VM-WB-MECH-027

VM-WB-MECH-027
Thermal Analysis for Shells with Heat Flow and Given Temperature

Overview

Reference:	Any standard Thermal Analysis book
Solver(s):	Ansys Mechanical
Analysis Type(s):	Thermal Stress Analysis
Element Type(s):	Shell

Test Case

A plate of length (L), width (W), and thickness (T) is fixed along the width on one edge and heat flow (Q) is applied on the same edge. The opposite edge is subjected to a temperature of 20 °C. Ambient temperature is 20 °C. To get accurate results, apply a sizing control with element size = 2.5e-2 m.

Find the maximum temperature, maximum total heat flux, maximum total deformation, and heat reaction at the given temperature.

Figure 30: Schematic

Material Properties

Geometric Properties

E = 2e11 Pa

ν = 0.0

Coefficient of thermal expansion α = 1.2e-5/°C

Thermal conductivity k = 60.5 W/m°C

Length L = 0.2 m

Width W = 0.05 m

Thickness T = 0.005 m

Heat flow Q = 5 W

Given Temperature = 20°C

Analysis

Heat Reaction = -(Total heat generated)

Heat flow due to conduction is given by:

where:

T_h = maximum temperature

T₁ = given temperature

Total heat flux is:

Temperature at a variable distance z from the fixed support is given by:

Thermal deformation in the z-direction is given by:

Results Comparison

Results	Target	Mechanical	Error (%)
Maximum Temperature (°C)	86.1157	86.116	0.0003
Maximum Total Heat Flux (W/m²)	2e4	2e4	0.000
Maximum Total Deformation (m)	7.93386e-5	7.9958e-5	0.781
Heat Reaction (W)	-5	-5	0.000