This equation from problem 2 is needed to solve problem 3.
Qa
Assuming cartesian coordinates,
Based on the given vector field,
............................................................( as given in question)
where and are unit vectors along x and y axes.
and Temperature field
we get
units.,
where and are unit vectors along x and y axes.
Therefore this shows that, heat is transferred in negative x direction along the x axis, and in positive y axis along the Y axis.
As depicted above using a schematic diagram.
Heat will go to the top and the left edges of the plate. Since no temperature variation along the z axis.
Qb
Gradient of temperature is given by
this operation on
gives,
(ans)
where and are unit vectors along x and y axes.
Qd
Since Heat transfer rate as a vector field is a vector quantity we can take Cartesian components of this vector along x and y axes.
Along x axis,
Based on the gradient field, Temperature is increasing along the positive x direction with respect to the x coordinates as
This means heat is transferred from positive x end of the plate to the negative x end of the plate along x axis.
Similarly
Along y axis,
Temperature is decreasing in the +y direction, this implies heat transfer is from negative y direction to the positive y direction.
Problem 2 temperature field. Problem 3 (Fourier's Law of Heat Flow) From a temperature field, w...
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