Thermal Property of Bio-material Physical Properties of Bio-Materials (VII) Poching Wu, Ph.D. Department of Bio-Mechatronic Engineering National Ilan University
Thermal Properties of Bio-material • Dimensional Characteristics: Shape, Size, Volume, Roundness, Sphericity, Unit Surface Area, Average Projected area • Density • Fluid Viscosity • Unit Surface Conductance • Latent Heat
Thermal Properties of Bio-material • Specific Heat • Thermal Conductivity • Mass Diffusivity or Diffusion Coefficient • Mass Transfer Coefficient • Coefficient of Thermal Expansion • Dimensionless Parameters
Specific Heat where • C = specific heat, kJ/kg·℃ • Q = the heat supplied, kJ • w = specific weight, kg/m3 • V = volume, m3 • m = mass, kg • Dt = Temperature Difference, ℃
The specific heat of a substance denotes the variation of the temperature with the amount of heat stored within the substance. • This equation indicates that C is also a function of temperature.
Measurement of Specific Heat • Siebel’s Equations • Method of Mixture • Method of Guarded-Plate • Method of Comparison Calorimeter • Method of Calculated Specific Heat • Method of Differential Scanning Calorimetry (DSC)
Siebel’s Equations (1892) For values above freezing, For values below freezing, where C = specific heat, BTU/lb·ºF M = moisture content of the material in percent wet basis, %. 0.2 is a constant assumed to be the specific heat of the solid. ※ 1 BTU/lb·ºF = 4.187 kJ/kg·℃
Haswell (1954) Rough rice Finished rice Oats
Method of Mixture where Cs = specific heat of sample, kJ/kg·℃ Cw = specific heat of water, 4.2 kJ/kg·℃ Cc = specific heat of calorimeter cup or bucket, kJ/kg·℃ Ww = weight of added water, kg Wc = weight of calorimeter cup or bucket, kg Ws = weight of sample, kg te = equilibrium temperature,℃ tw = initial water temperature,℃ ti = initial temperature of sample and calorimeter cup or bucket,℃
The accuracy of this method is based on the assumption that the unaccounted-for heat losses are negligible. Example: Cw = specific heat of water, 4.187 kJ/kg·℃ Cc = specific heat of calorimeter cup or bucket, 0.946 kJ/kg·℃ Ww = weight of added water, 0.254 kg Wc = weight of calorimeter cup or bucket, 0.054 kg Ws = weight of sample, 0.090 kg te = equilibrium temperature, 30℃ tw = initial water temperature, 21℃ ti = initial temperature of sample and calorimeter cup or bucket, 73℃ substituting the given information in the equation listed above yields Cs = 1.842 kJ/kg·℃
Method of Guarded-Plate where V = average voltage I = average current Θ = time, sec 3.41 = the conversion factor from watts to BTU/hr
Thermal ConductionFourier’s Law of Heat Conduction • k = thermal conductivity, W/m℃ • A = cross section area, m2 • dT/dx = temperature gradient, ℃/m
Factors affect the thermal conductivity • Temperature • the state of the substance • chemical composition • Physical (Cellular) structure • Density • Moisture Content • Moisture migration Heat conduction is usually interpreted either as molecular interchange of kinetic energy or electron drift (the mobility of free electrons)
Measurement of Thermal Conductivity Steady-State • Longitudinal Heat Flow Methods • Radial Heat Flow Methods Cylinder Without End Guards Cylinder With End Guards Sphere With Central Heating Source Concentric Cylinder Comparative Method • Heat of Vaporization Methods
Measurement of Thermal Conductivity Unsteady-State • Fitch Method • Line Heat Source Method • Plane Heat Source Method • Statistical Modeling Method • Frequency Response Method • Packed Bed Analysis Method
Heat Conduction EquationIn a Large Plane Wall Steady State: Transient:
Longitudinal Heat Flow Methods • k = thermal conductivity, W/m℃ • d = specimen thickness, m • q = measured rate of heat input, W • A = area of specimen, m2 • Dt = temperature difference between specimen surfaces normal to heat flow, ℃
Steady State: Transient:
Radial Heat Flow Methods(Cylinder without End Guards) • p = the power used by the central heater • L = the length of the cylinder • t1 and t2 = the temperatures of the specimen at radii r1 and r2 , respectively
Line Heat Source Methods • Q = heat input of the line heat source • L = length of the cylinder • t1 and t2 = temperatures at time q1 and q2 , respectively
Thermal Conductivity Probe Method • q’ = the heat input per foot of the line source • K = thermal conductivity of the medium infinite in size surrounding the line heat source • t1 and t2 = temperatures at time q1 and q2 , respectively
Time Correction for Probe Finite Diameter • q0 = the time correction factor • t1 and t2 = temperatures at time q1 and q2 , respectively To account for the fact that any real line heat source has a finite radius.
Where I = the input current in amps. R = the resistance of the heating wire in ohms. To determine the time correction factor θo: • Temperature, t, versus time, θ, can be plotted on graph paper with arithmetic scales. • Next, the instantaneous slope dt/dθ can be taken at several different times from this plot. • The third step is to plot the dt/dθ values against time on arithmetic scale graph paper and read the intercept on the time axis. This intercept is the time correction θo at which the rate of change of temperature dt/dθ becomes zero.