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Intro to PLUS by Leta Moser and Kristen Cetin

Intro to PLUS by Leta Moser and Kristen Cetin. PLUS accreditation Peer-Led Undergraduate Studying (PLUS) assists students enrolled by offering class-specific, weekly study groups.

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Intro to PLUS by Leta Moser and Kristen Cetin

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  1. Intro to PLUS by Leta Moser and Kristen Cetin • PLUS accreditation • Peer-Led Undergraduate Studying (PLUS) • assists students enrolled by offering class-specific, weekly study groups. • Students can attend any study group at any point in the semester to review for an exam, discuss confusing concepts, or work through practice problems. • http://www.utexas.edu/ugs/slc/support/plus

  2. Lecture Objectives: • Review - Heat transfer • Convection • Conduction • Radiation Analysis of a practical problem

  3. Example Problem –radiant barrier in attic

  4. Example Problem –heat transfer in window construction

  5. Convection

  6. Convection coefficient – h [W/m2K] or Heat flux area Specific heat flux Natural convection Forced convection L – characteristic length Nusselt number: h – natural convection k – air conduction L- characteristic length Convection Conduction

  7. Which surface in this classroom has the largest forced convection A. Window B. Ceiling C. Walls D. Floor Which surface has the largest natural convection

  8. How to calculate h ?What are the parametrs that affect h ?What is the boundary layer ?

  9. Laminar and Turbulent Flowforced convection

  10. Forced convection governing equations 1) Continuity 2) Momentum u, v – velocities n – air viscosity Non-dimensionless momentum equation Using L = characteristic length and U0 = arbitrary reference velocity ReL Reynolds number

  11. Forced convectiongoverning equations Energy equation for boundary layer  T –temperature,a – thermal diffusivity a=k/rcp, k-conductivity,r- density, cp –specific cap. Non-dimensionless energy equations Air temperature outside of boundary layer Wall temperature Prandtl number Reynolds number Momentum diffusivity Inertial force Thermal diffusivity Viscous force

  12. Simplified Equation for Forced convection General equation For laminar flow: For turbulent flow: For air: Pr ≈ 0.7, n = viscosity is constant, k = conductivity is constant Simplified equation: Or:

  13. Natural convection

  14. GOVERNING EQUATIONSNatural convection Continuity • Momentum which includes gravitational force • Energy u, v – velocities , n – air viscosity , g – gravitation, b≈1/T - volumetric thermal expansion T –temperature, – air temperature out of boundary layer, a –temperature conductivity

  15. Characteristic Number for Natural Convection Non-dimensionless governing equations Using L = characteristic length and U0 = arbitrary reference velocity Tw- wall temperature The momentum equation become Gr Multiplying by Re2 number Re=UL/n

  16. Grashof number Characteristic Number for Natural Convection Buoyancy forces Viscous forces The Grashof number has a similar significance for natural convection as the Reynolds number has for forced convection, i.e. it represents a ratio of buoyancy to viscous forces. General equation

  17. Natural convectionsimplified equations For laminar flow: For turbulent flow: For air: Pr ≈ 0.7, n = constant, k= constant, b= constant, g=constant Simplified equation: Even more simple Or: T∞ - air temperature outside of boundary layer, Ts - surface temperature

  18. Forced and/or natural convection In general, Nu = f(Re, Pr, Gr) natural and forced convection forced convection natural convection

  19. Combined forced and natural convention Churchill and Usagi approach : This equation favors a dominant term (h1 or h2), and exponent coefficient ‘n’ determines the value for hcombined when both terms have the same order of value

  20. Example of general forced and natural convection Equation for convection at cooled ceiling surfaces n

  21. What kind of flow is the most common for indoor surfaces A. Laminar B. Turbulent C. Transitional D. Laminar, transitional, and turbulent What about outdoor surfaces?

  22. Conduction

  23. Conductive heat transfer k - conductivity of material • Steady-state • Unsteady-state • Boundary conditions • Dirichlet Tsurface = Tknown • Neumann TS1 TS2 L h Tair

  24. Boundary conditions Biot number convention conduction

  25. Importance of analytical solution

  26. What will be the daily temperature distribution profile on internal surface for styrofoam wall? A. B. External temperature profile T time

  27. What will be the daily temperature distribution profile on internal surface for tin glass? A. B. External temperature profile T time

  28. Conduction equation describes accumulation

  29. Important numbers Convection Nusselt number Conduction Inertial force Reynolds number Viscous force Momentum diffusivity Prandtl number Thermal diffusivity Grashof number Buoyancy forces Viscous forces thermal internal resistance Biot number surface film resistance Reference book: Fundamentals of Heat and Mass Transfer, Incropera & DeWitt

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