Laminar-flow heat transfer in the entrance region of circular tubes

Heat transfer enhancement in nanofluids. A numerical approach

“…Though the water solution could be used to check for the accuracy of the numerical model, no analytical solution has been found in the literature for the simultaneous hydrodynamic and thermal development of laminar flow in a pipe. Some of the available solutions assume Langhaar velocity profiles as starting point [14], [15]. Others are the result of either numerical or curve fitting procedures [16], [17], [18].…”

“…The latter statement is confirmed by expressing the numerical data in terms of dimensionless parameters. Laminar developing flow heat transfer is generally expressed in terms of two dimensionless parameters: the Nusselt and the Graetz number [14], [15], [16], [17], [18], given by the following expressions:…”

Laminar flow heat transfer in ordinary and augmented tubes

“…The first Nusselt number for both cases can thus be evaluated as (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) The heat transfer in an elemental length of duct dZ is…”

“…As indicated by Siegwarth, the pressure variation in the core is hydrostatic. The pressure gradient in the X-direction can thus be assumed to be (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) where the subscript c is used to designate the core solution evaluated at the pipe wall. Employing Eq, (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) The detailed discussion of the procedure for choosing these variables is given in Appendix C. The X-direction momentum equation can thus be expressed in dimensionless form as follows:…”

Laminar flow heat transfer in ordinary and augmented tubes

“…Ulrichson and (1965) [17] Gl, 01, B2 and B3, Al, PI Numerical Schmitz [44] Oliver and Jenson (1964) [45] Mikillop (1964) [46] [59] Gl, 02, Bl, A2, P2 Numerical [60] Gl, 02, Bl, A2, P2 Numerical transfer in horizontal circular tubes (Gl, 01, B2, Al, P2) and the effects of the temperature dependency of both density and viscosity on heat trans fer in fully developed flows in circular tubes (Gl, 01, B1 and B2, A2, P2…”