Online: 1-56700-225-0

International Heat Transfer Conference 13
August, 13-18, 2006, Sydney, Australia

APPROXIMATE ANALYSIS FOR CONJUGATE HEAT TRANSFER IN SOLIDS UNDER STEADY CONVECTION

Get access (open in a dialog) DOI: 10.1615/IHTC13.p20.150
9 pages

Аннотация

A conducting solid, with its surface under a steady flow, extends upstream of a region of the solid which is held at constant temperature, the latter being above that of the approaching stream. The surface of the conducting solid in the upstream region has a temperature that falls monotonically with distance from the forward edge of the constant-temperature region. The local convective transport coefficient at a point on the surface, as the flow approaches that forward edge, depends in part on the variation of surface temperature upstream, while the temperature at that point on the solid depends on conduction from the constant-temperature region downstream. It is a conjugate problem. In numerical analysis of geometries with such regions a refined mesh may be introduced locally upstream and downstream to improve accuracy, but the mesh refinement is often arbitrary. A method is described here, based on dynamic programming, and embracing a form of multi-scale modelling where the scale involved is much coarser than when applying programs such as FLUENT and NEKTAR (Karniadakis & Sherwin (2005)), and which can provide estimates of the errors incurred when using a finite set of grid steps, not uniformly spaced, and so chosen as to minimize an error criterion. The computation is quick to execute. The method can be repeated with different numbers of steps used in dividing the convection field while keeping a single length scale of representation for the conducting solid in the region of interest.
The method is illustrated with a model where the temperature on the forward-projecting solid surface is approximated in steps each of constant but different temperature, with generally unequal steps in temperature and unequal lengths of steps in the direction of flow. The local heat transfer from the solid to the stream is computed by superposition from kernel solutions. (This implies applications where the mesh for the flow field is far from being set so fine as to seek to solve the local convection by good approximation inside the thermal boundary layer itself.) The temperature inside the solid is approximated by a smooth transcendental function with some adjustable parameters, and for a length scale larger than the lengths typical for each of a sequence of superpositions of application of kernel solutions for convection. The finite steps of the surface temperature used in approximation of the convection are set in height and length by dynamic programming, satisfying a criterion function that minimizes the integral least-squares difference of the stepped-temperature distribution from that of the temperature of the solid.