**Problem:**A solid copper cube of 10-cm edge length (\(\rho\) = 8954 kg/m³, \(c\) = 383 J/kg.K, \(k\) = 386 W/m.K) initially at a uniform temperature \(T_i\) = 250°C is suddenly immersed in a well-stirred fluid which is maintained at a uniform temperature \(T_{\infty}\) = 50°C. The heat transfer coefficient between the cube and the fluid is \(h = 200 \, \text{W/m}^2.\text{K}\).A. Check whether the lumped system analysis is suitable.B. Determine the temperature of the copper block at \(t = 5\) min after the immersion.---**Graphical Explanation:**1. **Diagrams:** - The first diagram depicts the solid copper cube with each edge being 10 cm and the initial temperature of the cube \(T_i = 250°C\). - The second diagram illustrates the cube being immersed in a well-stirred fluid maintained at a uniform temperature \(T_{\infty} = 50°C\), with the heat transfer coefficient \(h = 200 \, \text{W/m}^2.\text{K}\).---**Step-by-Step Solution:**### Part A: Lumped System Analysis**Lumped System Criterion:**The lumped system analysis is applicable if the Biot number \( \text{Bi} \) is much less than 1.\[ \text{Bi} = \frac{hL_c}{k} \]Where:- \( h \) = heat transfer coefficient- \( L_c \) = characteristic length of the object- \( k \) = thermal conductivity of the materialFor a cube, the characteristic length \( L_c \) is given by:\[ L_c = \frac{V}{A} \]- \( V \) is the volume of the cube\[ V = a^3 = (0.1\,m)^3 = 0.001\,m^3 \]- \( A \) is the surface area of the cube\[ A = 6a^2 = 6 \times (0.1\,m)^2 = 0.06\,m^2 \]Therefore, the characteristic length \( L_c \) is:\[ L_c =

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Answered: A. Check whether the lumped system…

A. Check whether the lumped system analysis is suitable. B. Determine the temperature of the copper block at t= 5 min after the immersion.

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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