Inscrição na biblioteca: Guest

ISSN Online: 2377-424X

ISBN Print: 0-89116-130-9

International Heat Transfer Conference 6
August, 7-11, 1978, Toronto, Canada

APPLICATION OF VARIATIONAL PRINCIPLES OF FIELD THEORY FOR MINIMIZING THERMAL RESISTANCE OF A SOLID WITH HEAT-EXCHANGING SURFACES

Get access (open in a dialog) DOI: 10.1615/IHTC6.320
pages 233-237

Resumo

On the basis of the general variational principle of minimum energy dissipation presented in integral form, the authors formulate the general problem on stationary heat distribution in a solid with heat-exchanging surfaces, with a given law of distribution of heat fluxes on them. The specific feature of formulating the problem is extension of the varied parameters in the energy dissipation functional from the variables characterizing the thermal state of each point of the solid's volume, i.e. the temperatures T and the local heat flux of thermal conductivity Jq, to the variables characterizing the position of each point of the boundary surface of the body with respect to a selected system of coordinates, i.e. the radius vector r. By varying the energy dissipation functional with respect to the three indicated variables of the state of the solid the authors obtained a system of nonlinear differential equations and the corresponding boundary conditions for the distribution of the temperature, the heat flux in the solid, and also for the distribution of the average curvature at each point of the boundary surface of the body in relation to its local temperature and the assigned law of heat exchange with the environment. A simultaneous solution of the above set of equations with the boundary conditions ensures a minimum of thermal resistance of a solid with heat-exchanging surfaces.