Governing Thermal Equations & Calculation Methodology
Designing a plate heat exchanger condenser requires evaluating multi-phase heat transport dynamics. Plate heat exchangers (PHE) possess extremely high thermal effectiveness relative to shell-and-tube alternatives due to their corrugated geometric patterns, promoting early boundary layer turbulence even at low Reynolds numbers.
1. Condensate Thermal Duty ($Q$)
Assuming pure saturated vapor enters without subcooling, total thermal duty depends on the phase change rate and latent heat of vaporization $h_{fg}$:
$$Q = \dot{m}_v \cdot h_{fg}$$Simultaneously, heat removed by the secondary liquid side balances this load:
$$Q = \dot{m}_c \cdot c_{p,c} \cdot (t_{c,out} - t_{c,in})$$2. Logarithmic Mean Temperature Difference ($\Delta T_{lm}$)
For single-component condensation occurring at constant saturation temperature $T_{sat}$, temperature differences at terminal channel ends simplify to:
$$\Delta T_1 = T_{sat} - t_{c,in}$$ $$\Delta T_2 = T_{sat} - t_{c,out}$$ $$\Delta T_{lm} = \frac{\Delta T_1 - \Delta T_2}{\ln\left(\frac{\Delta T_1}{\Delta T_2}\right)}$$3. Service Overall Heat Transfer Coefficient ($U_{service}$)
Fouling resistance ($R_f$) degrades heat flux over time. The operational transfer coefficient accounts for this thermal degradation:
$$\frac{1}{U_{service}} = \frac{1}{U_{clean}} + R_f$$4. Surface Area Requirement ($A_{total}$) & Plate Sizing
Total surface area needed to perform heat exchange duty is derived via Newton's Law of Cooling:
$$A_{total} = \frac{Q}{U_{service} \cdot \Delta T_{lm}}$$The minimal required plate count $N_p$ rounds up to an even integer to satisfy double-sided flow symmetry:
$$N_p = \left\lceil \frac{A_{total}}{A_{plate}} \right\rceil$$How to Use This Calculator
- Define Vapor Conditions: Enter the fluid saturation temperature ($T_{sat}$), vapor flow rate ($\dot{m}_v$), and specific enthalpy of condensation ($h_{fg}$).
- Define Cooling Parameters: Supply the inlet ($t_{c,in}$) and target outlet ($t_{c,out}$) temperatures of the secondary liquid alongside its specific heat ($c_{p,c}$).
- Set Plate Specifications: Input clean overall HTC, single plate surface area ($A_p$), and anticipated operational fouling factors ($R_f$).
- Execute Analysis: Click the Calculate Design Parameters button to generate key design output parameters instantly.