Correlations development for Nusselt number and friction factor in a dimpled surface heat exchanger tube

ABSTRACT

The present experimental investigation is focused on the study of heat transfer and pressure drop of heat exchanger tube fitted with dimpled ribs on the inner wall. The effect of geometrical parameters, predominantly the streamwise spacing, spanwise spacing, and dimpled depth to print diameter has been investigated. The heat exchanger tube has streamwise spacing ($x/d_d$) in range of 15–35, spanwise spacing ($y/d_d$) in range of 15–35, ratio of dimpled depth to print diameter ($e/d_d$) of 0.5–1.5, and Reynolds number ($R{e}_n$) ranges from 5,000 to 27,000. Experimental results show that the heat transfer and thermal hydraulic performance enhances by 4.19 times and 2.53 times, respectively, for of $x/d_d$ of 15, $y/d_d$ of 15, and $e/d_d$ of 1.0. The experimental data collected are utilized for the development of the statistical correlations for $N{u}_{rs}$ and $f_{rs}$ for selected values of roughness parameters and flow Reynolds number.

KEYWORDS:

• Energy
• heat exchanger
• stream wise spacing
• dimpled surface

Nomenclature

$A_p$ Area of tube $\left({\mathrm{m}}^2\right)$

$A_o$ Cross-section area of the orifice $\left(m^2\right)$

$C_d$ Coefficient of discharge of orifice

$C_p$ Specific heat of air $\left(J/kgK\right)$

$D$ Hydraulic diameter of tube (m)

$d_d$ Print diameter of dimpled rib (m)

$e$ Height of rib $\left(m\right)$

$e/d_d$ Dimpled depth to print diameter

$e/D$ Relative rib height

$f$ Friction factor

$f_{rs}$ Friction Factor of roughened heat exchanger tube

$f_{ss}$ Friction Factor of smooth surface heat exchanger tube

$h$ Convective heat-transfer coefficient $\left(W/m^{2}K\right)$

$\mathrm{\Delta }{h}_o$ Manometric height in U-tube manometer

k Conductivity of air (W/m°C)

L Length of test section (m).

$\dot{m}$ Mass flow rate of air $\left(kg/s\right)$

$N{u}_{rs}$ Nusselt Number of roughened heat exchanger tube

$N{u}_{ss}$ Nusselt Number of smooth surface heat exchanger tube

P Pitch of rib $\left(m\right)$

$P/e$ Relative rib pitch

$Pr$ Prandtl number of air

$\mathrm{\Delta }{p}_o$ Pressure drop across orifice plate$\left(\mathrm{N}/{\mathrm{m}}^2\right)$

$\mathrm{\Delta }{p}_d$ Pressure drop across test section $\left(\mathrm{N}/{\mathrm{m}}^2\right)$

$Q_u$ Heat-transfer rate to air $\left(\mathrm{W}\right)$

$R{e}_n$ Reynolds number

$S{t}_{rs}$ Stanton number

$T_i$ Inlet air temperature $\left({ }^{\circ }\mathrm{C}\right)$

T_o Average outlet air temperature (°C)

T_fm Mean air temperature (°C)

T_pm Mean plate temperature (°C)

V Flow velocity in pipe (m).

$x/d_d$ Streamwise spacing

$y/d_d$ Spanwise spacing

Greek symbols

${\eta }_p$ Thermal–hydraulic performance

$\beta$ Ratio of orifice diameter to pipe diameter

ρ_air Density of air $\left(\mathrm{k}\mathrm{g}/{\mathrm{m}}^3\right)$