Low Temperature

Heat Transfer

Thermal Conduction which defined as heat transfer without mass transfer

Thermal Convection

  1. Conduction in Solid

Natural Convection


  • Conductors possess a larger thermal conductivity integral.

Thermal Radiation

Radiation Exchange between Two Surfaces

  • large parallel plates
  • long concentric cylinders

General Laws - Any surface at finite temp absorbs, reflects and emit em radiation

  • thermal conductivity integral determine heat losses and heat interception
  • heat interception depends on thermalization temp, material properties, geometry system

Thermal design at low T

  • thermal resistance of the structural material
  • transient conduction process
  1. Conduction in Liquid
  • Thermal Conductivity decreases with temp
  • mostly negligible
  1. Conduction in Gas

Two different heat transfer regimes

  1. Free molecular regimes
  2. Hydrodynamic regime

Ideal Surface: Blackbody

  • absorbs incident radiation regardless wavelength and direction

Emissivity decreses withtemperater but increases with oxidation, impurities, dirt

Shielding and Multilayer Insulation

The reflecting layers reduce heat transfer by radiation

  • the insulating interlayers reduce heat transfer by conduction between reflecting layers
  • high vacuum reduces convection and residual gas conduction

An assembly of reflective films separated by insulating nterlayers operated under vacuum

simplest correlation :

  • n=1/4 for laminar regime
  • n=1/3 for turbulent regime

Forced Convection

Boiling Convection

Heat is transferred between a surface and the fluid

  • phase change
  • vapour bubble movement in vicinity

Heat transfer depends on

  • bubble growth rate
    • detachment frequency
    • number of nucleation sites
    • surface condition

Cooling Technique

  1. Baths

Use liquid bath - the system is immersed

  • direct/indirect method with no net liquid mass flow and main heat transfer pross due ti latent heat of vaporization
  • advantages : simplicity of the cryogenic design and operation, high transfer due to nucleate boiling, almost constant surface temperature
  • disadvantages : large quantity of cryogen to be handled
    -risk of pressure rise
  1. Forced Flow

To reduce the amount of cryogen - indirect cooling composed of network of peripheral tubes - advantages : adjustable heat transfer rate with mass flow rate - disadvantages : limited range of temperature cooling, the non uniform cooling

Single Phase Flow - disadvantages in the pressurization system, implementation of the circulation pump and its maintanance, implementation of heat exchanger system, temperature range limitation

Two Phase Flow - advantages in having an almost isothermal flow due to high heat transfer even at high vapour quality

  1. Natural and two phase circulation loops

Auto tuned mass flow rate system - the flow created by weight unbalance between the heated branc and the feeding branch of loop due to vaporization or decreased vapour density

Types of Circulation loops - Open Loop : boil off goes out of the system to be reliquefies before refilling the reservoir - Closed Loop : the vapour re-condensed in a closed reservoir wih a heat exchanger

Advantages : no need for a circulating system


Disadvantages : flow instabilities at low heat flux

  1. Cryogen- free cooling and The coupled system

Conductive thermal link between cryocooler and the low-temp device

Advantages : easy implementation, accurate as provide finite cooling power at a prescribed temp


Disadvantages: Working temperature higher, distribution of cooling power over the entire system, thermal diffusion in thermal link limits the cooling for transient events

Method to use a thermal link with a fluid

  1. Capillary - pumped devices
  • A flow is created by capillary pressure in porous medium at liquid/vapor interface
  • Heat pipe with a wick inside the pipe serving as porous media
  • Transfer 50 W between the cold source at 10 K
  1. Cryogenic Loop Heat pipe
  1. Oscillating Heat Pipe (OHP)
  • Heat pipe in a loop configuration to create mass flow rate
  • Transmit 40 W between cold source at 6 K

  • Consist of capillary tube, wound in serpentine manner, connecting the ends of the inlets


  • Advantages : utilized the pressure change due to volume expansion and contraction during a phase transition

  1. Vertical Thermosyphon
  • Used circulation loop and based on the weight unbalance but with sigle vertically oriented tube - The liquids flow down the wll and the vapour flows in a counter-current manner to the liquid at the centre of the tube - Transmit 20 W at 10 K
  1. Coupled Circulation Loop

Small natural circulation loop coupled with a cryocooler serve as a self sustaining thermal link

  • Composed of condenser separator cooled by second stage of cryocooler
  • Liquid helium flow through this loop and re-condensed in the condenser
  • Transfer 5000 W/m.m.K at 4.2 K