ReL=ρVLμ=VLνcap R e sub cap L equals the fraction with numerator rho cap V cap L and denominator mu end-fraction equals the fraction with numerator cap V cap L and denominator nu end-fraction = Free-stream velocity ( = Characteristic length ( = Kinematic viscosity of the fluid (
and uses the Nusselt correlation to find a heat transfer of approximately Cylinder in Crossflow (Problem 7-80)
To solve any convection problem, engineers rely on dimensionless numbers to scale fluid properties and predict system behavior. Reynolds Number (
Common in industrial shell-and-tube heat exchangers, this section covers fluid flowing perpendicular to a group of tubes. Tube banks are arranged in either or staggered configurations. Solving these problems requires calculating a modified maximum velocity ( Vmaxcap V sub m a x end-sub ReL=ρVLμ=VLνcap R e sub cap L equals the
Mastering Convection: A Guide to Heat and Mass Transfer Cengel 5th Edition Chapter 7
Drag Force (Cylinder/Sphere): FD=CDAfρV22Drag Force (Cylinder/Sphere): cap F sub cap D equals cap C sub cap D cap A sub f the fraction with numerator rho cap V squared and denominator 2 end-fraction Cfcap C sub f = Average friction coefficient CDcap C sub cap D = Drag coefficient Ascap A sub s = Total surface area Afcap A sub f = Frontal frontal area (projected area) 2. Flow Over Flat Plates
: Apply the appropriate correlation for the geometry (e.g., for laminar flow over a flat plate). The pipes hum, the room warms, and the
h¯=Nu¯⋅kLch bar equals the fraction with numerator modified cap N u with bar above center dot k and denominator cap L sub c end-fraction Step 5: Calculate the Heat Transfer Rate (
—Elias successfully tunes the system. The pipes hum, the room warms, and the 5th edition saves the day. step-by-step solution
If your answer differs from the manual, check your film temperature calculation or appendix look-up values first. A slight variance in fluid properties can throw off your final numbers. The pipes hum
Q̇=hAs(Ts−T∞)cap Q dot equals h cap A sub s open paren cap T sub s minus cap T sub infinity end-sub close paren Common Pitfalls to Avoid
). Finally, apply Newton's Law of Cooling to find the total heat transfer rate: