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Gshf Great Sensible Heat Factor

Reference data and engineering information about gshf great sensible heat factor for thermodynamics applications.

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Overview

Engineering reference data for Gshf Great Sensible Heat Factor in thermodynamics.

Key Formulas

First Law

ΔU=Q−W\Delta U = Q - W

Energy is conserved — heat added minus work done.

Ideal Gas Law

PV=nRTPV = nRT

Relates pressure, volume, and temperature of an ideal gas.

Heat Transfer

Q=mcΔTQ = mc\Delta T

Sensible heat transfer.

Carnot Efficiency

η=1−TC/TH\eta = 1 - T_C/T_H

Maximum efficiency between two temperatures.

Variables

SymbolDescriptionUnit
UUInternal energyJ
QQHeatJ
WWWorkJ
PPPressurePa
VVVolumem³
TTTemperatureK

Worked Example

The GSHF formula is applied to determine the combined sensible heat factor for a room, considering both internal loads and the conditioning of fresh air.

Given Data:

  • Sensible heat generated in the room, Qs=4 kWQ_s = 4 \text{ kW}
  • Latent heat generated in the room, Ql=1.4 kWQ_l = 1.4 \text{ kW} (implying Total heat, Qt=Qs+Ql=5.4 kWQ_t = Q_s + Q_l = 5.4 \text{ kW})
  • Mass flow rate of fresh air, mf=1000 kg/hm_f = 1000 \text{ kg/h}
  • Fresh air temperature, tf=28 °Ct_f = 28 \text{ °C}
  • Specific enthalpy of fresh air, hf=60 kJ/kgh_f = 60 \text{ kJ/kg}
  • Room air temperature, tr=22 °Ct_r = 22 \text{ °C}
  • Specific enthalpy of room air, hr=45 kJ/kgh_r = 45 \text{ kJ/kg}
  • Specific heat of air, cp≈1.0 kJ/(kg⋅°C)c_p \approx 1.0 \text{ kJ/(kg·°C)} or 1000 J/(kg⋅°C)1000 \text{ J/(kg·°C)}

Calculation:

First, convert the fresh air mass flow rate to kg/s: mf=1000 kg/h×1 h3600 s≈0.2778 kg/sm_f = 1000 \text{ kg/h} \times \frac{1 \text{ h}}{3600 \text{ s}} \approx 0.2778 \text{ kg/s}

The numerator represents the total sensible load: Numerator=Qs+mf⋅cp⋅(tf−tr)\text{Numerator} = Q_s + m_f \cdot c_p \cdot (t_f - t_r) =4 kW+(0.2778 kg/s)⋅(1.0 kJ/(kg⋅°C))⋅(28 °C−22 °C)= 4 \text{ kW} + (0.2778 \text{ kg/s}) \cdot (1.0 \text{ kJ/(kg·°C)}) \cdot (28 \text{ °C} - 22 \text{ °C}) =4 kW+(0.2778 kg/s)⋅(6 kJ/kg)= 4 \text{ kW} + (0.2778 \text{ kg/s}) \cdot (6 \text{ kJ/kg}) =4 kW+1.667 kW=5.667 kW= 4 \text{ kW} + 1.667 \text{ kW} = 5.667 \text{ kW}

The denominator represents the total load (sensible + latent): Denominator=Qt+mf⋅(hf−hr)\text{Denominator} = Q_t + m_f \cdot (h_f - h_r) =5.4 kW+(0.2778 kg/s)⋅(60 kJ/kg−45 kJ/kg)= 5.4 \text{ kW} + (0.2778 \text{ kg/s}) \cdot (60 \text{ kJ/kg} - 45 \text{ kJ/kg}) =5.4 kW+(0.2778 kg/s)⋅(15 kJ/kg)= 5.4 \text{ kW} + (0.2778 \text{ kg/s}) \cdot (15 \text{ kJ/kg}) =5.4 kW+4.167 kW=9.567 kW= 5.4 \text{ kW} + 4.167 \text{ kW} = 9.567 \text{ kW}

Finally, the Great Sensible Heat Factor (GSHF) is: GSHF=5.667 kW9.567 kW≈0.59GSHF = \frac{5.667 \text{ kW}}{9.567 \text{ kW}} \approx 0.59

Interpretation: A GSHF of 0.59 indicates that 59% of the total cooling load of the system (room load plus fresh air load) is sensible heat. This factor is crucial for selecting cooling coils, as it determines the required sensible cooling capacity relative to the total cooling capacity.

References

Source: engineeringtoolbox.com