# Documentation

 Symbol Name Unit T $T0_{gas}$ Gas reference temperature K $T_1$ Thermal resistance between one conductor and sheath K.m/W $t_1$ Thickness of insulation to sheath mm $t_{1t}$ Thickness of insulation to sheath, transient mm $T_2$ Thermal resistance of armour bedding K.m/W $t_2$ Thickness of bedding under armour mm $t_{2i}$ Thickness of insulation between conductors mm $T_3$ Thermal resistance of jacket K.m/W $t_3$ Thickness of serving over armour mm $T_{4d}$ Transient thermal resistance for daily load K.m/W $T_{4db}$ Correction of thermal resistance for backfill K.m/W $T_{4i}$ Thermal resistance of medium in the duct K.m/W $T_{4ii}$ Thermal resistance of the duct wall K.m/W $T_{4iii}$ Thermal resistance to ambient K.m/W $T_{4mu}$ Thermal resistance to ambient K.m/W $T_{4ss}$ Steady-state thermal resistance K.m/W $T_{4t}$ Equivalent thermal resistance for tunnel K.m/W $T_{4w}$ Transient thermal resistance for weekly load K.m/W $T_{4y}$ Transient thermal resistance for yearly load K.m/W $T_A$ Element A of equivalent thermal circuit K.m/W $T_a$ Star thermal resistance of air K.m/W $T_{a0}$ Apparent thermal resistance a K.m/W $t_{a,1}$ Thickness of 1st armour mm $t_{a,2}$ Thickness of 2nd armour mm $t_{ab}$ Thickness of armour bedding mm $T_{ab}$ Thermal resistance of armour bedding K.m/W $t_{ab,1}$ Thickness of 1st armour bedding mm $t_{ab,2}$ Thickness of 2nd armour bedding mm $T_{air}$ Absolute air temperature K $t_{ar}$ Thickness of armour mm $T_{at}$ Thermal resistance by convection, air to tunnel K.m/W $T_{axial}$ Axial thermal resistance due to the movement of air through the tunnel K.m/W $T_B$ Element B of equivalent thermal circuit K.m/W $T_{b0}$ Apparent thermal resistance b K.m/W $T_{bulk}$ Bulk temperature K $t_c$ Thickness of hollow conductor mm $T_C$ Element C of equivalent thermal circuit K.m/W $t_{comp}$ Thickness of compartment mm $T_{conv,ce}$ Thermal resistance by convection, conductor to enclosure K.m/W $T_{conv,od}$ Thermal resistance by convection, object to duct K.m/W $T_{conv,sa}$ Thermal resistance by convection, surface to air K.m/W $t_{corr}$ Thickness of corrugation filling mm $t_{cs}$ Thickness of conductor shield mm $t_{ct}$ Thickness of conductor tape mm $T_d$ Internal thermal resistance for dielectric losses K.m/W $t_d$ Thickness of duct mm $T_e$ External thermal resistance of tunnel K.m/W $t_{EMF}$ Time step to calculate current source s $t_{encl}$ Thickness of enclosure mm $T_{eq}$ Equivalent thermal resistance K.m/W $t_f$ Thickness of filler/belt insulation mm $T_{gas}$ Absolute gas temperature K $T_i$ Thermal resistance of insulation K.m/W $t_i$ Thickness of insulation mm $t_{icore}$ Thickness of core insulation mm $t_{ins}$ Thickness of insulation mm $T_{ins}$ Thermal resistance of insulation K.m/W $T_{int}$ Internal thermal resistance for current losses K.m/W $t_{is}$ Thickness of insulation screen mm $T_{is}$ Thermal resistance of insulation screen K.m/W $t_j$ Thickness of jacket mm $T_j$ Thermal resistance of jacket K.m/W $t_{jj}$ Thickness of additional layer over jacket mm $t_k$ Duration of short-circuit s $T_L$ Thermal longitudinal resistance K.m/W $T_{mh}$ Mutual thermal resistance between rated and crossing object K.m/W $T_{mh,v}$ Mutual thermal resistance per slice K.m/W $T_o$ Thermal resistance of the oil in the pipe K.m/W $t_{prot}$ Thickness of protective cover mm $T_{prot}$ Thermal resistance of protective cover K.m/W $T_r$ Total thermal resistance K.m/W $T_{rad,ce}$ Radiation thermal resistance, conductor to enclosure K.m/W $T_{rad,od}$ Radiation thermal resistance, object to duct K.m/W $T_{rad,sa}$ Radiation thermal resistance, surface to air K.m/W $T_{rad,sun}$ Solar radiation thermal resistance K.m/W $T_{riser}$ Thermal resistance of riser/J-tubes in air/water K.m/W $T_s$ Star thermal resistance of object K.m/W $T_{sa}$ Thermal resistance by convection, surface to air K.m/W $t_{sc}$ Thickness of the screen mm $t_{scb}$ Thickness of screen bedding mm $T_{scb}$ Thermal resistance of screen bedding K.m/W $t_{scs}$ Thickness of screen serving mm $T_{scs}$ Thermal resistance of screen bedding K.m/W $t_{sh}$ Thickness of the sheath mm $t_{sha}$ Total thickness between separate sheath and armour mm $t_{shj}$ Thickness of sheath jacket mm $T_{shj}$ Thermal resistance of sheath jacket K.m/W $t_{skid}$ Thickness of skid wires mm $t_{sp}$ Thickness of steel pipe mm $T_{st}$ Radiation thermal resistance, surface to tunnel K.m/W $T_{surf}$ Absolute surface temperature K $t_t$ Wall thickness m $T_t$ Star thermal resistance of tunnel K.m/W $T_{tot}$ Total thermal resistance, transient K.m/W $T_{tr}$ Thermal resistance of trough K.m/W $T_{tw}$ Thermal resistance of tunnel wall K.m/W $T_{wall}$ Thermal resistance of pipe wall K.m/W $\mathrm{tan} \delta_i$ Loss factor of insulation $\tau$ Transient load period s $\tau_{ar}$ Armour angle rad $\tau_L$ Transient load period for deep burial s $\theta_{2K}$ Temperature rise for 2K criterion °C $\theta_a$ Ambient temperature °C $\theta_{abs}$ Absolute temperature K $\theta_{air}$ Ambient air temperature °C $\theta_{ar}$ Temperature of armour °C $\theta_{at}$ Air temperature with load °C $\theta_{at,0}$ Air temperature with no load °C $\theta_{at,i}$ Air temperature of previous iteration cycle °C $\theta_{at,L}$ Air temperature in tunnel at outlet °C $\theta_{at,z}$ Air temperature in tunnel at z °C $\theta_c$ Temperature of conductor °C $\theta_{c,z}$ Conductor temperature at z °C $\theta_{cmax}$ Max. conductor temperature °C $\theta_{cmaxeo}$ Max. emergency overload conductor temperature °C $\theta_{cmaxsc}$ Max. short-circuit conductor temperature °C $\theta_{de}$ Temperature of duct outer wall °C $\theta_{di}$ Temperature of duct inner wall °C $\theta_{dm}$ Mean temperature of the medium in the duct °C $\theta_e$ External temperature of the object °C $\theta_{encl}$ Temperature of enclosure °C $\theta_f$ Temperature of filler for multi-core cables type SS with sheath °C $\theta_{film}$ Film temperature °C $\theta_{gas}$ Gas temperature °C $\theta_{hs}$ Temperature of heat source °C $\theta_{kf}$ Final temperature °C $\theta_{ki}$ Initial temperature °C $\theta_{kmax}$ Maximal temperature of non-insulation material °C $\theta_{max}$ Temperature of conductor at end of emergency loading °C $\theta_o$ Outer surface temperature °C $\theta_{o,L}$ Temperature of the surface of object at outlet °C $\theta_{o,z}$ Temperature of the surface of object at z °C $\theta_{omax}$ Max. outer surface temperature °C $\theta_R$ Rated current transient to steady-state ratio $\theta_s$ Temperature of screen/sheath °C $\theta_{sc}$ Temperature of screen °C $\theta_{sh}$ Temperature of sheath °C $\theta_{sp}$ Temperature of steel pipe °C $\theta_{spf}$ Mean temperature of the medium in the steel pipe °C $\theta_{surf}$ Surface temperature °C $\theta_t$ Temperature of inner tunnel wall °C $\theta_{t,L}$ Temperature of tunnel wall at outlet °C $\theta_{t,z}$ Temperature of tunnel wall at z °C $\theta_{tm}$ Mean temperature between surface and air in tunnel or trough °C $\theta_{to}$ Temperature of outer tunnel wall °C $\theta_{to,z}$ Temperature of outer tunnel wall at z °C $\theta_w$ Water temperature °C $\theta_x$ Critical soil temperature °C $TQ$ Cable thermal time constant s