A Nonlinear Heat Equation with Temperature-Dependent Parameters
نویسنده
چکیده
A nonlinear partial differential equation of the following form is considered: u − div ( a(u)∇u ) + b(u) |∇u| = 0, which arises from the heat conduction problems with strong temperature-dependent material parameters, such as mass density, specific heat and heat conductivity. Existence, uniqueness and asymptotic behavior of initial boundary value problems under appropriate assumptions on the material parameters are established for onedimensional case. Existence and asymptotic behavior for two-dimensional case are also proved.
منابع مشابه
Numerical Analysis of Transient Heat Transfer in Radial Porous Moving Fin with Temperature Dependent Thermal Properties
In this article, a time dependent partial differential equation is used to model the nonlinear boundary value problem describing heat transfer through a radial porous moving fin with rectangular profile. The study is performed by applying a numerical solver in MATLAB (pdepe), which is a centered finite difference scheme. The thermal conductivity and fin surface emissivity are linearly ...
متن کاملEstimation of Thermoelastic State of a Thermally Sensitive Functionally Graded Thick Hollow Cylinder: A Mathematical Model
The object of the present paper is to study temperature distribution and thermal stresses of a functionally graded thick hollow cylinder with temperature dependent material properties. All the material properties except Poisson’s ratio are assumed to be dependent on temperature. The nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity is reduced t...
متن کاملVariation of Parameters Method for Thermal Analysis of Straight Convective- Radiative Fins with Temperature Dependent Thermal Conductivity
In this study, thermal performance across straight convecting- radiating fin with temperature dependent thermal conductivity is considered. The variation of parameters (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Pertinent parameters such as thermo geometric and radiat...
متن کاملThermal Analysis of Convective-Radiative Fin with Temperature-Dependent Thermal Conductivity Using Chebychev Spectral Collocation Method
In this paper, the Chebychev spectral collocation method is applied for the thermal analysis of convective-radiative straight fins with the temperature-dependent thermal conductivity. The developed heat transfer model was used to analyse the thermal performance, establish the optimum thermal design parameters, and also, investigate the effects of thermo-geometric parameters and thermal conducti...
متن کاملCasson Fluid Flow with Variable Viscosity and Thermal Conductivity along Exponentially Stretching Sheet Embedded in a Thermally Stratified Medium with Exponentially Heat Generation
The motion of temperature dependent viscosity and thermal conductivity of steady incompressible laminar free convective (MHD) non-Newtonian Casson fluid flow over an exponentially stretching surface embedded in a thermally stratified medium are investigated. It is assumed that natural convection is induced by buoyancy and exponentially decaying internal heat generation across the space. The dim...
متن کامل