heat-transfer

Heat Transfer

Engineering-science skill for conduction, convection, and heat exchanger calculations. Built for chemical and petroleum engineering tutoring, equipment screening, and sanity checks on thermal problems.

Units: SI by default. Use K, W, m, s, kg unless the user specifies field units.

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Module 1 - Conduction

def conduction_plane_wall_q(k_W_mK, area_m2, delta_T_K, thickness_m):
    """
    Fourier law for 1D steady conduction through a plane wall.
    q = k A dT / L
    """
    if thickness_m <= 0:
        return None
    return k_W_mK * area_m2 * delta_T_K / thickness_m

def conduction_cylinder_q(k_W_mK, length_m, t_inner_K, t_outer_K,
                          r_inner_m, r_outer_m):
    """
    Radial conduction through a cylinder.
    q = 2*pi*k*L*(Ti-To) / ln(ro/ri)
    """
    import math
    if r_outer_m <= r_inner_m or r_inner_m <= 0:
        return None
    return (2.0 * math.pi * k_W_mK * length_m * (t_inner_K - t_outer_K) /
            math.log(r_outer_m / r_inner_m))

def thermal_resistance_plane(thickness_m, k_W_mK, area_m2):
    """Conduction resistance for a plane wall."""
    if k_W_mK <= 0 or area_m2 <= 0:
        return None
    return thickness_m / (k_W_mK * area_m2)

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Module 2 - Convection And Overall U

def convection_q(h_W_m2K, area_m2, delta_T_K):
    """
    Newton's law of cooling.
    q = h A dT
    """
    return h_W_m2K * area_m2 * delta_T_K

def convective_resistance(h_W_m2K, area_m2):
    """Convective thermal resistance."""
    if h_W_m2K <= 0 or area_m2 <= 0:
        return None
    return 1.0 / (h_W_m2K * area_m2)

def overall_u_from_resistances(resistances_m2K_W):
    """
    Overall heat-transfer coefficient from resistances on a common area basis.
    U = 1 / sum(R)
    """
    r_total = sum(resistances_m2K_W)
    if r_total <= 0:
        return None
    return 1.0 / r_total

Typical scales

Service	Typical h range
Free convection gas	5 to 25 W/m2-K
Forced convection liquid	100 to 5,000 W/m2-K
Condensation	1,000 to 20,000 W/m2-K
Boiling	2,500 to 100,000 W/m2-K

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Module 3 - Heat Exchangers

def lmtd(delta_t1_K, delta_t2_K):
    """
    Log-mean temperature difference.
    """
    import math
    if delta_t1_K <= 0 or delta_t2_K <= 0:
        return None
    if abs(delta_t1_K - delta_t2_K) < 1e-12:
        return delta_t1_K
    return (delta_t1_K - delta_t2_K) / math.log(delta_t1_K / delta_t2_K)

def heat_exchanger_duty(U_W_m2K, area_m2, lmtd_K, correction_factor=1.0):
    """
    Heat exchanger duty.
    q = U A F LMTD
    """
    return U_W_m2K * area_m2 * correction_factor * lmtd_K

def epsilon_ntu_effectiveness(ntu, c_r, flow="counter"):
    """
    Effectiveness for simple counterflow or parallel-flow exchangers.
    """
    import math
    if flow == "parallel":
        return (1.0 - math.exp(-ntu * (1.0 + c_r))) / (1.0 + c_r)
    # counterflow
    if abs(1.0 - c_r) < 1e-12:
        return ntu / (1.0 + ntu)
    return ((1.0 - math.exp(-ntu * (1.0 - c_r))) /
            (1.0 - c_r * math.exp(-ntu * (1.0 - c_r))))

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Module 4 - Transient Heating And Cooling

def biot_number(h_W_m2K, l_c_m, k_W_mK):
    """Biot number for lumped-capacitance screening."""
    if k_W_mK <= 0:
        return None
    return h_W_m2K * l_c_m / k_W_mK

def lumped_temperature(T_inf, T_initial, h_W_m2K, area_m2,
                       rho_kg_m3, volume_m3, cp_J_kgK, time_s):
    """
    Lumped capacitance temperature response.
    Valid when Bi < 0.1.
    """
    import math
    tau = rho_kg_m3 * volume_m3 * cp_J_kgK / (h_W_m2K * area_m2)
    return T_inf + (T_initial - T_inf) * math.exp(-time_s / tau)

Interpretation

• Bi < 0.1: lumped model usually acceptable
• Large Bi: internal gradients matter; do not use lumped capacitance

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Output Format

When using this skill, structure the answer as:

1. System and assumptions
2. Governing heat-transfer mode(s)
3. Equations and unit basis
4. Numerical result
5. Physical reasonableness check

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Learning Resources

Resource	Notes
Incropera, DeWitt, Bergman, Lavine	Standard heat transfer text
LearnChemE heat transfer playlist	Worked ChBE-style examples
MIT OCW heat transfer notes	Good derivations and dimensionless groups