## THERMAL SCIENCE

International Scientific Journal

### Thermal Science - Online First

online first only
### Two conjugate convection boundary layers of counter forced flow

**ABSTRACT**

In this study, the conjugate heat transfer problem of two laminar forced convection boundary layers of counter flow on the opposite sides of a conductive wall is analyzed by employing the integral method. The analysis is conducted in a dimensionless framework to generalize the solution. The dimensionless parameters affecting the thermal interaction between the two convection layers are deduced from the analysis. These parameters give a measure of the relative importance of interactive heat transfer modes. Mean Nusselt number data are obtained for a wide range of the main affecting parameters.

**KEYWORDS**

PAPER SUBMITTED: 2016-05-02

PAPER REVISED: 2016-07-02

PAPER ACCEPTED: 2016-07-14

PUBLISHED ONLINE: 2016-08-07

- Karvinen, R., Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems, J. of Heat Transfer, 134 (2012), pp. 1-9.
- Dorfman, A., Conjugate Problems in Convective Heat Transfer, Boca Raton: CRC Press 2009.
- Merlin, J.H., Pop, I., Conjugate Free Convection on a Vertical Surface, Int. J Heat and Mass Transfer, 39(1996), pp. 1527-1534.
- Bejan, A., Anderson, R., Heat Transfer across a Vertical Impermeable Partition Imbedded in Porous Medium, Int. J Heat and Mass Transfer, 24(1981), pp. 1237-1245.
- Kimura, S., Heat Transfer through a Vertical Wall Separating Porous-Porous or Porous-Fluid Reservoirs at Different Temperatures, J of Energy Research, 27(2003), pp. 891-905.
- Bejan, A., Anderson, R., Natural Convection at the Interface between a Vertical Porous Layer and an Open Space, J. of Heat Transfer, 105(1981), pp 124-120.
- Sparrow, E.M., AFGRI, M., Fluid-to-Fluid Conjugate Heat Transfer for a Vertical Pipe-Internal Forced Convection and External Natural Convection, J. of Heat Transfer, 102(1980), pp. 402-407.
- Shu, J-J., Pop, I., Thermal Interaction between Free Convection and Forced Convection along a Vertical Conducting Wall, Heat and Mass Transfer, 35(1999), pp. 33-38.
- Mosaad, M., Al-Hojer, M., Thermal Interaction between Two Vertical Systems of Free and Forced Convection, Thermophysics and Heat Transfer, 20(2006), pp. 305-312.
- Luikov, A., Conjugate Convective Heat Transfer Problems, Heat Mass Transfer, 17(1975), pp.257-267.
- Mosaad, M., Laminar Forced Convection Conjugate Heat Transfer over a Flat Plate, Heat and Mass Transfer, 35(1999), pp.371-375.
- Karvinen, R., Note on Conjugated Heat Transfer in a Flat Plate, Letters in Heat and Mass Transfer, 5(1978), pp.197-202.
- Treviño, C., Becerra, G., Méndez, F., The Classical Problem of Convective Heat Transfer in Laminar Flow over a Thin Finite Thickness Plate with Uniform Temperature at the Lower Surface, Heat Mass Transfer, 40(1997), pp.3577-3580
- Lindstedt M, Karvinen, R., Conjugate Heat Transfer in a Plate-one Surface at Constant Temperature and the Other Cooled by Forced or Natural Convection, Heat and Mass Transfer, 66,(2013), pp. 489-495.
- Lehtinen, A., Karvinen, R., Analytical Solution for a Class of Flat Plate Conjugate Convective Heat Transfer Problems, Frontiers in Heat and Mass Transfer (FHMT), 2(2011), 6 pages. DOI: 10.5098/hmt.v2.4.3004.
- Payvar, P., Convective Heat Transfer to Laminar Flow over a Plate of Finite Thickness, Heat Mass Transfer, 20,(1977), pp. 431-433.
- Chida, K., Surface Temperature of a Flat Plate of Finite Thickness under Conjugate Laminar Forced Convection Heat Transfer Condition, Heat and Mass Transfer, 43(2000), pp. 639-642.
- Treviño, C., Liñán, A., External Heating of a Flat Plate in a Convective Flow, Int. J Heat Mass Transfer, 27(1984), pp.1067-1073.
- Hajmohammadi, M.R., Nourazar, S.S., Conjugate Forced Convection Heat Transfer from a Heated Flat Plate of Finite Thickness and Temperature-Dependent Thermal Conductivity, Heat Transfer Engineering, 35(2014), pp. 863-874.
- Alinejad, J., Samarbakhsh, S. , Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation, Applied Mathematics, 2(2012), 10 pages, doi:10.1155/2012/587834
- Sparrow, E. M., Abraham, J. P. , Universal Solutions for the Streamwise Variation of the Temperature of a Moving Sheet in the Presence of a Moving Fluid, Int. J. of Heat and Mass Transfer, 48(2005), pp. 3047-3056.
- Abraham, J.P. , Sparrow, E.M. , Friction Drag Resulting from the Simultaneous Imposed Motion of a Freestream and its Bounding Surface, Int. J. of Heat and Fluid Flow, 26(2005), pp. 289-295.
- Esfahani, J.A. , Alinejad, J., Lattice Boltzmann Simulation of Viscous-Fluid Flow and Conjugate Heat Transfer in a Rectangular Cavity with a Heated Moving Wall, Thermophysics and Aeromechanics, 20(2013), pp 613-620.
- Plaschko, P., High Peclet Number Heat Exchange between Co-Current Streams, Arch. Appl. Mech., 70(2000), pp. 597-611.
- Mosaad, M., Thermal Interaction between Two Forced-Convection Boundary Layers across a Conductive Solid Wall, Heat Transfer - Asian Res., (2016). onlinelibrary.wiley.com/doi/10.1002/htj.21217.
- Vera, M., Liñán, A., Laminar Counter-Flow Parallel-Plate Heat Exchangers: Exact and Approximate Solutions, Int. J. Heat Mass Transfer, 53(2010), pp. 4885-4898.
- Vera, M., Liñán, A., Exact Solution for the Conjugate Fluid-Fluid Problem in the Thermal Entrance Region of Laminar Counter-Flow Heat Exchangers, Int. J. of Heat and Mass Transfer, 54(2011), pp. 490-499.
- Viskanta, R., Abrams, M., Thermal Interaction of Two Streams in Boundary Layer Flow Separated by a Plate, Int. J Heat and Mass Transfer, 14(1971), pp. 1311-1321.
- Medina, M., Luna, E., Treviño, C., Numerical Solution of the Conjugate Heat Transfer between Forced Counter Flowing Streams, Heat and Mass Transfer, 30(1995), pp. 297-302.
- Baehr, H.D., Karl Stephan, K., Heat and Mass Transfer, 3rd. revised edition, Springer, New York, 2011.