Author: Chia-Hsun Hsieh, Cornell University

Problem Specification

1. Pre-Analysis & Start-Up

2. Geometry

3. Mesh

4. Physics Setup

5. Numerical Solution

6. Numerical Results

7. Verification & Validation

Exercises

Comments

# Exercise

## Problem Statement

Consider a pair of concentric cylinders with a ** height** of

**. The**

*24 mm***has a radius of**

*smaller cylinder***. The**

*12 mm***and**

*inner***radius of the**

*outer***is**

*larger, hollow cylinder***and**

*24 mm***, respectively. The same boundary condition and the initial condition from the shell and specimen tutorial will be used:**

*25 mm***on the outer surface of the larger, hollow cylinder, and**

*Convection***for each emitting surface. The larger, hollow cylinder will be set to**

*two radiation boundary conditions***and the smaller cylinder will be set to**

*22 degress Celsius***.**

*-273.15 degrees Celsius*## Analytic Solution

Assume only the inner surface of the larger, hollow cylinder and the cylindrical surface of the smaller cylinder are emitting radiation. Also assume the surfaces are gray and diffuse. The net radiation of an emitting surface of this concentric cylinder, two-surface enclosure is give below:

In this convention, the ** subscript "1"** denotes the smaller cylinder and the

**denotes the larger, hollow cylinder. Since this is a two-surface enclosure problem, we can expect the**

*subscript "2"***for each surface to be 1. All the radiation emitted by one surface is intercepted by the other surface. The notation of the above equation is the net radiation of the smaller cylinder.**

*view factor*The analytic solution shows the net radiation of the smaller cylinder is ** -0.428 watts**.

## ANSYS result

Solve this problem with the same procedure for the shell and specimen tutorial. First solve the ** steady state** model and transfer the data to

**to complete the simulation. Make sure you use the same step end time and the same boundary and initial conditions.**

*transient analysis*From the tabular data, the net radiation of the smaller cylinder is ** -0.423 watts** at the step end time. ANSYS result shows a

**deviation from the analytic solution. Hence we can verify that the view factor and radiation heat transfer are computed correctly in this set up. This also verifies the validity of the shell and specimen model.**

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