Answered: Given a metallic block comprising of 2…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

Given a metallic block comprising of 2 unknown materials namely A and B (as shown in Figure 1 below).

1. You are tasked to determine the heat flux (W/cm²) for node at coordinate (2, 2) using finite-difference approximations using Elliptical Equation (Control Volume Approach) for the temperature gradients at this node.

2. Estimate the flux value in the horizontal direction in materials A and B, and determine if these two fluxes should be equal.

3. Calculate the vertical flux in materials A and B. Should these two fluxes be equal?

The following values for the constants is as provided here: Δz = 0.5 cm, h =10 cm, k_a = 0.3 W/cm · C, k_b = 0.5 W/cm · C and nodal temperatures are T₂₂ = 51.6^oC, T₂₁ = 74.2^oC, T₂₃ = 45.3^oC, T₃₂ = 38.6^oC and T₁₂ = 87.4^oC

Insulated
h
(1, 1)
(4,2)
h→
Material A
h/2
Convection
Material B
Δz
Insulated

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