Assignment 3 Steady State Heat Transfer MTRL 361 - 2023

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University of British Columbia *

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CHAPTER 12

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Material Science

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Dec 6, 2023

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docx

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THE UNIVERSITY OF BRITISH COLUMBIA Department of Materials Engineering MTRL 361 Assignment #3 – 1D Steady Sate Conductive Heat Transfer through Multiple Interfaces Date: Monday, October 13 th , 2023 Due: Sunday, October 29 rd , 2023 (11:59 pm, 23:59) Continuous Slab Casting of Steel In a conventional continuous slab casting process, heat is transported out of the system through the mould's external surfaces (mould/env. interface) to water while the slab is located within the mould. See schematic diagram Figure 1. Figure 1 – Schematic Diagram of Slab Casting Mould area At the midpoint of the wide face, it is reasonable to assume that the heat transport is 1-D. Furthermore, adopting an Eulerian frame of reference (i.e., the observer is not moving with the strand), the temperature field is invariant with time for a location at a specific distance from the meniscus. 1/4
In this problem, you will need to solve for the temperature distribution in the system, given the metal temperature at the centerline of the casting and the temperature of the cooling water within the mould. The conductivities of the various materials and the heat transfer coefficients at the interfaces will be given. Your calculations need to be completed in Python, and your executable file for Layers 1 through 3 must be uploaded to Canvas for you to receive a mark . Each question should be completed in a separate computational cell in Python, with the question number – e.g., Layer 1 Q1.1 – clearly labelled at the beginning of the computational cell. Theory and Background An easy way to solve this type of problem is to use the thermal circuit method. For more details on the thermal circuit method, please refer to class notes. Referring to Figure 2, the following resistances and approximate temperatures are identified in the system at some (unknown) location below the meniscus. You may assume that the strand ½ thickness is 50 mm. The material properties of the various components and the interfacial heat transfer coefficients are given in Table 1. Figure 2 – Schematic diagram of the series resistances making up the overall resistance to heat transfer through a section of a continuous casting slab and the resulting steady state temperature distribution[1,2]. 2/4
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