University:
California State University, Northridge
Course:
ME 584 | Modeling and Simulation of Dynamic Systems
Academic year:

2010
Views:

46

Pages:

12
Author:

Helen Wall

Chp6 1 Modeling Thermal Systems Chp6 3 Basic Effects Chp6 4 Thermal Systems • Thermal Systems: – Energy is stored and transferred as heat – Exhibit static and dynamic behavior (resistance, capacitance, time constants. Thermal inductance does not exist.) – Nonlinear, variable-coefficient, distributed-parameter models • Units: – Temperature T [0C, K, 0F, R] – Heat flow rate Q [J/s, BTU/hr] • Thermal effects – – – – Conduction Convection Radiation Heat Storage Capacity Chp6 5 Chp6 6 Thermal Conduction • Conduction: Ability of materials to conduct heat • Fourier’s law of heat conduction Qh dT   kt A dx Qh : heat transfer A : surface area kt : thermal conductivi ty T : Temperature Minus sign indicates … Temperature drops in direction of heat flow Chp6 7 Kt: Metal V. Liquid/Gas Kt=Kt(T) => Nonlinear heat conduction equation Chp6 8 Conduction Through a Flat Plate T T T   kt A   kt A x x L where T  T2  T1 Qh  kt A Express as an impedance ( similar to a resistor ) : Q L R h  T Ak t kc What is Req ? km Req  Rc  Rm  What is Qh ? Qh  T2  T1 Req Lc L  m Ak c Ak m Chp6 9 Conduction in Various Shapes • Axial conduction in a rod kt A Qh  (T1  T2 ) L • Radial conduction in a cylinder Qh  (Ti  T0 ) (Ti  T0 )  R p  Rc ln (rc / ri )  ln (r0 / rc ) 2k p L 2kc L • With coated surface Qh  (Ti  T0 ) (Ti  T0 )  R p  Rc ln (rc / ri )  ln (r0 / rc ) 2k p L 2kc L Chp6 10 Thermal Convection • Convection: Heat transfer between a surface and a fluid exposed to surface via free or forced convection • Newton’s law of cooling: Qh  h(Ts  T ) A where Ts  solid ' s surface temperature T  temperature of free  stream fluid (constant ) h  convection coefficien t , a function of  properties of fluid (e.g .,  ,  ,kt , C p ),  solid ' s geometric configurat ion,  free  stream fluid flow patterns Chp6 11 Thermal Resistance and Convection Coefficient • Resistance Qh 1 Qh  hAT  R   T hA • Typical Values for Convection Coefficient, h’s Chp6 12 Thermal Radiation Radiation: heat transfer (when energy is high) without presence of surrounding medium Heat transfer from ideal black body of surface area A : Qh  T 4 A where   Stefan  Boltzmann constant Btu / hr 9 Watt  1.714  10 9  56 . 68  10 ft 2 R 4 m2 K 4 Net radian t heat tra nsfer betw een two bo dies : Qh  Fe FvA(TH4  TL4 ) where Fe  correction factor emissivity less than black body  Fv  view factor accounts for lost radiation  TH  high temperature TL  low temperature Chp6 13 Thermal Capacitance • Capacitance: ability to store heat dT (assume no temperatur e gradient in mass) dt M : mass of object C p : specific heat Qh  MC p • Specific heat of various substances

Modeling Thermal Systems. Basic Effects