Table A.1 Nomenclature Symbol Unit Description A m 2 Area (surface) a m, / Thickness, fraction of refrigerant seen by a single highfield

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1 Appendix See Tables A.1, A.2 and A.3. Table A.1 Nomenclature Symbol Unit Description A m 2 Area (surface) a m, / Thickness, fraction of refrigerant seen by a single highfield region a 0 / Geometry factor for effective heat-transfer coefficient B T = Vs m 2 Magnetic flux density, magnetic induction b / Number of high-field regions Bi / Biot number C / Clausius Clapeyron factor c J kg 1 K 1 Specific heat capacity (J m 1 K 1 ) D d / Fluid dispersion factor d m Diameter, thickness E V m 1, J Electric field (electric field intensity), exergy _E W Exergy flux e J m 3 (J kg 1 ) Specific exergy _e W m 2 Specific exergy flux F N Force f Hz = s 1, / Frequency f F / Fanning friction factor g m s 2 Gravitational acceleration Gz / Graetz number H A m 1 Magnetic field intensity h J m 3 (J kg 1 ) Specific enthalpy I A Electric current I p A Pyroelectric current J A m 2 Current density Springer International Publishing Switzerland 2015 A. Kitanovski et al., Magnetocaloric Energy Conversion, Green Energy and Technology, DOI /

2 452 Appendix Table A.1 Symbol Unit Description j / Colburn heat-transfer factor k J K 1 Boltzmann constant K 1 / Leakage coefficient K 2 / Loss factor L m Length M A m 1 Magnetization M 0 Am 1 kg 1 Specific magnetization M* / Figure of merit for the permanent magnet assembly m kg, A m 2 Mass, magnetic moment _m f kg s 1 Mass flow rate N /, / Demagnetization factor, number of wire turns in the coil Nu / Nusselt number P W, As m 2, / Power, polarization, fraction of AMR cycle where magnet is in use p P, V s, As m 2 Pressure, magnetic pole, pyroelectric coefficient Pr / Prandtl number Δp Pa (bar) Pressure drop q J m 3 (J kg 1 ) Specific heat _q W m 2,Wkg 1 Specific heat flux, heat flux density Q J Heat _Q W Heat power, heat flux R m 2 KW 1 Thermal resistance Re / Reynolds number r m Radius, distance s J m 3 K 1 (J kg 1 K 1 ), m, Specific entropy, thickness of surfactant layer, thickness m Δs J kg 1 K 1 Specific entropy change St / Stanton number T K, Nm Temperature, magnetic torque T K Average temperature t s, VsA m 3 Time, torque density U / Utilization factor u J m 3 (J kg 1 ) Specific internal energy V m 3 Volume v m s 1,m 3 kg 1 Velocity, specific volume W J Work (energy) w J m 3 (J kg 1 ) Specific work (specific energy) _w W m 2 Rate of specific work

3 Appendix 453 Table A.1 Symbol Unit Description Δx / Fluid strokes length (the fraction of fluid that is displaced with respect to all the volume of fluid in the AMR) α Wm 2 K 1, /, / Heat-transfer coefficient, ratio between magnetic and thermal energy of particles, ratio of thermal conductivity between solid and liquid β degree Angle between vorticity and field direction _c s 1 Shear rate δ m Diameter, thickness ε / Porosity, strain ε 0 As V 1 m 1 Electric permittivity of vacuum η /, Pa s Efficiency, dynamic viscosity ϑ C Temperature κ Wm 1 K 1 Thermal conductivity tensor Λ T 2/3 Magnetic characterization parameter λ Wm 1 K 1 Thermal conductivity λ F m Spin relaxation length μ Vs A 1 m 1 Magnetic permeability μ 0 Vs A 1 m 1 Magnetic permeability of vacuum ν m 2 s 1 Kinematic viscosity ξ /, / Exergy efficiency, Riemann zeta function π VK 1 Peltier coefficient ρ kg m 3 Density ρ Α Vs m 2 Surface density of magnetic poles σ As m 2, MPa Surface charge density, stress τ s, /, Pa Time period, relative time, shear stress τ 0 Pa Yield stress ϕ degrees, / Angle, fraction χ / Susceptibility Table A.2 Symbol A AC AB ad AH amb AMR app Subscripts Description Austenite Cold side element A Path A-B Adiabatic Hot side element A Ambient Active magnetic regenerator Apparent

4 454 Appendix Table A.2 Symbol appl ATD B BTD c C CA CB CB cool ci const cool corr crit CTD D dem dw E eff el f fi f-m gap H h HA HB HC high HT i in is L low m mag Description Applied Thermal diode A Bingham Thermal diode B Conduction, coercivity, cold, cooling Curie, Carnot, cold, cooling Cold part of thermal diode A Cold part of thermal diode B Cold part of thermal diode C Index of magnetic characterization parameter Intrinsic coercivity Constant Index of magnetic characterization parameter Corresponding Critical Thermal diode C Device Demagnetization De-twinned Constant electric field, electrical Effective Electric Fluid Final, finish Fluid-material Air gap Constant magnetic field, hot, heating Hot, heat sink, hydraulic Hot part of thermal diode A Hot part of thermal diode B Hot part of thermal diode C High-field region Heat transfer Initial Inlet, internal Isothermal Liquid phase Low-field region Mass, magnetic, magnetization Magnetization, (permanent) magnet

5 Appendix 455 Table A.2 Symbol Description max Maximum mc Magnetocaloric mcm Magnetocaloric material MCE Magnetocaloric effect min Minimum out Outlet, external p Constant pressure (isobaric), particle Peltier Peltier module q Specific heat R Refrigeration r Relative, remanent, rectification ref Reference reg Regeneration rel Relative rem Remanence rot Rotational S Spin, saturation s Solid, isentropic st Start sat Saturation stat Static surr Surrounding T Isothermal, constant temperature t Technical tw Twinned TD Thermal diode V Volume VFF Volume fraction of the particles including their surfactant layer vis Viscous w Wall 0 Gap, external 25 The maximum value of figure of merit for the permanent magnet assembly π Heating power of Peltier effect σ Constant stress

6 456 Appendix Table A.3 Abbreviations Abbreviation A AER AMR CHEX COP ECE EsCE EDL EICE ELE ER EWOD FF FHD GM GMR HHEX HIT HTS JT LCA LTS M MC MCE MCM MHD MR MRF MVE MWCNT PE SMES TD Description Austenite Active electrocaloric regenerator Active magnetic regenerator, active magnetic regeneration Cold heat exchanger, heat source heat exchanger Coefficient of performance Electrocaloric effect Elastocaloric effect Double electric layer Electrowetting on insulator-coated electrodes Electrowetting on line electrodes Electrorheologic Electrowetting on dielectric Ferrofluid Ferrohydrodynamics Gifford McMahon Giant magnetoresistance effect Hot heat exchanger, heat sink heat exchanger Hetero-structured integrated thermionics High-temperature superconducting Joule Thomson Life cost assessment Low-temperature superconducting Martensite Multilayer capacitor Magnetocaloric effect Magnetocaloric material Magnetohydrodynamic Magnetorheological Magnetorheological fluid Magnetoviscous effect Multiwall carbon nanotubes Pyroelectric element Superconducting magnetic energy-storage systems Thermal diode

MAGGIE a highly efficient cooling device

MAGGIE a highly efficient cooling device Nini Pryds nipr@dtu.dk Technical University of Denmark Department of Energy Conversion and Storage Why do we want a caloric cooling/heating? ØNo Greenhouse effect