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Sensible Heat Factor (SHF) during heating and humidification Given h1 = enthalpy of air entering the heating coil, h2 = enthalpy of air leaving the heating coil, and hA = enthalpy of air at the end of the humidification process, the sensible heat factor is defined as which of the following ratios?

Difficulty: Medium

Correct Answer: SHF = (h2 - h1) / (hA - h1)

Explanation:


Introduction / Context:
In air-conditioning psychrometrics, the sensible heat factor (SHF) quantifies how much of the total heat added or removed is sensible (temperature change) versus latent (moisture change). For a heating and humidification process, air is first heated (sensible addition) and then moisture is added (latent addition). Correctly formulating SHF ensures accurate coil sizing and process line plotting on the psychrometric chart.



Given Data / Assumptions:

  • h1: enthalpy at the coil inlet (state 1).
  • h2: enthalpy at the coil outlet after sensible heating (state 2).
  • hA: final air state after humidification (state A).
  • Steady flow and negligible heat losses to surroundings.


Concept / Approach:
By definition, SHF = sensible heat / total heat for the process of interest. In this sequence, sensible heat is represented by the change from h1 to h2, while total heat added is from h1 to hA. Therefore SHF = (h2 - h1) / (hA - h1). This ratio lies between 0 and 1, with smaller values indicating larger latent components.



Step-by-Step Solution:

Identify sensible portion: heating at essentially constant humidity ratio from state 1 to 2 → enthalpy change = h2 - h1.Identify total heat added: overall change from state 1 to final state A → enthalpy change = hA - h1.Form ratio: SHF = (h2 - h1) / (hA - h1).Check bounds: if no humidification (hA = h2), SHF = 1; if only latent addition (h2 = h1), SHF = 0.


Verification / Alternative check:
On the psychrometric chart, the process 1→2 is a nearly horizontal line (constant humidity ratio), and 2→A is a roughly vertical/up-right move (moisture addition). The slope of the overall process line relates to SHF, and the above formula matches the geometry.



Why Other Options Are Wrong:

(hA - h2) / (hA - h1): represents the latent share, not the sensible share.(hA - h1) / (h2 - h1): reciprocal of SHF.(h2 - h1) / hA or (h1 - h2) / (hA - h2): not dimensionally or conceptually aligned with sensible-to-total heat.



Common Pitfalls:
Confusing SHF for cooling with SHF for heating-humidification; always identify the sensible leg and total leg for the specific process path under consideration.



Final Answer:

SHF = (h2 - h1) / (hA - h1)

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