# Investigation of Natural Convection Heat Transfer Along a Uniformly Heated Vertical Plate

- 18 Downloads

## Abstract

Natural convection heat transfer along a vertical plate with uniform heat fluxes ranging from 400 to 1000 \(\hbox {W m}^{-2}\) was investigated by using air. The local surface temperatures on the heated surface were calculated by utilizing correlations existing in the literature. Computational analysis was also performed to determine the local wall temperatures for natural convection. The results of computational analysis of the velocity distribution of the fluid in the hydrodynamic boundary layer are presented as well as the thermal distribution in the velocity boundary layer, respectively. The local temperatures determined by those correlations were compared both with each other and then with the results of the computational analysis. The local temperature results obtained in the computational analysis were in good agreement with one of those correlations and demonstrate that the increase in uniform wall heat flux causes both an increase in the local wall temperature and an increase in the velocity of air in the hydrodynamic boundary layer. It was observed that local wall temperature had risen with the increase in the distance from the plate edge.

## Keywords

Natural convection Uniform wall heat flux A vertical plate Air Computational analysis## List of symbols

*g*Gravity constant \((\hbox {m s}^{-2})\)

- \({Gr}^{*}\)
Modified Grashof number (–)

*h*Convection heat transfer coefficient \((\hbox {W m}^{-2}\hbox {K}^{-1})\)

*k*Thermal conductivity \((\hbox {W m}^{-1} \hbox {K}^{-1})\)

*Nu*Nusselt number (–)

*P*Pressure (Pa)

*Pr*Prandtl number (–)

- \(\dot{q}\)
Heat flux \((\hbox {W m}^{-2})\)

*Ra*Rayleigh number (–)

- \({Ra}^{*}\)
Modified Rayleigh number (–)

*T*Temperature (K)

*u*,*v*Average fluid velocity components \((\hbox {m s}^{-1})\)

*x*,*y*Cartesian coordinates (m)

## Greek symbols

- \(\alpha \)
Thermal diffusivity \((\hbox {m}^{2} \hbox {s}^{-1})\)

- \(\beta \)
Volumetric thermal expansion coefficient \((\hbox {K}^{-1})\)

- \(\theta \)
Plate angle (\(^{\circ }\))

- \(\mu \)
Dynamic viscosity \((\hbox {kg m }^{-1}\hbox {s}^{-1})\)

- \(\upnu \)
Kinematic viscosity \((\hbox {m }^{2}\hbox {s}^{-1})\)

- \(\rho \)
Mass density \((\hbox {kg m}^{-3})\)

## Subscripts

- atm
Atmospheric

- f
Film temperature conditions

- in
Inlet

- out
Outlet

- w
Wall

*y*Local

- \(\infty \)
Ambient conditions

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.Dubey, S.; Sarvaiya, J.N.; Seshadri, B.: Temperature dependent photovoltaic (PV) efficiency and its effect on PV production in the word-a review. Energy Procedia
**33**, 311–321 (2013)CrossRefGoogle Scholar - 2.Mittelman, G.; Alshare, A.; Davidson, J.H.: A model and heat transfer correlation for rooftop integrated photovoltaics with a passive air cooling channel. Solar Energy
**83**, 1150–1160 (2009)CrossRefGoogle Scholar - 3.Lee, Y.; Taya, A.A.O.: Finite element thermal analysis of a solar photovoltaic modüle. Energy Procedia
**15**, 413–420 (2012)CrossRefGoogle Scholar - 4.Vliet, G.C.: Natural convection local heat transfer on constant-heat-flux inclined surface. J. Heat Transf.
**91**(4), 511–517 (1969)CrossRefGoogle Scholar - 5.Vliet, G.C.; Liu, C.K.: An experimental study of turbulent natural convection boundary layers. J. Heat Transf.
**91**(4), 517–531 (1969)CrossRefGoogle Scholar - 6.Vliet, G.C.; Ross, D.C.: Turbulent natural convection on upward and downward facing inclined constant heat flux surfaces. J. Heat Transf.
**97**(4), 549–554 (1975)CrossRefGoogle Scholar - 7.Dotson, J.P.: Heat transfer from a vertical plate by free convection, MS thesis. Purdue University (1954)Google Scholar
- 8.Fujii, T.; Fujii, M.: The dependence of local Nusselt number on Prandtl number in the case of free convection along a vertical surface with uniform heat flux. Int. J. Heat Mass Transf.
**19**, 121–122 (1976)CrossRefGoogle Scholar - 9.Churchill, S.W.; Ozoe, H.: A correlation for laminar free convection from a vertical plate. J. Heat Transf.
**95**(4), 540–541 (1973)CrossRefGoogle Scholar - 10.Aydın, O.; Guessous, L.: Fundamental correlations for laminar and turbulent free convection from a uniformly heated vertical plate. Int. J. Heat Mass Transf.
**44**, 4605–4611 (2001)CrossRefzbMATHGoogle Scholar - 11.Kobus, C.J.; Guessous, L.; Raiker, V.: Modeling natural convection heat transfer from a uniformly heated vertical plate. Paper no. IMECE2003-42754, pp. 363–368 (2003)Google Scholar
- 12.Laein, R.P.; Rashidi, S.; Abolfazli Edfahani, J.: Experimental investigation of nanofluid free convection over the vertical and horizontal flat plates with uniform heat flux by PIV. Adv. Powder Technol.
**27**, 312–322 (2016)CrossRefGoogle Scholar - 13.Fahiminia, M.; Naserian, M.M.; Goshayeshi, H.R.; Majidian, D.: Investigation of natural convection heat transfer coefficient on extended vertical base plates. Energy Power Eng.
**3**, 174–180 (2011)CrossRefGoogle Scholar - 14.Saha, S.C.; Brown, R.J.; Gu, Y.T.: Scaling for the Prandtl number of the natural convection boundary layer of an inclined flat plate under uniform surface heat flux. Int. J. Heat Mass Transf.
**55**, 2394–2401 (2012)CrossRefGoogle Scholar - 15.Teymourtash, A.R.; Khonakdar, D.R.; Raveshi, M.R.: Natural convection on a vertical plate with variable heat flux in supercritical fluids. J. Supercrit. Fluids
**74**, 115–127 (2013)CrossRefGoogle Scholar - 16.Pantokratoras, A.: Laminar free-convection in glycerol with variable physical properties adjacent to a vertical plate with uniform heat flux. Int. J. Heat Mass Transf.
**46**, 1675–1678 (2003)CrossRefzbMATHGoogle Scholar - 17.Zitzmann, T.; Cook, M.; Pfrommer, P.: Simulation of steady-state natural convection using CFD. In: Ninth International IBPSA Conference, Montreal, Canada, pp. 1449–1456 (2005)Google Scholar
- 18.Khan, W.A.; Aziz, A.: Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux. Int. J. Thermal Sci.
**50**, 1207–1214 (2011)CrossRefGoogle Scholar - 19.Perovic, B.D.; Klimenta, J.L.; Tasic, D.S.; Peuteman, J.L.G.; Klimenta, D.O.; Andjelkovic, L.N.: Modeling the effect of the inclination angle on natural convection from a flat plate, the case of a photovoltaic module. Thermal Sci.
**21**, 925–938 (2017)CrossRefGoogle Scholar - 20.Guha, A.; Pradhan, K.: A unified integral theory of laminar natural convection over surfaces at arbitrary inclination from horizontal to vertical. Int. J. Thermal Sci.
**111**, 475–490 (2017)CrossRefGoogle Scholar - 21.Bejan, A.: Convection Heat Transfer, pp. 112–113. Wiley, New York (1984)zbMATHGoogle Scholar
- 22.Bouafia, M.; Hamimid, S.; Guellal, M.: Non-Boussinesq convection in a square cavity with surface thermal radiation. Int. J. Thermal Sci.
**96**, 236–247 (2015)CrossRefGoogle Scholar - 23.Huang, J.; Stern, F.: A method to compute ship exhaust plumes with waves and wind. Int. J. Numer. Meth. Fluids (2010). https://doi.org/10.1002/fld