Analytical Heat Transfer Analysis under Boundary Conditions of the Forth Kind (Conjugate)

Abram Dorfman


The conjugate heat transfer approach is a contemporary powerful tool for solution of heat transfer problems, and numerous results obtained numerically for different particular industrial and natural topics are now available. In contrast, this article presents analytical solutions of laminar (exact) and turbulent thermal boundary layer equations and formulate general features of conjugate convective heat transfer. These analytical results differ in principle from those gained by common methods based on heat transfer coefficients which in fact are empirical means. Two forms, in series and in integral, of analytical expressions for heat flux at arbitrary body surface temperature provide the high accurate calculations using the first form when the series converges fast applying the second one otherwise. On the base of these fundamental relations, the simple methods of solution of the conjugate heat transfer problems for thin and thermally thin plate are developed. Analysis of presented solutions shows that: (i) the surface temperature head variation and Biot number for isothermal surface are the basic characteristics defining the conjugate heat transfer intensity, (ii) the effect of temperature head gradient on the heat transfer coefficient is similar to influence of velocity gradient on friction coefficient: the positive gradients in both cases lead to growing coefficients, and decreasing velocity or temperature head results in lessening of appropriate coefficients and separation flow or heat flux inversion which is analogous to separation phenomenon, (iii) the basic relation in the form of series is a general boundary condition containing known particular cases.


Analytical Solutions, Laminar Flows, Turbulent Flows, Conjugate Heat Transfer, Gradient Analogy

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