22:16
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4G 100\%
Project Transport 2567
Project
616 411Transport Phenomena
You can use any software to solve problems
Consider a solid plate as shown below, two solid plates are connected and they have different temperatures, thermal conductivities, and densities. At the top of surface plate 2, there is convective heat transfer to the ambient air (temperature \( T_{\infty} \), and heat transfer coefficient h).
Assume T is a function of y only
The rate of frictional heating at the contact surface between two solids \( \left(\mathrm{H}_{s}\right) \) is expressed by
\[
H_{s}=f \delta U
\]
\( \boldsymbol{U}= \) the relative velocity of the solids,
\( \delta= \) the force per unit area holding the solids in contact (i-e., normal to the interface) \( =\rho_{\mathrm{i}} \mathrm{L}_{\mathrm{i}} \mathrm{g} \) \( \mathrm{f}= \) the coefficient of dry friction for the materials involved.
( \( \rho_{i}= \) density of plate \( i, L_{i}= \) Height of plate \( i, g= \) gravity \( ) \)
(a) Determine temperature profiles in both plates at the steady-state when both plates are in the rest (not moving)
(b) Plot temperature profile in both plates
c) If plate 2 moves horizontally at speed \( \boldsymbol{U} \), plate 1 is in the rest. Determine the steady-state temperature profile in the plates affected from the rate of interfacial energy generation
The interfacial balance: \( q_{y}^{(i)}\left(L_{i}\right)+H_{s}=. q_{y}^{(i+1)}\left(L_{i+1}\right) ; \mathrm{i}= \) plate i
\begin{tabular}{|c|c|}
\hline Parameters & Values \\
\hline \( \mathrm{T}_{0} \) & 100 C \\
\hline \( \mathrm{T}_{\infty} \) & 30 C \\
\hline \( \mathrm{k}_{1} \) & \( 80 \mathrm{~W} \cdot \mathrm{~m}^{-1} \cdot \mathrm{~K}^{-1} \) \\
\hline \( \mathrm{k}_{2} \) & \( 50 \mathrm{~W} \cdot \mathrm{~m}^{-1} \cdot \mathrm{~K}^{-1} \) \\
\hline
\end{tabular}
