d) Can we define the convection resistance for a unit surface area as the invers
ID: 2088839 • Letter: D
Question
d) Can we define the convection resistance for a unit surface area as the inverse of the convection heat transfer coefficient? e) Consider steady heat transfer through the wall of a room in winter. The convection heat transfer coefficient at the outer surface of the wall is three times that of the inner surface as a result of the wind surface of the wall do you think the temperature will be closer to the surrounding air tem 0 The thermal resistance networks can also be used approximately for multidimensional problems results? kind of multidimensional problems will the thermal resistance approach give adequate being infinitely long 8 What is an infinitely long cylinder? When is it proper to treat an actual cylinder as being infinitely and when is it not? Expi teady operation? t be used for a solid cylinder or sphere in s Can the thermal resistance concept s of insulation? How is it defined for a cylindrical layer? insulati hat is the critical radiusExplanation / Answer
d)
From Newton's law of cooling, The convection heat transfer = Q = hA(Tw - Ts )
Where h = convection heat transfer coefficient
A = Area
Tw = Wall temperature
Ts = Surroundings temperature.
From the analogy of electrical current flow, we can also write heat flow as a ratio of temperature difference to the thermal resistance.
Q = (Tw - Ts ) / (1/h*A)
Where thermal convection resistance = Rth = 1/h*A
For unit surface area, it can be written as Rth = 1/h.
So for the unit surface area, thermal convection resistance is defined as the inverse of the convective heat transfer coefficient.
e)
The outer surface of the wall will have temperature closer to the surrounding air temperature.
it is said that the convective heat transfer coefficient at the outer surface of the wall is three times to the inner surface of the wall, so the outer surface of the wall will dissipate heat quickly owing to have higher heat transfer coefficient compare to the inner surface. So the outer surface will come to thermal equilibrium with outside temperature quickly compared to the inner wall.
f)
the thermal resistance networks can also be used for multidimensional problems approximately under the following conditions.
1) Any plane wall normal to the x-axis is isothermal. ( Temperature vary in x-direction only)
2) Any plane parallel to the x-axis is adiabatic. This means heat transfer occurs in x-direction only.
Under this two conditions, multi-dimension problems can be converted to one dimension and we can use thermal resistance network.
g)
When one dimension of the cylinder is higher compared to two other dimensions or change in the other two dimensions is negligible in compared to the third dimension, the cylinder is said to be infinitely long.
h)
yes, thermal resistance concept can be used for solid cylinder or sphere.
Critical radius of insulation
In simple words “ The insulation radius at which resistance to heat flow is minimum called as critical radius.”
We know that by adding more insulation to a wall always decreases heat transfer. The thicker the insulation, the lower the heat transfer rate. This is expected, since the heat transfer area A is constant, and adding insulation always increases the thermal resistance of the wall without affecting the convection resistance. Adding insulation to a cylindrical piece or a spherical shell, however, is a different matter. The additional insulation increases the conduction resistance of the insulation layer but decreases the convection resistance of the surface because of the increase in the outer surface area for convection. The heat transfer from the pipe may increase or decrease, depending on which effect dominates.
In the cylindrical layer, the critical radius is defined as the ratio of the thermal conductance coefficient of insulation divided by external thermal convection coefficient.
Critical radius of cylinder = Rcr = K / h.
k= Thermal conductance coefficinet
h = external convective coefficient.
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