Mr. Education

Convection Convection is defined as, " conduction + bulk fluid motion " . Velocity boundary layer   ↠  due to viscosity effects  Thermal Boundary Layer   ↠  due to temperature gradient due to thermal exchange among the adjacent layers. Boundary Layer Equation We will be identifying the energy terms of a control volume which lies within the thermal boundary layer. Some used assumptions are: Incompressible Flow Steady State conditions Constant thermophysical properties of fluid Velocity boundary layer > Thermal boundary layer Local and Average Convective Coefficient  Convective coefficient vary from point to point. Dimensionless Parameters 1. Reynold's Number  It is the ratio of inertial forces to viscous forces. It tells about the type of flow (turbulent or laminar). 2. Prandtl Number  It is a fluid property which tells the relation between velocity and thermal boundary layer. For gases  ↠  δ  =  δt For liquid metal  ↠  δt  >>  δ For oil  ↠  δt  <<  δ 3. Nus

Radiation Radiation effects are significant at high temperature. No material medium required. Every body above 0 kelvin emit electromagnetic waves (disturbance of photons). Radiation heat fluxes: Emissive Power (E)   ⇔  rate of emitted radiations. It is a function of temperature. Irradiation (G)   ⇔  rate of incident radiation on a body. Radiosity (J)  ⇔  total radiation that leaves the surface. Net Radiative Flux   ⇔  it is difference between radiation outgoing to radiation incoming. Solid Angle: Radiation Intensity: It is defined as, "rate of emitted radiation per unit area per spectral intensity (wavelength) per solid angle". Blackbody Radiations It is a hypothetical body with: No reflection and transmission. Radiation intensity is governed by Planck distribution 1. Wien's Displacement Law To find maximum emissive power, differentiate function with respect to wavelength and put it equals to zero. 2. Stefan - Boltzmann Law For finding total emissive power, integrate wh

Lump It is defined as, "a body which has constant temperature with respect to position". Temp = function(time). Lump Capacitance Ques: When to apply lump capacitance method? Ans: Apply when  Temperature is the function of time not space. When Biot Number is near or equal to zero. The validity of lumped capacitance method is: References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge.  Photoshoped pics  are developed.  Some pics and GIF from Google.   Videos from YouTube ( Engineering Sights ).

Steady State Heat Conduction We assumes that there is: No internal heat generation Steady state conditions  Isotropic material  1-D heat transfer Conductive Resistance Convective Resistance Radiative Resistance Composite Wall Chart for Thermal Resistance and Heat Transfer Contact Resistance Critical Radius of Insulation (Only for Cylindrical and Spherical Case) Keep it mind the following things: Sphere wall   ↠  Temperature profile is inverse of radius . Rectangular Wall   ↠  Temperature profile is linear . Cylindrical Wall   ↠  Temperature profile is Logarithmic . If r actual < r cr   →  heat loss increases. If r actual > r cr   →  heat loss decreases. For Free Convection (air)  →  no fan (external source, h ≈ 5 W/m2.K , k ≈ 0.01 W/m.K ). Note: Thermal Insulation  for an aircraft References: Material from Class Lectures + Book named Fundamentals of Heat and Mass Transfer by Theodore L. Bergman + My knowledge.  Photoshoped pics  are developed.  Some pics and GIF from Google. 

Extended Surface Heat Transfer Heat transfer of any body can be enhanced by: Increase in h (convective coefficient, increase by forced convection e.g.: fan). Increase temperature difference (T s -T ∞ ) Increase in area (A) However by changing the above parameters, you counter certain conditions: If h is increase  ↠  cost increased. T ∞   ↠  cannot be controlled. Only area (A) is feasible. Fin Equation Case A: Uniform Cross-sectional Area Case B: Fin of Uniform Cross-sectional Area & Insulated Fin Tip Case B: Fin of Uniform Cross-sectional Area & of Infinite Length Fin Performance Factors Following are the fin performance factors: 1. Fin Effectiveness  Fin is used to enhance heat transfer (Cost added and complexity associated with fins). It is the ratio between heat transfer with fin and heat transfer without fin.  If ε fin > 1  ↠  fin enhancing heat transfer increase. If  ε fin  < 1  ↠  material lost, heat transfer decrease. If  ε fin  = 1  ↠  material lost. 2. Fin Ef

Conduction Rate Equation (or Fourier Law of Heat Conduction) According to the Fourier Law of Heat Conduction, steady state heat transfer is directly proportional to change in temperature and inversely proportional to the thickness. Proportionality is valid for all materials. Heat Flux   →  heat per unit perpendicular area (isothermal surface). Thermal Properties of Matter 1. Thermal Conductivity It is defined as, "the ability of a material to conduct heat". For anisotropic material (different k in different directions) For isotropic material (k is same in all direction) 2. Thermal Diffusivity It is defined as, "material ability to conduct heat relative to its ability to store thermal energy". Heat Diffusion Equation There cases for Heat diffusion equation, which are: For isotropic material   →  k become constant. Steady state condition   →  No change with time (energy storage = 0). For 1D and no internal heat generation   →  equation reduced to q x '' (he