I have a cable which dissipates Q_total and I need to determine the surface temperature of the insulation T_ins and the surface temperature of the conductor T_cond.
There is an insulating layer with the thermal resistance R_cond and the convective thermal resistance R_conv. The radiation component is neglected. From the geometry of the insulating layer I can obtain R_cond, but for R_conv I need to calculate the convection coefficient via the Nusselt-number. I have an empirical equation for the Nusselt-number, but the Rayleigh-number calculation requires the value of T_ins - T_ambient,air.
So I have the following equation:
Q_total = (1/R_total) * (T_cond - T_ambient,air)
with R_total = R_cond + R_conv = R_cond + Nu * lambda/L.
Where lambda is the thermal conductivity and $L$ the length of the cable. There are two unknown values in this equation T_cond and T_ins, because Nu depends on T_ins and Q_total depends on T_cond. Is there a way to calculate the temperatures or do I have to define a temperature?
Furthermore I cannot determine the film temperature because T_ins is unknown. At which temperature should I determine the thermodynamic properties for the Rayleigh- and Prandtl-number calculation? I would really appreciate your help.
There is an insulating layer with the thermal resistance R_cond and the convective thermal resistance R_conv. The radiation component is neglected. From the geometry of the insulating layer I can obtain R_cond, but for R_conv I need to calculate the convection coefficient via the Nusselt-number. I have an empirical equation for the Nusselt-number, but the Rayleigh-number calculation requires the value of T_ins - T_ambient,air.
So I have the following equation:
Q_total = (1/R_total) * (T_cond - T_ambient,air)
with R_total = R_cond + R_conv = R_cond + Nu * lambda/L.
Where lambda is the thermal conductivity and $L$ the length of the cable. There are two unknown values in this equation T_cond and T_ins, because Nu depends on T_ins and Q_total depends on T_cond. Is there a way to calculate the temperatures or do I have to define a temperature?
Furthermore I cannot determine the film temperature because T_ins is unknown. At which temperature should I determine the thermodynamic properties for the Rayleigh- and Prandtl-number calculation? I would really appreciate your help.
