The unit of overall heat transfer coefficient is
W/m 2K
Overall Heat Transfer Coefficient: Understanding Its Unit
The overall heat transfer coefficient, commonly symbolized as \(U\), is a pivotal concept in the field of heat transfer, particularly in the context of heat exchangers and insulation. It quantifies the rate at which heat is transferred through a unit area for every unit of temperature difference between the two primary fluid streams or regions.
Heat Transfer Coefficient Definition
The overall heat transfer coefficient effectively lumps together all the individual thermal resistances present in a heat transfer path. This includes resistances due to convection on both fluid sides, conduction through solid walls, and potentially fouling layers. It provides a single value to characterize the combined heat transfer performance of a system.
Formula for Overall Heat Transfer
The fundamental equation that relates the rate of heat transfer to the overall heat transfer coefficient, the heat transfer area, and the temperature difference is:
\[Q = U A \Delta T\]
Let's break down each term in this formula:
- \(Q\): This represents the total rate of heat transfer, which is the amount of energy transferred per unit of time. Its standard International System of Units (SI unit) is Watts (\(\text{W}\)).
- \(U\): This is the overall heat transfer coefficient, which we are trying to determine the unit for.
- \(A\): This denotes the heat transfer surface area across which the heat transfer occurs. Its SI unit is square meters (\(\text{m}^2\)).
- \(\Delta T\): This signifies the overall temperature difference driving the heat transfer. Its SI unit is Kelvin (\(\text{K}\)) or degrees Celsius (\(^\circ\text{C}\)), where a difference of 1 K is equivalent to 1 \(^\circ\text{C}\).
Deriving the Unit of Overall Heat Transfer Coefficient
To find the unit of the overall heat transfer coefficient (\(U\)), we need to rearrange the heat transfer formula \(Q = U A \Delta T\) to isolate \(U\):
\[U = \frac{Q}{A \Delta T}\]
Now, we can substitute the SI units for each of the quantities on the right side of the equation:
- Unit of \(Q\) (Heat transfer rate) = \(\text{W}\)
- Unit of \(A\) (Heat transfer area) = \(\text{m}^2\)
- Unit of \(\Delta T\) (Temperature difference) = \(\text{K}\)
Plugging these units into the rearranged equation for \(U\):
\[\text{Unit of } U = \frac{\text{W}}{(\text{m}^2) \cdot (\text{K})}\]
Thus, the unit of the overall heat transfer coefficient is \(\text{W/m}^2\text{K}\).
Analyzing the Options for Overall Heat Transfer Coefficient
Let's compare our derived unit with the given options:
- Option 1: \(\text{W/m}^3\text{K}\) - This unit is incorrect for the overall heat transfer coefficient.
- Option 2: \(\text{W/m}^2\text{K}\) - This unit perfectly matches our derivation for the overall heat transfer coefficient.
- Option 3: \(\text{W/m}^2\) - This unit represents heat flux, which is the heat transfer rate per unit area. It does not include the temperature difference term.
- Option 4: \(\text{W/mK}\) - This unit is for thermal conductivity (\(k\)), a material property that describes its ability to conduct heat. It is different from the overall heat transfer coefficient.
Based on the detailed derivation and analysis, the correct unit for the overall heat transfer coefficient is \(\text{W/m}^2\text{K}\).
Important Questions from Convection
An ic engine has a bore and a stroke length of 4 cm each. The total surface area through which heat transfer takes place in cm2 is.
Which of the following is not the regimes of pool boiling?
Nucleate boiling regime is formed approximately between
[ΔTexcess = excess temperature]Analogy between momentum and heat transfer is known as
For flow through a pipe of radius R, the velocity and temperature distribution are as follows:
\(u\left( {r,x} \right) = {C_1},and\ T\left( {r,x} \right) = {C_2}{\left[{1 - (\frac{r}{R})^3} \right]}\), where C1 and C2 are constants. The bulk mean temperature is given by \({T_m} = \frac{2}{{{u_m}{R^2}}}\mathop \smallint \limits_0^R u\left( {r,x} \right)T\left( {r,x} \right)rdr,\)
with Um being the mean velocity of flow. The value of Tm is
