VM-WB-MECH-077

VM-WB-MECH-077
Heat Transfer in a Bar with Variable Sheet Thickness

Overview

Reference:

Incropera, F. P., & DeWitt, D. P. (2002). Heat and Mass Transfer (5th ed.). John Wiley & Sons, Inc.

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Solver(s):

Ansys Mechanical

Analysis Type(s): Static Thermal Analysis
Element Type(s): Shell

Test Case

A 10 x 50 mm plate with a thickness varying from 1 mm to 4 mm is maintained at temperatures of 100 °C and 200 °C as shown below. Find the following:

  • Temperatures at mid of the surface.

  • Heat flow reactions on end edges.

Figure 103: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
E = 2.0 x 1011 Pa
v = 0
α = 1.2 x 10-5 1/°C
k = 60.5 W/m°C
Plate Dimensions : 10 X 50 mm.
Thickness Variation : 1 mm to 4 mm
Temperature (T1) on edge (@ 1mm thickness) = 100 °C
Temperature (T2)on edge (@ 4mm thickness) = 200 °C

Analysis

Heat flow due to conduction is given by:

(2)

The area for conduction varies from A1 to A2. The area Ay at any distance y is given as:

(3)

Inserting Equation 3 in equation Equation 2 and integrating the equation from 0 to L,

(4)

Temperature at any point y is given as:

(5)

Results Comparison

ResultsTargetMechanicalError (%)
Heat reaction at T1 (W) 2.6182.6188 0.031
Heat reaction at T2 (W) -2.618-2.6188 0.031
Temperature at mid of surface (°C)166.083166.090.004