⚗ ChemE Tools

What The Flux

The calculator site your professors wish they built. Free tools for heat transfer, mass balance, fluids, thermo, and reaction engineering — built by a ChemE student surviving it with you.

🔥
Sensible Heat
Heat transfer for a temperature change
$$Q = m C_p \Delta T$$
Energy causing temperature change without phase change. For liquid water $C_p \approx 4184\ \text{J/kg·K}$.
Please fill in all fields.
Heat Transfer Q
—J
🧱
Fourier Conduction
Steady-state conduction through a flat wall
$$q = \dfrac{k A \Delta T}{L}$$
Thermal resistance $R_{th} = L/(kA)$. Composite walls in series: $R_{total} = \sum L_i/(k_i A)$.
All fields required; L nonzero.
Heat Rate q
—W
🌡
Convection (Newton's Law)
Surface heat flux from h, area, and ΔT
$$q = h A \left(T_s - T_\infty\right)$$
Free convection in air: $h \approx 2{-}25\ \text{W/m}^2\text{K}$. Forced liquid: $h \approx 500{-}10{,}000\ \text{W/m}^2\text{K}$.
Please fill in all fields.
Convective Heat Rate q
—W
〰
Nusselt → h
Convection coefficient from Nusselt number
$$h = \dfrac{Nu \cdot k}{L_c}$$
$L_c$ is diameter for pipe flow, length for flat plate. Get $Nu$ from Dittus-Boelter, Churchill-Bernstein, etc.
All fields required; L_c nonzero.
h (W/m²·K)
—W/m²·K
🔵
Prandtl Number
Ratio of momentum to thermal diffusivity
$$Pr = \dfrac{\mu C_p}{k}$$
$Pr \ll 1$: liquid metals. $Pr \approx 1$: gases. $Pr \gg 1$: viscous liquids. Appears in virtually all convective HT correlations.
All fields required; k nonzero.
Prandtl Number
—
☀
Radiation Heat Transfer
Net radiative flux between two surfaces
$$q = \varepsilon \sigma A \left(T_1^4 - T_2^4\right)$$σ = 5.67×10⁻⁸ W/m²·K⁴
Stefan-Boltzmann law. $\varepsilon=1$ for blackbody. T must be in Kelvin. $T^4$ dependence dominates at high temperatures.
All fields required; ε between 0–1.
Radiative Heat Rate q
—W
♨
LMTD Calculator
Log mean temperature difference
$$\Delta T_{lm} = \dfrac{\Delta T_1 - \Delta T_2}{\ln(\Delta T_1 / \Delta T_2)}$$
Counter-current: $\Delta T_1=T_{h,in}-T_{c,out}$, $\Delta T_2=T_{h,out}-T_{c,in}$. Counter-current always gives larger LMTD.
ΔT values must be positive.
Log Mean ΔT
—°C
📐
Heat Exchanger Area
Required area from duty, U, and LMTD
$$A = \dfrac{Q}{U \Delta T_{lm}}$$
Liquid–liquid S&T: $U \approx 300{-}1000\ \text{W/m}^2\text{K}$. Gas–gas: $U \approx 10{-}50\ \text{W/m}^2\text{K}$.
All fields required; U and ΔTlm nonzero.
Required Area A
—m²
🔗
Overall Heat Transfer Coefficient U
U from convection and wall conduction resistances
$$\frac{1}{U} = \frac{1}{h_i} + \frac{t}{k} + \frac{1}{h_o}$$
Flat-wall approximation. For cylindrical walls use log-mean area. Add fouling: $1/U = 1/h_i + R_{f,i} + t/k + R_{f,o} + 1/h_o$.
All fields required and nonzero.
Overall Coefficient U
—W/m²·K
⏱
Biot Number
Check lumped capacitance validity
$$Bi = \dfrac{h L_c}{k}$$Lumped valid if Bi < 0.1
$L_c=V/A_s$. Sphere: $r/3$; cylinder: $r/2$; plane wall: $L/2$. If $Bi < 0.1$, object is spatially uniform.
All fields required; k nonzero.
Biot Number
—
📉
Lumped Capacitance T(t)
Transient temperature decay (Bi < 0.1)
$$T(t) = T_\infty + (T_i - T_\infty)\, e^{-t/\tau}$$τ = ρVCp/(hAs)
At $t=\tau$, object has covered ~63% of temperature change. Only valid when $Bi < 0.1$.
All fields required; τ nonzero.
Temperature at time t
—°C
Mass & Energy Balance
⚖
Mass Balance
Steady-state single-component balance
$$\dot{m}_{accum} = \dot{m}_{in} - \dot{m}_{out}$$
At steady state accumulation = 0. Nonzero means mass is changing with time.
Please fill in all fields.
Accumulation Rate
—kg/s
🧪
Mixing Concentration
Outlet concentration for two streams
$$C_{out} = \dfrac{F_1 C_1 + F_2 C_2}{F_1 + F_2}$$
Component balance on a mixing tee, no reaction, complete mixing.
All fields required; total flow nonzero.
Mixed Concentration
—
⚡
Open System Energy Balance
Steady-flow heat duty
$$\dot{Q} = \dot{m} C_p \Delta T$$
Neglects KE, PE, shaft work. For phase-change: $\dot{Q}=\dot{m}(C_p\Delta T+\Delta H_{vap})$.
Please fill in all fields.
Heat Duty Q̇
—W
Fluid Mechanics
🌊
Reynolds Number
Determine flow regime
$$Re = \dfrac{\rho v D}{\mu}$$
Pipe: $Re<2300$ laminar, $2300{-}4000$ transitional, $>4000$ turbulent.
All fields required; μ nonzero.
Reynolds Number
—
💧
Pipe Velocity from Flow Rate
Average velocity from Q and diameter
$$v = \dfrac{4Q}{\pi D^2}$$
Average cross-sectional velocity for fully developed pipe flow. Feeds directly into Re and Darcy-Weisbach.
Both fields required; D nonzero.
Average Velocity v
—m/s
🌀
Bernoulli Equation
Pressure at point 2 from point 1 conditions
$$P_2 = P_1 + \tfrac{1}{2}\rho(v_1^2-v_2^2)+\rho g(z_1-z_2)$$
Inviscid, steady, incompressible, along a streamline. For real systems subtract head loss term $\rho g h_L$.
All fields required.
Pressure P₂
—Pa
📉
Darcy–Weisbach ΔP
Frictional pressure drop in a pipe
$$\Delta P = f_D \dfrac{L}{D} \dfrac{\rho v^2}{2}$$
Laminar: $f_D=64/Re$. Turbulent: use Swamee-Jain below. Fanning $f=f_D/4$.
All fields required; D nonzero.
Pressure Drop ΔP
—Pa
🔩
Friction Factor (Swamee-Jain)
Explicit turbulent friction factor
$$f_D = \dfrac{0.25}{\left[\log_{10}\!\left(\dfrac{\varepsilon/D}{3.7}+\dfrac{5.74}{Re^{0.9}}\right)\right]^2}$$
Explicit Colebrook approximation, ~3% accuracy. Auto-switches to $f_D=64/Re$ for laminar flow.
All fields required; D nonzero.
Darcy Friction Factor f_D
—
Thermodynamics
💨
Ideal Gas Law
Solve for pressure
$$P = \dfrac{nRT}{V}$$R = 8.314 J/mol·K
Valid at low P, high T relative to critical point. Non-ideal: $PV=ZnRT$.
All fields required; V nonzero.
Pressure
—Pa
🔵
Van der Waals EOS
Real gas pressure from T and V
$$P = \dfrac{nRT}{V-nb} - a\dfrac{n^2}{V^2}$$
CO₂: $a=0.364\ \text{Pa·m}^6/\text{mol}^2$, $b=4.267\times10^{-5}\ \text{m}^3/\text{mol}$.
All fields required; (V−nb) must be positive.
Pressure
—Pa
🫧
Antoine Vapor Pressure
Saturation pressure from temperature
$$\log_{10} P^{sat} = A - \dfrac{B}{C+T}$$
Defaults: water, T in °C, $P^{sat}$ in mmHg, valid 60–150°C. Always verify constant units.
All fields required.
Vapor Pressure Psat
—(units per constants)
💧
Clausius-Clapeyron
Vapor pressure at a new temperature
$$\ln\!\frac{P_2}{P_1}=-\frac{\Delta H_{vap}}{R}\!\left(\frac{1}{T_2}-\frac{1}{T_1}\right)$$
T in Kelvin; pressure units cancel. Assumes constant $\Delta H_{vap}$ and ideal vapor.
All fields required; T₁ and T₂ nonzero.
Vapor Pressure P₂
—same units as P₁
⚙
Carnot Efficiency
Maximum thermal efficiency
$$\eta_{Carnot} = 1 - \dfrac{T_C}{T_H}$$
Theoretical maximum for any heat engine. Both T in Kelvin. Real cycles achieve 30–45% of this.
T_H must be greater than T_C and nonzero.
Carnot Efficiency η
—%
❄
COP — Refrigerator / Heat Pump
Coefficient of performance
$$COP_{ref}=\dfrac{T_C}{T_H-T_C}\quad COP_{hp}=\dfrac{T_H}{T_H-T_C}$$
Carnot (maximum) COPs. Real systems achieve 40–60% of these. $COP_{hp}=COP_{ref}+1$ always.
T_H must be greater than T_C.
COP (Ref / Heat Pump)
—
🔧
Isentropic Compression/Expansion
Outlet temperature for adiabatic process
$$\frac{T_2}{T_1}=\left(\frac{P_2}{P_1}\right)^{\!\frac{\gamma-1}{\gamma}}$$
Reversible adiabatic ideal gas. Diatomic (air): $\gamma\approx1.4$. Monatomic: $\gamma\approx1.67$.
All fields required; P₁ and γ nonzero.
Outlet Temperature T₂
—K
🔄
Reactor Conversion
Fractional conversion from molar flows
$$X=\dfrac{F_{A0}-F_A}{F_{A0}}$$
Defined on limiting reactant A. Batch: $X=(N_{A0}-N_A)/N_{A0}$. Always 0–1.
All fields required; F_A0 nonzero.
Conversion X
—%
🧫
CSTR Volume
Required volume for a given conversion
$$V=\dfrac{F_{A0}X}{-r_A}$$
Perfect mixing — exit = interior conditions. Rate $-r_A$ evaluated at exit $X$.
All fields required; -r_A nonzero, X between 0–1.
Reactor Volume V
—m³
🔬
PFR Volume (1st Order)
Levenspiel integral for first-order reaction
$$V=\dfrac{F_{A0}}{kC_{A0}}\ln\!\left(\dfrac{1}{1-X}\right)$$
Integrated for irreversible 1st order liquid-phase reaction $-r_A=kC_{A0}(1-X)$. PFR outperforms single CSTR for positive-order reactions.
All fields required; k, C_A0 nonzero, X between 0–0.9999.
Reactor Volume V
—m³
⏳
Space Time τ
Reactor residence time
$$\tau=\dfrac{C_{A0}V}{F_{A0}}$$
Time to process one reactor volume of feed at inlet conditions. $Da=\tau k$ for 1st order.
All fields required; F_A0 nonzero.
Space Time τ
—s
📈
Arrhenius Rate Constant
k₂ from k₁, Eₐ, T₁, T₂
$$k_2=k_1\exp\!\left[-\frac{E_a}{R}\!\left(\frac{1}{T_2}-\frac{1}{T_1}\right)\right]$$
$R=8.314\ \text{J/mol·K}$. 10°C rise roughly doubles $k$ for $E_a\approx50{-}80\ \text{kJ/mol}$.
All fields required; T₁ and T₂ nonzero.
Rate Constant k₂
—same units as k₁
⏱
Reaction Half-Life
t₁/₂ for 1st and 2nd order
$$t_{1/2}^{(1)}=\dfrac{\ln2}{k}\qquad t_{1/2}^{(2)}=\dfrac{1}{kC_{A0}}$$
1st order half-life is concentration-independent. 2nd order depends on $C_{A0}$.
All fields required; k and C_A0 nonzero.
Half-Life (1st / 2nd order)
—
🦠
Michaelis-Menten
Enzyme reaction rate
$$-r_A=\dfrac{V_{max}C_A}{K_M+C_A}$$
$K_M$ = substrate at half-max rate. $C_A\ll K_M$: pseudo-1st order. $C_A\gg K_M$: zeroth order.
All fields required.
Reaction Rate -r_A
—mol/m³·s
🔢
Damköhler Number
Reaction rate vs. flow rate
$$Da=\tau\cdot k\quad\text{(1st order)}$$
$Da\ll1$: low conversion. $Da\gg1$: high conversion. CSTR: $X=Da/(1+Da)$.
Both fields required.
Damköhler Number Da
—
0️⃣
0th Order Batch
C_A vs. time, zeroth-order reaction
$$C_A=C_{A0}-kt$$
Rate independent of concentration. Stops at $t=C_{A0}/k$.
All fields required.
Concentration C_A
—mol/m³
1️⃣
1st Order Batch
C_A vs. time, first-order reaction
$$C_A=C_{A0}\,e^{-kt}$$
Most common kinetic form. $t_{1/2}=\ln2/k$ is constant.
All fields required.
Concentration C_A
—mol/m³
2️⃣
2nd Order Batch
C_A vs. time, second-order reaction
$$\dfrac{1}{C_A}=\dfrac{1}{C_{A0}}+kt$$
For $-r_A=kC_A^2$. Plot $1/C_A$ vs. $t$ — linear with slope $k$.
All fields required.
Concentration C_A
—mol/m³
Mass Transfer
💧
Fick's Law
Molar flux from concentration gradient
$$J_A=D_{AB}\dfrac{C_{A1}-C_{A2}}{\Delta z}$$
Gases: $D_{AB}\sim10^{-5}\ \text{m}^2/\text{s}$. Liquids: $\sim10^{-9}\ \text{m}^2/\text{s}$.
All fields required; Δz nonzero.
Molar Flux J_A
—mol/m²·s
🔀
Convective Mass Transfer
Flux from mass transfer coefficient k_c
$$N_A=k_c\left(C_{A,s}-C_{A,\infty}\right)$$
Analog of Newton's law of cooling. Chilton-Colburn: $k_c=h/(\rho C_p Le^{2/3})$.
Please fill in all fields.
Molar Flux N_A
—mol/m²·s
〽
Sherwood Number → k_c
Mass transfer coefficient from Sh
$$k_c=\dfrac{Sh\cdot D_{AB}}{L_c}$$
Turbulent pipe: $Sh=0.023Re^{0.8}Sc^{1/3}$.
All fields required; L_c nonzero.
Mass Transfer Coeff. k_c
—m/s
📊
Schmidt Number
Ratio of momentum to mass diffusivity
$$Sc=\dfrac{\mu}{\rho D_{AB}}$$
$Sc\ll1$: liquid metals. $Sc\approx1$: gases. $Sc\gg1$: liquids. Analog of Prandtl.
All fields required; ρ and D_AB nonzero.
Schmidt Number Sc
—
Unit Converter
🌡 Temperature
→
—
→
—
→
—
⚡ Pressure
→
—
→
—
→
—
→
—
💧 Volumetric Flow
→
—
→
—
⚖ Mass & Density
→
—
→
—
⚡ Energy & Power
→
—
→
—
→
—
📐 Viscosity
→
—
→
—
Formula Reference

Heat Transfer

$Q=mC_p\Delta T$
Sensible heat
$Q=UA\Delta T_{lm}$
HX duty
$q=kA\Delta T/L$
Fourier conduction
$q=hA(T_s-T_\infty)$
Newton's cooling
$h=Nu\cdot k/L_c$
Nusselt → h
$Pr=\mu C_p/k$
Prandtl number
$q=\varepsilon\sigma A(T_1^4-T_2^4)$
Radiation
$Bi=hL_c/k$
Biot number
$T(t)=T_\infty+(T_i-T_\infty)e^{-t/\tau}$
Lumped cap.

Fluid Mechanics

$Re=\rho vD/\mu$
Reynolds number
$v=4Q/(\pi D^2)$
Pipe velocity
$\Delta P=f_D(L/D)\rho v^2/2$
Darcy-Weisbach
$f_D=64/Re$
Laminar friction
$P_2=P_1+\tfrac{1}{2}\rho(v_1^2-v_2^2)+\rho g\Delta z$
Bernoulli

Thermodynamics

$PV=nRT$
Ideal gas
$P=nRT/(V-nb)-an^2/V^2$
van der Waals
$\log P^*=A-B/(C+T)$
Antoine
$\eta=1-T_C/T_H$
Carnot efficiency
$T_2/T_1=(P_2/P_1)^{(\gamma-1)/\gamma}$
Isentropic

Reaction Engineering

$X=(F_{A0}-F_A)/F_{A0}$
Conversion
$V=F_{A0}X/(-r_A)$
CSTR design eq.
$V=(F_{A0}/kC_{A0})\ln(1/(1-X))$
PFR 1st order
$k_2=k_1e^{-E_a/R(1/T_2-1/T_1)}$
Arrhenius
$C_A=C_{A0}-kt$
0th order batch
$C_A=C_{A0}e^{-kt}$
1st order batch
$1/C_A=1/C_{A0}+kt$
2nd order batch
$Da=\tau k$
Damköhler

Mass Transfer

$J_A=D_{AB}(C_{A1}-C_{A2})/\Delta z$
Fick's law
$N_A=k_c(C_{A,s}-C_{A,\infty})$
Convective flux
$k_c=Sh\cdot D_{AB}/L_c$
Sherwood → k_c
$Sc=\mu/(\rho D_{AB})$
Schmidt number

Dimensionless Numbers

$Re=\rho vL/\mu$
Reynolds
$Nu=hL/k$
Nusselt
$Pr=\mu C_p/k$
Prandtl
$Bi=hL_c/k$
Biot
$Sh=k_cL/D_{AB}$
Sherwood
$Sc=\mu/(\rho D_{AB})$
Schmidt
$Le=Sc/Pr=\alpha/D_{AB}$
Lewis
$Da=\tau k$
Damköhler
What The Flux v0.5Surviving ChemE, one calculator at a time.