heat transfer -凯发k8网页登录

solve conduction-dominant heat transfer problems with convection and radiation occurring at boundaries

address challenges with thermal management by analyzing the temperature distributions of components based on material properties, external heat sources, and internal heat generation for steady-state and transient problems.

the heat transfer equation is a parabolic partial differential equation that describes the distribution of temperature in a particular region over given time:

$ρ c \frac{\partial t}{\partial t} - \nabla \cdot (k \nabla t) = q$

a typical programmatic workflow for solving a heat transfer problem includes these steps:

create a special thermal model container for a steady-state or transient thermal model.
define 2-d or 3-d geometry and mesh it.
assign thermal properties of the material, such as thermal conductivity k, specific heat c, and mass density ρ.
specify internal heat sources q within the geometry.
specify temperatures on the boundaries or heat fluxes through the boundaries. for convective heat flux through the boundary $h t c (t - t_{\infty})$ , specify the ambient temperature $t_{\infty}$ and the convective heat transfer coefficient htc. for radiative heat flux $ε σ (t^{4} - t_{\infty}^{4})$ , specify the ambient temperature $t_{\infty}$ , emissivity ε, and stefan-boltzmann constant σ.
set an initial temperature or initial guess.
solve and plot results, such as the resulting temperatures, temperature gradients, heat fluxes, and heat rates.
approximate dynamic characteristics of a thermal model by using reduced order modeling (rom).

functions

thermal model setup

	create model
	assign thermal properties of a material for a thermal model
	specify internal heat source for a thermal model
	specify boundary conditions for a thermal model
	set initial conditions or initial guess for a thermal model
	solve structural analysis, heat transfer, or electromagnetic analysis problem
	assemble finite element matrices
	reduce structural or thermal model
	recover full-model transient solution from reduced-order model (rom)
	linearize structural or thermal model
	specify inputs to linearized model
	specify outputs of linearized model

solutions at nodal and custom locations

	interpolate temperature in thermal result at arbitrary spatial locations
	evaluate temperature gradient of thermal solution at arbitrary spatial locations
	evaluate heat flux of thermal solution at nodal or arbitrary spatial locations
	evaluate integrated heat flow rate normal to specified boundary

visualization

	plot solution or mesh for 2-d problem
	plot solution or surface mesh for 3-d problem
	plot pde geometry
	plot pde mesh
	create and plot pde visualization object

thermal model properties

	find thermal material properties assigned to a geometric region
	find heat source assigned to a geometric region
	find thermal boundary conditions assigned to a geometric region
	find thermal initial conditions assigned to a geometric region

live editor tasks

create and explore visualizations of pde results in the live editor

objects

	thermal model object
`reducedthermalmodel`	reduced-order thermal model
	steady-state thermal solution and derived quantities
	transient thermal solution and derived quantities
	modal thermal solution

properties

	thermal material properties assignments
	heat source assignments
	boundary condition for thermal model
	initial temperature at mesh nodes
	initial temperature over a region or region boundary
	algorithm options for solvers
	pde visualization of mesh and nodal results

topics

thermal analysis workflow

solve a heat equation that describes heat diffusion in a block with a rectangular cavity.
perform a 3-d transient heat transfer analysis of a heat sink.
analyze a 3-d axisymmetric model by using a 2-d model.
perform a 3-d transient heat conduction analysis of a hollow sphere made of three different layers of material, subject to a nonuniform external heat flux.
solve the heat equation with a source term.
solve the heat equation with a temperature-dependent thermal conductivity.
use partial differential equation toolbox™ and simscape™ driveline™ to simulate a brake pad moving around a disc and analyze temperatures when braking.
axisymmetric thermal and structural analysis of disc brake
simplify analysis of a disc brake by using an axisymmetric model for thermal and thermal stress computations.

general pde workflow

nonlinear heat transfer in thin plate
perform a heat transfer analysis of a thin plate.