The existing equations for the thermal performance evaluation, at equal pumping power for the artificially roughened and smooth surfaced multitube and rectangular duct heat exchangers, have been critically reviewed because the literature survey indicates that a large number of researchers have not interpreted these equations correctly. Three of the most widely used equations have been restated with clearly defined constraints and conditions for their application. Two new equations have been developed for the design constraints not covered earlier. 1. Introduction Artificial roughness in the form of ribs or baffles has been employed to enhance heat transfer in conventional heat exchangers, gas turbine blade cooling channels, and solar air heaters. However, the enhancement in heat transfer is also associated with significant increase in pressure drop and pumping power. Various thermal performance evaluation criteria, which take account of both heat transfer enhancement and pumping power, have been suggested for these enhanced performance surfaces based on different design constraints and objectives [1–6]. However, the criterion based on equal pumping power for the roughened and smooth surfaces suggested by Webb and Eckert [2] has been most widely used [7–41]. The performance ratios used by different researchers for the multitube heat exchangers are The Stanton number, St, Nusselt number, Nu, and the friction factor, , without subscript refer to the rough surface and with the subscript, , refer to the smooth surface. The ratio of heat transfer coefficients for the rough and smooth surfaces, , in (2) is replaced by the ratio of the overall heat transfer coefficients, , when heat transfer between two fluids is considered. The heat transfer coefficient or in (2) is calculated at the Reynolds number for the smooth surfaced tubes, which is defined by One of the old references where an equation similar to (1) has been given is that of Walker and Wilkie [1] for flow along the axis of a cluster of heated roughened rods in a smooth channel for the fixed mass flow rate and pumping power as constraints and the flow area as variable. Webb and Eckert [2], while discussing three different design objectives for multitube heat exchangers, proposed (1) for the design objective of enhanced heat transfer rate at equal pumping power for the roughened and smooth tubes. However, they developed this equation for a particular set of constraints and this equation is applicable only when a condition of specified ratio of mass velocities through the smooth and rough tubes is
References
[1]
V. Walker and D. Wilkie, “The wider application of roughened heat transfer surfaces as developed for advanced gas-cooled reactors,” in Proceedings of Symposium on High Pressure Gas as a Heat Transfer Medium, London, UK, 1967, paper no. 26.
[2]
R. L. Webb and E. R. G. Eckert, “Application of rough surfaces to heat exchanger design,” International Journal of Heat and Mass Transfer, vol. 15, no. 9, pp. 1647–1658, 1972.
[3]
A. E. Bergles, A. R. Blumenkrantz, and J. Taborek, “Performance evaluation criteria for enhanced heat transfer surfaces,” in Proceedings of the 5th International Heat Transfer Conference, vol. 2, pp. 239–243, Tokyo, Japan, 1974.
[4]
K. W. Boer, “Payback of solar systems,” Solar Energy, vol. 20, pp. 225–232, 1978.
[5]
K. Altfeld, W. Leiner, and M. Fiebig, “Second law optimization of flat-plate solar air heaters—part I: the concept of net exergy flow and the modeling of solar air heaters,” Solar Energy, vol. 41, no. 2, pp. 127–132, 1988.
[6]
A. Cortés and R. Piacentini, “Improvement of the efficiency of a bare solar collector by means of turbulence promoters,” Applied Energy, vol. 36, no. 4, pp. 253–261, 1990.
[7]
W. J. White and L. White, “The effect of rib profile on heat transfer and pressure loss properties of transversely ribbed roughened surfaces,” in Augmentation of Heat Transfer, A. E. Bergles and R. L. Webb, Eds., pp. 44–54, ASME, New York, USA, 1970.
[8]
F. Williams, M. A. M. Pirie, and C. Warburton, “Heat transfer from surfaces roughened by ribs,” in Augmentation of Heat Transfer, A. E. Bergles and R. L. Webb, Eds., pp. 36–43, ASME, New York, USA, 1970.
[9]
F. Williams and J. Watts, “The development of rough surfaces with improved heat transfer performance and a study of the mechanisms involved,” in Proceedings of 4th International Heat Transfer Conference, vol. 2, pp. 1–11, Paris, France, 1970.
[10]
M. J. Lewis, “Optimising the thermohydraulic performance of rough surfaces,” International Journal of Heat and Mass Transfer, vol. 18, no. 11, pp. 1243–1248, 1975.
[11]
J. C. Han, J. S. Park, and C. K. Lei, “Heat transfer enhancement in channels with turbulence promoters,” Journal of Engineering for Gas Turbines and Power, vol. 107, pp. 628–635, 1985.
[12]
J. C. Han and J. S. Park, “Developing heat transfer in rectangular channels with rib turbulators,” International Journal of Heat and Mass Transfer, vol. 31, no. 1, pp. 183–195, 1988.
[13]
S. C. Lau, R. T. Kukreja, and R. D. Mcmillin, “Effects of V-shaped rib arrays on turbulent heat transfer and friction of fully developed flow in a square channel,” International Journal of Heat and Mass Transfer, vol. 34, no. 7, pp. 1605–1616, 1991.
[14]
S. C. Lau, R. D. McMillin, and J. C. Han, “Turbulent heat transfer and friction in a square channel with discrete rib turbulators,” Journal of Turbomachinery, vol. 113, no. 3, pp. 360–366, 1991.
[15]
K. B. Muluwork, S. C. Solanki, and J. S. Saini, “Study of heat transfer and friction in solar air heaters roughened with staggered discrete ribs,” in Proceedings of 4th ISHMT-ASME Heat and Mass Transfer Conference and 15th Heat and Mass Transfer Conference, pp. 391–398, IAT, Pune, India, 2000.
[16]
A. E. Momin, J. S. Saini, and S. C. Solanki, “Heat transfer and friction in solar air heater duct with V-shaped rib roughness on absorber plate,” International Journal of Heat and Mass Transfer, vol. 45, no. 16, pp. 3383–3396, 2002.
[17]
S. V. Karmare and A. N. Tikekar, “Heat transfer and friction factor correlation for artificially roughened duct with metal grit ribs,” International Journal of Heat and Mass Transfer, vol. 50, no. 21-22, pp. 4342–4351, 2007.
[18]
K. R. Aharwal, B. K. Gandhi, and J. S. Saini, “Experimental investigation on heat-transfer enhancement due to a gap in an inclined continuous rib arrangement in a rectangular duct of solar air heater,” Renewable Energy, vol. 33, no. 4, pp. 585–596, 2008.
[19]
S. B. Bopche and M. S. Tandale, “Experimental investigations on heat transfer and frictional characteristics of a turbulator roughened solar air heater duct,” International Journal of Heat and Mass Transfer, vol. 52, no. 11-12, pp. 2834–2848, 2009.
[20]
M. E. Taslim, T. Li, and D. M. Kercher, “Experimental heat transfer and friction in channels roughened with angled, V-shaped, and discrete ribs on two opposite walls,” Journal of Turbomachinery, vol. 118, no. 1, pp. 20–28, 1996.
[21]
S. W. Ahn, “The effects of roughness types on friction factors and heat transfer in roughened rectangular duct,” International Communications in Heat and Mass Transfer, vol. 28, no. 7, pp. 933–942, 2001.
[22]
X. Gao and B. Sundén, “Heat transfer and pressure drop measurements in rib-roughened rectangular ducts,” Experimental Thermal and Fluid Science, vol. 24, no. 1-2, pp. 25–34, 2001.
[23]
L. Wang and B. Sunden, “Performance comparison of some tube inserts,” International Communication of Heat and Mass Transfer, vol. 29, no. 1, pp. 45–56, 2002.
[24]
S. W. Moon and S. C. Lau, “Heat transfer between blockages with holes in a rectangular channel,” Journal of Heat Transfer, vol. 125, no. 4, pp. 587–594, 2003.
[25]
L. Wang and B. Sunden, “Experimental investigation of local heat transfer in a square duct with various-shaped ribs,” Heat and Mass Transfer, vol. 43, no. 8, pp. 759–766, 2007.
[26]
P. Promvonge and C. Thianpong, “Thermal performance assessment of turbulent channel flows over different shaped ribs,” International Communications in Heat and Mass Transfer, vol. 35, no. 10, pp. 1327–1334, 2008.
[27]
A. Layek, J. S. Saini, and S. C. Solanki, “Effect of chamfering on heat transfer and friction characteristics of solar air heater having absorber plate roughened with compound turbulators,” Renewable Energy, vol. 34, no. 5, pp. 1292–1298, 2009.
[28]
K. R. Aharwal, B. K. Gandhi, and J. S. Saini, “Heat transfer and friction characteristics of solar air heater ducts having integral inclined discrete ribs on absorber plate,” International Journal of Heat and Mass Transfer, vol. 52, no. 25-26, pp. 5970–5977, 2009.
[29]
A. Lanjewar, J. L. Bhagoria, and R. M. Sarviya, “Experimental study of augmented heat transfer and friction in solar air heater with different orientations of W-Rib roughness,” Experimental Thermal and Fluid Science, vol. 35, no. 6, pp. 986–995, 2011.
[30]
S. Singh, S. Chander, and J. S. Saini, “Investigations on thermo-hydraulic performance due to flow-attack-angle in V-down rib with gap in a rectangular duct of solar air heater,” Applied Energy, vol. 97, pp. 907–912, 2012.
[31]
K. Ko and N. K. Anand, “Use of porous baffles to enhance heat transfer in a rectangular channel,” International Journal of Heat and Mass Transfer, vol. 46, no. 22, pp. 4191–4199, 2003.
[32]
O. N. Sara, T. Pekdemir, S. Yapici, and M. Yilmaz, “Heat-transfer enhancement in a channel flow with perforated rectangular blocks,” International Journal of Heat and Fluid Flow, vol. 22, no. 5, pp. 509–518, 2001.
[33]
D. L. Gee and R. L. Webb, “Forced convection heat transfer in helically rib-roughened tubes,” International Journal of Heat and Mass Transfer, vol. 23, no. 8, pp. 1127–1136, 1980.
[34]
R. Sethumadhavan and M. Raja Rao, “Turbulent flow heat transfer and fluid friction in helical-wire-coil-inserted tubes,” International Journal of Heat and Mass Transfer, vol. 26, no. 12, pp. 1833–1845, 1983.
[35]
R. Sethumadhavan and M. Raja Rao, “Turbulent flow friction and heat transfer characteristics of single- and multistart spirally enhanced tubes,” Journal of Heat Transfer, vol. 108, no. 1, pp. 55–61, 1986.
[36]
T.-M. Liou and J.-J. Hwang, “Effect of ridge shapes on turbulent heat transfer and friction in a rectangular channel,” International Journal of Heat and Mass Transfer, vol. 36, no. 4, pp. 931–940, 1993.
[37]
J.-J. Hwang and T.-M. Liou, “Augmented heat transfer in a rectangular channel with permeable ribs mounted on the wall,” Journal of Heat Transfer, vol. 116, no. 4, pp. 912–920, 1994.
[38]
T.-M. Liou, W. B. Wang, and Y. J. Chang, “Holographic interferometry study of spatially periodic heat transfer in a channel with ribs detached from one wall,” Journal of Heat Transfer, vol. 117, no. 1, pp. 32–39, 1995.
[39]
J.-J. Hwang, T. Y. Lia, and T.-M. Liou, “Effect of fence thickness on pressure drop and heat transfer in a perforated-fenced channel,” International Journal of Heat and Mass Transfer, vol. 41, no. 4-5, pp. 811–816, 1998.
[40]
R. Karwa, “Experimental studies of augmented heat transfer and friction in asymmetrically heated rectabgular ducts with ribs on the heated wall in transverse, inclined, v-continous and v-discrete pattern,” International Communications in Heat and Mass Transfer, vol. 30, no. 2, pp. 241–250, 2003.
[41]
K. Ichimiya, “Effects of several roughness elements on an insulated wall for heat transfer from the opposite smooth heated surface in a parallel plate duct,” Journal of Heat Transfer, vol. 109, no. 1, pp. 68–73, 1987.
[42]
R. Karwa, R. D. Bairwa, B. P. Jain, and N. Karwa, “Experimental study of the effects of rib angle and discretization on heat transfer and friction in an asymmetrically heated rectangular duct,” Journal of Enhanced Heat Transfer, vol. 12, no. 4, pp. 343–355, 2005.
