One-Dimensional Quasilinear Heat Flow with Boundary Conditions Periodic in Time

Abstract

If thermal conductivity and specific heat are taken as linear functions of temperature, a nonlinear heat-conduction equation results. For small nonlinearities an approximate first-order analytical solution may be obtained in certain cases. The present analysis deals with one-dimensional problems with periodic boundary conditions. Only the steady-state solution (i.e. , one which is periodic in time) is considered. Solutions are obtained for the following cases: (1) Semi-infinite solid with sinusoidal boundary temperature, (2) thick slab with sinusoidal temperature at one boundary and constant temperature at the other, and (3) thick slab with prescribed heat flux (a constant term plus a sinusoidal term) at one boundary, constant temperature at the other. The effects of the nonlinearities are discussed; they are found to be surprisingly small.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1959
Accession Number
ADA280852

Entities

Organizations

  • Johns Hopkins University

Tags

DTIC Thesaurus Topics

  • Coefficients
  • Conductivity
  • Differential Equations
  • Engineering
  • Equations
  • Frequency
  • Heat Flux
  • Heat Transfer
  • Heat Transmission
  • Internal Combustion Engines
  • Mechanical Engineering
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Specific Heat
  • Steady State
  • Surface Temperature
  • Thermal Conductivity

Fields of Study

  • Mathematics

Readers

  • Control Systems Engineering.
  • Fluid Dynamics.
  • Thermal Physics or Thermal Science.