Heat transfer7/13/2023 In this example, however, the cooling flux depends not only on but also on the pad temperature. To solve for the temperature field of the ceramic, a first idea might be to build a single 2D system and model the cooling pad as a heat flux boundary condition. The right and bottom surfaces of the ceramic are assumed to be thermally insulated. Ī constant heat flux is applied on the top of the ceramic. The cooling flux is proportional to the temperature difference between the pad and the ceramic with a heat transfer coefficient. At the left surface the ceramic is cooled down by attaching to a thin pad with a cooling flux through it. As an example, consider a 2D ceramic strip with an uniform initial temperature at. The following section demonstrates how to model heat transfer phenomena defined in different spatial dimensions. Heat Transfer Model with Mixed Dimensions Note that for the effective heat capacity is the smallest. One equation describes the temperature field in the solid region and the other equation models the temperature in the fluid region: To model heat transfer within a porous medium, one approach, called a direct approach, is to build a coupled PDE with two heat equations with material coefficients suitable for each phase. Due to its special thermal and mechanical properties, porous materials have been widely used in many industrial applications such as vibration suppression, heat insulation and sound absorption. ![]() Porous media are multiphase objects with a solid skeleton portion and a porous region that is filled with a fluid. This mechanism may not be available when modeling the pulsed heat source with an If or similar statement.ĭetails about modeling heat pulses are presented in the appendix section: Possible Issues and Workarounds for Modeling Heat Pulses. While it would also be possible to make use of an If statement to model the dynamic or pulsed heat source, the use of WhenEvent has the distinct advantage that NDSolve has special mechanisms build in to detect the events during the time integration. The heat source is then turned on and off when the central temperature reaches or, resulting in an oscillating temperature field. With a constant cooling flux applied on both sides, heat continuously flows out of the domain and brings down the room temperature. The simulation begins with an uniform temperature at. The energy balance within the domain can be described by the following equation: The heat flux represents the net energy that exits through the boundaries. The red circle in the middle represents a heat source, which denotes thermal energy that is generated inside the domain. The total energy within the control volume is then equal to the product. In the above graphics, is the density and is the internal energy per unit mass. Consider balancing the energy generated within a unit volume domain with the energy flowing through the boundary of the domain. To derive the heat equation start from energy conservation. The term denotes a heat source within the domain, and is explained in the Source Types section. If the simulation medium is a solid then this term is zero. This term is only present if the medium allows for an internal flow. This will then result in a nonlinear heat equation.Ī second part is a convective term: with a flow velocity for modeling internal heat convection. The thermal conductivity may very well depend on the temperature itself. First and foremost there is a diffusive term: with a thermal conductivity. ![]() The specific heat capacity is a material property that specifies the amount of heat energy that is needed to raise the temperature of a substance with unit mass by one degree Kelvin.īeside the time derivative part the PDE is made up of several components. The partial differential equation (PDE) model describes how thermal energy is transported over time in a medium with density and specific heat capacity. The dependent variable in the heat equation is the temperature, which varies with time and position.
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