Please solve $4,5,$& $6$: Consider the following configuration. A $10$ m long slab A $($horizontal direction$)$ generates heat at the rate of ${10}^6\frac{W}{m^3}.$ It is covered by a plate B $,$ acting as a buffer. A fluid moves over the buffer plate B$,$ purely because the upper plate moves with a velocity of $0\mathrm{.}1\frac{m}{s}.$ There is no pressure gradient pushing the fluid. The mean fluid temperature at the left end is $20C.$ The flow can be assumed to be fully developed thermally and hydrodynamically. The following table can be used for all properties. The entire assembly is insulated from all sides.

Insulated

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Find

The steady$-$state velocity profile in the fluid in the vertical direction $(1)$

The steady state temperature profile in the fluid in the vertical direction as a function of the interface temperature between B and Fluid $-$ call it $T_s(2).$ Note that this $T_s$ will change along the length, and so will $T_m.$

Nuselt number at the B$-$Fluid interface as we did in the class $(2)$

Temperature profile in layers A and B in the vertical direction in terms of $T_s(2)$

What is the maximum temperature within the entire assembly, and where is it$?(2)$

What will be the outlet temperature of the fluid for a $10$ m long assembly? $(1)$

You can use the following equations to begin with for the first three questions:

$\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}+u\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{x}}+v\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{y}}=-\frac{\text{d}\text{e}\text{l}\text{P}}{\text{d}\text{e}\text{l}\text{x}}+(\frac{de{l}^{2}u}{del{x}^2}+\frac{de{l}^{2}u}{del{y}^2})$

$c_p\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{t}}+c_{p}u\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{x}}+c_{p}v\frac{\text{d}\text{e}\text{l}\text{T}}{\text{d}\text{e}\text{l}\text{y}}=k(\frac{de{l}^{2}T}{del{x}^2}+\frac{de{l}^{2}T}{del{y}^2})$