Takhar and Beg (1997)
contains the statement, &&The heat transfer rate is however enhanced by the magnetic "eld (for positive values of the Eckert number) since the #uid is heated and temperature gradients become reduced between the #uid and the plate, with important potential applications in MHD power generators, material processing and geothermal systems containing electricallyconducting #uids''. If this statement were true, then the results in the paper would indeed be of considerable technological importance.
One would expect an enhancement of heat rate to be associated with an increase rather than a reduction of temperature gradient, and the text at the bottom of page 93 is in accord with that expectation. It is clear that the abstract contains a typographical error. But even when that error is corrected, the statement claims the opposite of what one would expect on physical grounds. The transverse magnetic "eld should inhibit #ow in the streamwise direction, leading to a reduction in convective heat transfer. Closer examination of the paper (Figures 3 and4) shows that the authors have shown that the non-dimensional temperature gradient at the surface, denoted by ( , 0), increases with the Hartmann number Ha. The authors have referred to ( , 0) as the &&local heat transfer parameter'', but in fact the appropriate local heat transfer parameter is the local Nusselt number Nu V , which is given by equation ( 29) of the paper, Nu V "! ( , 0);(Re V ), where Re V "U x/ is the local Reynolds number. The authors have shown that Nu V increases with Ha provided that Re V is held constant. However, the e!ect of introducing an applied transverse magnetic "eld will be to reduce the free-stream velocity U and hence to reduce Re V . It follows that the conclusion of the authors regarding increase of heat transfer is invalid.
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On the right-hand side of their equation ( 2), Takhar and Beg have a Darcy term ( ! u)/k together with the MHD term Bu. The authors (together with many other authors) have overlooked the fact that the pressure gradient that balances the viscous term in the simple Darcy equation is the gradient of the intrinsic pressure (not the pressure averaged over an r.e.v), and hence it is the intrinsic velocity (Darcy velocity divided by porosity) and not the Darcy velocity which has to appear, multiplied by B, in the MHD term. Thus the last term in equation (2) should read Bu/ . Readers should compare the factors of which appear elsewhere in equation (2).
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The authors have modelled the viscous dissipation in the porous medium by a term (*u/*y) in their equation (3). Here u denotes the Darcy velocity, the average over a representative elementary volume (r.e.v) of the pore velocity u N . However, the r.e.v. average of (*u N /*y) is not (*u/*y), so the authors' term is clearly