传热学上海交通大学Introductionto Convection 2.pptVIP

HEAT TRANSFER Boundary Layer Similarity Parameters The boundary layer equations (velocity, mass, energy continuity) represent low speed, forced convection flow. Advection terms on the left side and diffusion terms on the right side of each equation, such as: Advection Diffusion Non-dimensionalize the equations by setting: Boundary Layer Similarity Parameters (Cont’d) The boundary layer equations can be rewritten in terms of the non-dimensional variablesContinuityx-momentumenergy With boundary conditions Boundary Layer Similarity Parameters (Cont’d) From the non-dimensionalized boundary layer equations, dimensionless groups can be seen Reynolds #Prandtl #Substituting gives the boundary layer equations: Back to the convection heat transfer problem… Solutions to the boundary layer equations are of the form: Rewrite the convective heat transfer coefficient Define the Nusselt number as: Nusselt number for a prescribed geometry (For a prescribed geometry, is known) ? Many convection problems are solved using Nusselt number correlations incorporating Reynolds and Prandtl numbers The Nusselt number is to the thermal boundary layer what the friction coefficient is to the velocity boundary layer. Heat transfer coefficient, simple example Given:Air at 20oC flowing over heated flat plate at 100oC. Experimental measurements of temperatures at various distances from the surface are as shown Find: convective heat transfer coefficient, h Heat transfer coefficient, simple example Solution:Recall that h is computed by From Table A-4 in Appendix, at a mean fluid temperature (average of free-stream and surface temperatures) the air conductivity, k is ? 0.028 W/m-K Temperature gradient at the plate surface from experimental data is -66.7 K/mm = -66,700 K/m So, convective heat transfer coefficient is: Example: Experimental results for heat transfer over a flat p