Consider steady one-dimensional heat transfer through a plane wall exposed to convection from both sides to environments at known temperatures T[infinity]1 and T[infinity]2 with known heat transfer coefficients h1 and h2. Once the rate of heat transfer has been evaluated, explain how you would determine the temperature of each surface.

Now find the temperature of each surface, we have that the the temperature on the left side of the wall is T∞₁ - Q/h₁A and  the temperature on the right side of the wall is T∞₂ + Q/h₂A.

Note: kindly find an attached diagram to the complete question given below.

Sources: The diagram/image was researched and taken from Slader website.

Explanation:

Solution

Let us consider the rate of heat transfer through the plane wall which can be obtained from the relations given below:

Q = T∞₁ -T₁/1/h₁A = T₁ -T₂/L/kA =T₂ -T∞₂/1/h₂A

= T∞₁  - T∞₂/1/h₁A + L/kA + 1/h₂A

Here

The convective heat transfer coefficient on the left side of the wall is h₁, while the convective heat transfer coefficient on the right side of the wall is h₂. the thickness of the wall is L, the thermal conductivity of the wall material is k, and the heat transfer area on one side of the wall is A. Q is refereed to as  heat transfer.

Thus

Let us consider the convection heat transfer on the left side of the wall which is given below:

Q = T∞₁ -T₁/1/h₁A

T₁ = T∞₁ - Q/h₁A

Therefore the temperature on the left side of the wall is T∞₁ - Q/h₁A

Now

Let us consider the convection heat transfer  on the left side of the wall which is given below:

Q= T₂ -T∞₂/1/h₂A

T₂ = T∞₂ + Q/h₂A

Therefore the temperature on the right side of the wall is T∞₂ + Q/h₂A

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