A non-deforming, extrude insulating material’s heat transmission coefficient is given as 0,029 W/m-K. 100C temperature difference is measured through 20mm thick insulating material. What is the heat flux transmitting inside 2mx2m sized insulating material? What is the velocity of heat transmission? Please instil the knowns and unknowns by delienating the sequence. Please write your all assumptions in detailed.

Consider the insulating material as shown in figure below:

The following assumptions are made for the heat transfer though the insulating material

1) Steady-state conduction: Here the temperature is the function of x. While the Area A, is not a function of direction i.e. x, and thermal conductivity k is not a function of temperature T. 

2) Fourier's law of conduction is applicable for this condition

$\frac{\mathrm{q}}{\mathrm{A}}= -\mathrm{k}\frac{\mathrm{dT}}{\mathrm{dx}}$              (equation 1)

Where, q/A = Heat flux (W/m²)

Integrating the above equation yields a straight line equation. That is why, in the above figure, the temperature profile is a straight line with negative slope. If k becomes a function of temperature, the temperature profile would change.

Given: k = 0.029 W/m.k

           $∆\mathrm{T} = {\mathrm{T}}_1-{\mathrm{T}}_2= 100{ }^{\mathrm{o}}\mathrm{C}$

            x = thickness = 20 mm = 0.02 m

 Required: (q/A) =?

From equation 1;

$\frac{\mathrm{q}}{\mathrm{A}}= -\mathrm{k}\frac{\mathrm{dT}}{\mathrm{dx}}$

$\frac{\mathrm{q}}{\mathrm{A}}= \frac{∆\mathrm{T}}{{\displaystyle \frac{\mathrm{x}}{\mathrm{k}}}}$

$\frac{\mathrm{q}}{\mathrm{A}}= \frac{100}{{\displaystyle \frac{0.02}{0.029}}}$

Heat flux = $\frac{\mathbf{q}}{\mathbf{A}}\mathbf{=}\mathbf{ }\mathbf{145}\mathbf{ }\mathbf{W}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$                 (Answer a)