Methods to evaluate convection heat transfer Empirical(experimentalanalysis Use experimental measurements in a controlled lab setting to correlate heat and/or mass transfer in terms of the appropriate non-dimensional parameters Theoretical or Analytical approach Solving of the boundary layer equations for a particular geometry Example · Solve for t* Use evaluate the local nusselt number Nu Compute local convection coefficient, hx Use these(integrate)to determine the average convection coefficient over the entire surface Exact solutions possible for simple cases Approximate solutions also possible using an integralmethod Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 6 Methods to evaluate convection heat transfer • Empirical(experimental) analysis – Use experimental measurements in a controlled lab setting to correlate heat and/or mass transfer in terms of the appropriate non-dimensional parameters • Theoretical or Analytical approach – Solving of the boundary layer equations for a particular geometry. – Example: • Solve for T* • Use evaluate the local Nusselt number, Nux • Compute local convection coefficient, hx • Use these (integrate) to determine the average convection coefficient over the entire surface – Exact solutions possible for simple cases. – Approximate solutions also possible using an integral method
Empirical method to obtain heat transfer coefficient How to set up an experimental test? Let' s say you want to know the heat transfer rate of an airplane wing(with fuel inside) flying at steady conditions wing surface What are the parameters involved? Ⅴ Telocity, wing length. L Prandtl number, Pr -viscosity, u Nusselt number. Nu Which of these can we control easily? Looking for the relation Experience has shown the following relation works well Nu=cRe pr L r Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 7 Empirical method to obtain heat transfer coefficient • How to set up an experimental test? • Let’s say you want to know the heat transfer rate of an airplane wing (with fuel inside) flying at steady conditions…………. • What are the parameters involved? – Velocity, –wing length, – Prandtl number, –viscosity, – Nusselt number, • Which of these can we control easily? • Looking for the relation: Experience has shown the following relation works well: T ,U Twing surface U L Pr Nu m n Nu = C Re L Pr
Empirical method to obtain heat transfer coefficient Experimental test setup Power input L Insulation Measure current(hence heat transfer )with various fluids and test conditions for t. u fluid properties are typically evaluated at the mean film temperature T+t Nur=C Re "mPr/ P CRet APr Log Re Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 8 T ,U = Power input insulation L Empirical method to obtain heat transfer coefficient • Experimental test setup • Measure current (hence heat transfer) with various fluids and test conditions for • Fluid properties are typically evaluated at the mean film temperature T ,U 2 + T T T s f
Analytical Solution- Laminar Flow Assume Steady, incompressible, laminar flow Constant fluid properties For flat plate TU Boundary layer equations 0 Continui ax a au au au Momentum l-+1 Energy aT aT 02T Blasius developed a similarity solution to the hydrodynamic equations in 1908 based on the stream function, y(x,y) Heat Transfer Su Yongkang School of Mechanical Engineering
Heat Transfer Su Yongkang School of Mechanical Engineering # 9 Analytical Solution – Laminar Flow • Assume: – Steady, incompressible, laminar flow – Constant fluid properties – For flat plate, • Boundary layer equations • Blasius developed a similarity solution to the hydrodynamic equations in 1908 based on the stream function, (x,y) = 0 + y v x u 2 2 y u y u v x u u = + 2 2 y T y T v x T u = + Continuity Momentum Energy T ,U Ts y