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The mysterious connection of heat energy: Why are heat flow and interfaces so critical in engineering design?
With the widespread use of computer technology, the contemporary conjugate convection heat transfer model came into being, replacing the previous empirical proportional relationship between heat flow and temperature difference. This model is based on a rigorous mathematical description of the heat exchange between an object and a fluid, an interaction that occurs as the two objects interact. The different physical processes and solutions of the governing equations are considered separately, allowing these problems to be analyzed in their own subdomains.
Historical BackgroundCo-spectral heat conduction problems involve heat exchange between systems, and this interface can be regarded as the contact point between two different physical states.
In 1961, Theodore L. Perelman first proposed the problem of heat conduction when a liquid passes around an object and successfully created a model for it, which also led to the birth of the term "conjugate heat conduction problem". He subsequently developed this method further with A.V. Luikov. During this period, many researchers began to use different methods to solve simple problems, combining solutions of objects and fluids at their interfaces. An early conjugate solution is included in Dorfman's book.
Conjugation Problem Statement
The conjugate convection heat transfer problem consists of a set of equations that reflect the differences between the two systems in the object and fluid domains and include the following important aspects:
Object Domain
Involves transient or steady-state conduction equations, such as Laplace's or Poisson's equations, or simplified one-dimensional equations for thin bodies.
Fluid Domain
For laminar flows: Navier-Stokes equations and the energy equation or simplified equations for boundary layers at large Reynolds numbers and creeping flow at small Reynolds numbers. For turbulent flows: Reynolds-averaged Navier-Stokes equations and the energy equation or the boundary layer equations for large Reynolds numbers.
Initial Boundary and Conjugate Conditions
These conditions define the spatial distribution of variables in the dynamic and heat equations at the initial time, including the no-slip condition and other commonly used dynamic conditions. The conjugate condition requires that the continuity of the thermal field be maintained at the object/fluid interface, that is, the temperature and heat flow of the object and the fluid near the interface must be equal: T(+) = T(-), q(+) = q(-).
Solution
Numerical methods
One way to achieve conjugation is through iteration. Each solution for a body or fluid generates boundary conditions for another component. This process is repeated alternately under different boundary conditions until it finally converges.
Analytical Method
By combining the solution of the conduction equation with the Duhamel integral, the conjugate problem can be transformed into the heat conduction equation with only the object, which expands the scope of the problem to include different flow types, pressure gradients, and unsteady temperature changes.
Application Scope
From simple examples in the 1960s, conjugate heat transfer methods have evolved into powerful tools for simulating and studying a wide variety of natural phenomena and engineering systems, ranging from aerospace and nuclear reactors to complex processes such as heat treatment and food processing. This approach has a wide range of applications and has been further confirmed and expanded in the literature in recent years.
The wide application of the conjugate method has been verified in real cases in many fields and has become an indispensable part of engineering design.
As technology advances and needs change, how will we use these thermal connections to push the boundaries of engineering design in the future?
