Professor! Today's topic is kiln thermal analysis, right? What exactly is that?

It involves analyzing the cross-sectional temperature distribution and external wall heat loss in rotary kilns and tunnel kilns. It's used to evaluate refractory degradation and energy-efficient design.

What kind of equations are involved in kiln thermal analysis?

The governing equations for kiln thermal analysis are the energy conservation equation, the Navier-Stokes equations for fluid flow, and the radiative heat transfer equation.

How do you actually solve these equations using a computer?

We use spatial discretization with the Finite Element Method (FEM). This involves assembling the element stiffness matrices and constructing the global stiffness equation.

What does the matrix solution algorithm entail specifically?

We solve the system of equations using either direct methods (LU decomposition, Cholesky decomposition) or iterative methods (Conjugate Gradient method, GMRES method). For large-scale problems, preconditioned iterative methods are particularly effective.

Kiln Thermal Analysis

Category: 熱解析 | Integrated 2026-04-06

CAE visualization for kiln analysis theory - technical simulation diagram

キルン（窯炉）熱解析

Theory and Physics

Overview

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Teacher! Today's topic is about kiln thermal analysis, right? What is it about?

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Cross-sectional temperature distribution and external wall heat loss for rotary kilns and tunnel kilns. Evaluation of refractory degradation and energy-saving design.

Governing Equations

$$ q = \frac{T_i - T_o}{\sum \frac{\ln(r_{j+1}/r_j)}{2\pi k_j L}} $$

$$ Q_{loss} = h_o A_o (T_{shell} - T_{amb}) $$

Discretization Methods

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How do you actually solve these equations on a computer?

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We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.

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We perform transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

Matrix Solution Algorithms

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What exactly are matrix solution algorithms?

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We solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Solver	Classification	Memory Usage	Applicable Scale
LU decomposition	Direct Method	O(n²)	Small to Medium Scale
Cholesky decomposition	Direct Method (Symmetric Positive Definite)	O(n²)	Small to Medium Scale
PCG Method	Iterative Method	O(n)	Large Scale
GMRES method	Iterative Method	O(n·m)	Large Scale / Non-symmetric
AMG Preconditioner	Preprocessing	O(n)	Very Large Scale

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So, if you cut corners on the finite element method part, you'll pay for it later. I'll keep that in mind!

Implementation in Commercial Tools

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So, what software can be used to perform kiln thermal analysis?

Tool Name	Developer/Current	Main File Formats
Ansys Fluent	Ansys Inc.	.cas, .dat, .msh, .jou
Simcenter STAR-CCM+	Siemens Digital Industries Software	.sim, .java, .csv
Abaqus FEA (SIMULIA)	Dassault Systèmes SIMULIA	.inp, .odb, .cae, .sta, .msg
Ansys Mechanical (formerly ANSYS Structural)	Ansys Inc.	.cdb, .rst, .db, .ans, .mac
COMSOL Multiphysics	COMSOL AB	.mph

Vendor Lineage and Product Integration History

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Does each software have a dramatic origin story?

Ansys Fluent

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Next is about Ansys Fluent. What's the story?

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Developed by Fluent Inc. Acquired by Ansys in 2006. A general-purpose CFD solver based on unstructured grids.

Current affiliation: Ansys Inc.

Simcenter STAR-CCM+

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Next is about Simcenter STAR. What's the story?

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Developed by CD-adapco. Acquired by Siemens in 2016 and integrated into the Simcenter brand. Known for polyhedral meshing.

Current affiliation: Siemens Digital Industries Software

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After hearing this, I finally understand why development is so important!

Abaqus FEA (SIMULIA)

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What exactly is Abaqus FEA?

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Developed in 1978 by HKS (Hibbitt, Karlsson & Sorensen). Acquired by Dassault Systèmes in 2005 and integrated into the SIMULIA brand.

Current affiliation: Dassault Systèmes SIMULIA

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Wow, the story of development is super interesting! Tell me more.

File Formats and Interoperability

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Are there any points to note when transferring data between different software?

Format	Extension	Type	Overview
STEP	.stp/.step	Neutral CAD	ISO 10303 compliant 3D CAD data exchange format. Supports geometry + PMI.
IGES	.igs/.iges	Neutral CAD	Early CAD data exchange standard. Has issues with surface data compatibility. Migration to STEP is progressing.
CGNS	.cgns	CFD Data	CFD General Notation System. Standard exchange format for CFD results.

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When converting models between different solvers, attention must be paid to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.