Dimensionless parameter among the following options is

Question

Specific heat, coefficient of viscosity, and thermal conductivity are related in the

Answer 1

A quantity is dimensionless only when its defining ratio cancels all physical units, leaving a pure number.

heat exchanger effectiveness: defined as actual heat transfer divided by maximum possible heat transfer, both in watts, so the units cancel completely.
humid heat of air-water vapour mixture: carries units of $\text{kJ/kg.K}$, it is a specific heat term, not dimensionless.
humid volume of air-water vapour mixture: measured in $\text{m}^3/\text{kg}$, a volume per unit mass, so it has dimensions.
overall heat transfer coefficient: expressed in $\text{W/m}^2.\text{K}$, again a dimensional quantity.

Only effectiveness survives the unit check, so option A is correct.

Answer 2

A quantity is dimensionless only when its defining ratio cancels all physical units, leaving a pure number.

heat exchanger effectiveness: defined as actual heat transfer divided by maximum possible heat transfer, both in watts, so the units cancel completely.
humid heat of air-water vapour mixture: carries units of $\text{kJ/kg.K}$, it is a specific heat term, not dimensionless.
humid volume of air-water vapour mixture: measured in $\text{m}^3/\text{kg}$, a volume per unit mass, so it has dimensions.
overall heat transfer coefficient: expressed in $\text{W/m}^2.\text{K}$, again a dimensional quantity.

Only effectiveness survives the unit check, so option A is correct.

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