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The capacity-rate ratio divides the smaller by the larger heat-capacity rate of the two fluids.
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Formula
Cr dimensionless; C=ṁcp in W/K
| Symbol | Meaning | Unit |
|---|---|---|
| Heat-capacity-rate ratio | dimensionless | |
| Smaller and larger fluid heat-capacity rates ṁcp | W/K |
C_r=\frac{C_{min}}{C_{max}}C=ṁcp is the power needed to change a stream temperature by one kelvin. Thus 0≤Cr≤1. Cr is a parameter in ε-NTU analysis; alone it does not determine exchanger area or effectiveness without NTU and flow arrangement.
C=ṁcp is the power needed to change a stream temperature by one kelvin. Thus 0≤Cr≤1. Cr is a parameter in ε-NTU analysis; alone it does not determine exchanger area or effectiveness without NTU and flow arrangement.
The capacity-rate ratio divides the smaller by the larger heat-capacity rate of the two fluids.
Base equation for the target quantity
Preserve signs, boundary conditions and units when rearranging.
Work through the numerical example for “Heat-capacity-rate ratio of a heat exchanger” and check its unit and magnitude.
For C1=2 kW/K and C2=5 kW/K, Cr=0.40.
Substituting a related quantity that shares the same symbol.
Use variable definitions and check: Cr dimensionless; C=ṁcp in W/K.
Formula cluster
The capacity-rate ratio divides the smaller by the larger heat-capacity rate of the two fluids.
For C1=2 kW/K and C2=5 kW/K, Cr=0.40.
Calculate the heat-capacity-rate parameter for exchanger analysis.
Here is how to work through a typical Heat-capacity-rate ratio of a heat exchanger (Cr = Cmin/Cmax) task step by step:
Task
Work through the numerical example for “Heat-capacity-rate ratio of a heat exchanger” and check its unit and magnitude.
Solution path
For C1=2 kW/K and C2=5 kW/K, Cr=0.40.
C=ṁcp is the sensible heat rate a stream absorbs or releases per kelvin of temperature change. Its unit is W/K. Phase change or strongly varying cp can make a constant rate inadequate. Cr is one ε-NTU parameter; it does not encode geometry or flow arrangement. Application: Calculate the heat-capacity-rate parameter for exchanger analysis. The numerical example For C1=2 kW/K and C2=5 kW/K, Cr=0.40 anchors the idea in a concrete measurement case. The corresponding units are Cr dimensionless; C=ṁcp in W/K. For C1=2 kW/K and C2=5 kW/K, Cr=0.40. This checks that the reference quantities are compatible.
Cmin is the smaller of two positive capacity rates divided by Cmax, so the ratio lies between zero and one. Values outside suggest swapped inputs, negative data or inconsistent units. Cr is one ε-NTU parameter; it does not encode geometry or flow arrangement. The corresponding units are Cr dimensionless; C=ṁcp in W/K. For C1=2 kW/K and C2=5 kW/K, Cr=0.40. This checks that the reference quantities are compatible. Scope: C=ṁcp is the power needed to change a stream temperature by one kelvin. Thus 0≤Cr≤1. Cr is a parameter in ε-NTU analysis; alone it does not determine exchanger area or effectiveness without NTU and flow arrangement. A practical application is Calculate the heat-capacity-rate parameter for exchanger analysis.
Together with NTU, Cr affects how closely an exchanger approaches maximum transfer. The relation depends on counterflow, parallel flow and other arrangements. Cr alone cannot predict heat rate without inlet states, flow and area. Cr is one ε-NTU parameter; it does not encode geometry or flow arrangement. Scope: C=ṁcp is the power needed to change a stream temperature by one kelvin. Thus 0≤Cr≤1. Cr is a parameter in ε-NTU analysis; alone it does not determine exchanger area or effectiveness without NTU and flow arrangement. A practical application is Calculate the heat-capacity-rate parameter for exchanger analysis.
Write the quantity and unit from the variable list next to every value: Cr dimensionless; C=ṁcp in W/K. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example For C1=2 kW/K and C2=5 kW/K, Cr=0.40. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Cr is one ε-NTU parameter; it does not encode geometry or flow arrangement.
The background states this starting condition: C=ṁcp is the power needed to change a stream temperature by one kelvin. Thus 0≤Cr≤1. Cr is a. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Cr is one ε-NTU parameter; it does not encode geometry or flow arrangement.
Quanta exam set
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